Problem: a1() -> b1() a1() -> c1() b1() -> b2() c1() -> c2() a2() -> b2() a2() -> c2() b2() -> b3() c2() -> c3() a3() -> b3() a3() -> c3() b3() -> b4() c3() -> c4() a4() -> b4() a4() -> c4() b4() -> b5() c4() -> c5() a5() -> b5() a5() -> c5() b5() -> b6() c5() -> c6() a6() -> b6() a6() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Proof: sorted: (order-sorted) 0:a1() -> b1() a1() -> c1() b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() 1:b1() -> b2() c1() -> c2() a2() -> b2() a2() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() 2:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() a3() -> b3() a3() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() 3:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() a4() -> b4() a4() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() 4:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() a5() -> b5() a5() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() 5:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() a6() -> b6() a6() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() ----- sorts [0>6, 1>6, 2>6, 3>6, 4>6, 5>6] sort attachment (non-strict) a1 : 0 b1 : 6 c1 : 6 b2 : 6 c2 : 6 a2 : 1 b3 : 6 c3 : 6 a3 : 2 b4 : 6 c4 : 6 a4 : 3 b5 : 6 c5 : 6 a5 : 4 b6 : 6 c6 : 6 a6 : 5 b7 : 6 ----- 0:a1() -> b1() a1() -> c1() b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Church Rosser Transformation Processor: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c1() -> c2() c2() -> c3() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 1, [c3] = 4, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 4 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c1() = 4 >= 4 = c2() c2() = 4 >= 4 = c3() c3() = 4 >= 1 = c4() c4() = 1 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c1() -> c2() c2() -> c3() c5() -> c6() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 4, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 4, [b3] = 0, [c1] = 0 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c1() = 0 >= 0 = c2() c2() = 0 >= 0 = c3() c5() = 4 >= 4 = c6() c6() = 4 >= 0 = b7() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c1() -> c2() c2() -> c3() c5() -> c6() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 1, [b3] = 0, [c1] = 0 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c1() = 0 >= 0 = c2() c2() = 0 >= 0 = c3() c5() = 1 >= 0 = c6() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c1() -> c2() c2() -> c3() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [b3] = 0, [c1] = 4 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c1() = 4 >= 4 = c2() c2() = 4 >= 0 = c3() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c1() -> c2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [b5] = 0, [b4] = 0, [b3] = 0, [c1] = 1 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c1() = 1 >= 0 = c2() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 4, [b2] = 4, [b5] = 4, [b4] = 4, [b3] = 4 orientation: b1() = 4 >= 4 = b2() b2() = 4 >= 4 = b3() b3() = 4 >= 4 = b4() b4() = 4 >= 4 = b5() b5() = 4 >= 0 = b6() b6() = 0 >= 0 = b7() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 1, [b1] = 0, [b2] = 0, [b5] = 0, [b4] = 0, [b3] = 0 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b6() = 1 >= 0 = b7() problem: b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() Matrix Interpretation Processor: dim=1 interpretation: [b1] = 4, [b2] = 4, [b5] = 0, [b4] = 0, [b3] = 4 orientation: b1() = 4 >= 4 = b2() b2() = 4 >= 4 = b3() b3() = 4 >= 0 = b4() b4() = 0 >= 0 = b5() problem: b1() -> b2() b2() -> b3() b4() -> b5() Matrix Interpretation Processor: dim=1 interpretation: [b1] = 0, [b2] = 0, [b5] = 0, [b4] = 1, [b3] = 0 orientation: b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b4() = 1 >= 0 = b5() problem: b1() -> b2() b2() -> b3() Matrix Interpretation Processor: dim=1 interpretation: [b1] = 4, [b2] = 4, [b3] = 0 orientation: b1() = 4 >= 4 = b2() b2() = 4 >= 0 = b3() problem: b1() -> b2() Matrix Interpretation Processor: dim=1 interpretation: [b1] = 1, [b2] = 0 orientation: b1() = 1 >= 0 = b2() problem: Qed 1:b1() -> b2() c1() -> c2() a2() -> b2() a2() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Church Rosser Transformation Processor: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() c1() -> c2() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 1 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 0 >= 0 = c3() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() c1() = 1 >= 0 = c2() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 1, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 0 >= 0 = c3() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 1 >= 0 = b2() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 4, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 4 >= 4 = c3() c3() = 4 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() c4() -> c5() c5() -> c6() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b2] = 0, [c6] = 0, [c4] = 4, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 4, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 0 >= 0 = c3() c4() = 4 >= 4 = c5() c5() = 4 >= 0 = c6() c6() = 0 >= 0 = b7() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() c4() -> c5() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b2] = 0, [c6] = 1, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 0 >= 0 = c3() c4() = 0 >= 0 = c5() c6() = 1 >= 0 = b7() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() c4() -> c5() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b2] = 0, [c4] = 1, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 0 >= 0 = c3() c4() = 1 >= 0 = c5() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c2() -> c3() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 1, [b6] = 0, [b2] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c2() = 1 >= 0 = c3() problem: b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b2] = 4, [b5] = 0, [b4] = 4, [b3] = 4 orientation: b2() = 4 >= 4 = b3() b3() = 4 >= 4 = b4() b4() = 4 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() problem: b2() -> b3() b3() -> b4() b5() -> b6() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 4, [b2] = 0, [b5] = 4, [b4] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b5() = 4 >= 4 = b6() b6() = 4 >= 0 = b7() problem: b2() -> b3() b3() -> b4() b5() -> b6() Matrix Interpretation Processor: dim=1 interpretation: [b6] = 0, [b2] = 0, [b5] = 1, [b4] = 0, [b3] = 0 orientation: b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b5() = 1 >= 0 = b6() problem: b2() -> b3() b3() -> b4() Matrix Interpretation Processor: dim=1 interpretation: [b2] = 4, [b4] = 0, [b3] = 4 orientation: b2() = 4 >= 4 = b3() b3() = 4 >= 0 = b4() problem: b2() -> b3() Matrix Interpretation Processor: dim=1 interpretation: [b2] = 1, [b3] = 0 orientation: b2() = 1 >= 0 = b3() problem: Qed 2:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() a3() -> b3() a3() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Church Rosser Transformation Processor: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() c1() -> c2() c2() -> c3() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 4 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() c1() = 4 >= 4 = c2() c2() = 4 >= 0 = c3() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() c1() -> c2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 1 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() c1() = 1 >= 0 = c2() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 4, [b2] = 4, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 4 >= 4 = b2() b2() = 4 >= 0 = b3() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 1, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 1 >= 0 = b2() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() c4() -> c5() c5() -> c6() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c6] = 0, [c4] = 4, [c3] = 4, [b5] = 0, [b4] = 0, [c5] = 1, [b3] = 0 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 4 >= 4 = c4() c4() = 4 >= 1 = c5() c5() = 1 >= 0 = c6() c6() = 0 >= 0 = b7() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c6] = 1, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [b3] = 0 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 0 >= 0 = c4() c6() = 1 >= 0 = b7() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() c3() -> c4() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c4] = 0, [c3] = 1, [b5] = 0, [b4] = 0, [b3] = 0 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c3() = 1 >= 0 = c4() problem: b3() -> b4() b4() -> b5() b5() -> b6() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b5] = 4, [b4] = 4, [b3] = 4 orientation: b3() = 4 >= 4 = b4() b4() = 4 >= 4 = b5() b5() = 4 >= 0 = b6() b6() = 0 >= 0 = b7() problem: b3() -> b4() b4() -> b5() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 1, [b5] = 0, [b4] = 0, [b3] = 0 orientation: b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b6() = 1 >= 0 = b7() problem: b3() -> b4() b4() -> b5() Matrix Interpretation Processor: dim=1 interpretation: [b5] = 0, [b4] = 4, [b3] = 4 orientation: b3() = 4 >= 4 = b4() b4() = 4 >= 0 = b5() problem: b3() -> b4() Matrix Interpretation Processor: dim=1 interpretation: [b4] = 0, [b3] = 1 orientation: b3() = 1 >= 0 = b4() problem: Qed 3:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() a4() -> b4() a4() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Church Rosser Transformation Processor: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() c1() -> c2() c2() -> c3() c3() -> c4() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 4 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() c1() = 4 >= 4 = c2() c2() = 4 >= 0 = c3() c3() = 0 >= 0 = c4() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() c1() -> c2() c3() -> c4() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 1, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 0 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() c1() = 0 >= 0 = c2() c3() = 1 >= 0 = c4() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() c1() -> c2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 1 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() c1() = 1 >= 0 = c2() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 4, [b2] = 4, [c6] = 0, [c4] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 4 >= 4 = b2() b2() = 4 >= 0 = b3() b3() = 0 >= 0 = b4() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() b3() -> b4() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 1 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b3() = 1 >= 0 = b4() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() b1() -> b2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 1, [b2] = 0, [c6] = 0, [c4] = 0, [b5] = 0, [b4] = 0, [c5] = 0 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 1 >= 0 = b2() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c5() -> c6() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c6] = 0, [c4] = 4, [b5] = 0, [b4] = 0, [c5] = 4 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 4 >= 4 = c5() c5() = 4 >= 0 = c6() c6() = 0 >= 0 = b7() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c6] = 1, [c4] = 0, [b5] = 0, [b4] = 0, [c5] = 0 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 0 >= 0 = c5() c6() = 1 >= 0 = b7() problem: b4() -> b5() b5() -> b6() b6() -> b7() c4() -> c5() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c4] = 1, [b5] = 0, [b4] = 0, [c5] = 0 orientation: b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c4() = 1 >= 0 = c5() problem: b4() -> b5() b5() -> b6() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b5] = 4, [b4] = 4 orientation: b4() = 4 >= 4 = b5() b5() = 4 >= 0 = b6() b6() = 0 >= 0 = b7() problem: b4() -> b5() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 1, [b5] = 0, [b4] = 0 orientation: b4() = 0 >= 0 = b5() b6() = 1 >= 0 = b7() problem: b4() -> b5() Matrix Interpretation Processor: dim=1 interpretation: [b5] = 0, [b4] = 1 orientation: b4() = 1 >= 0 = b5() problem: Qed 4:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() a5() -> b5() a5() -> c5() b5() -> b6() c5() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Church Rosser Transformation Processor: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() c1() -> c2() c2() -> c3() c3() -> c4() c4() -> c5() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 4 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() c1() = 4 >= 4 = c2() c2() = 4 >= 0 = c3() c3() = 0 >= 0 = c4() c4() = 0 >= 0 = c5() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() c1() -> c2() c3() -> c4() c4() -> c5() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 4, [c3] = 4, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 0 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() c1() = 0 >= 0 = c2() c3() = 4 >= 4 = c4() c4() = 4 >= 0 = c5() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() c1() -> c2() c3() -> c4() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 1, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 0 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() c1() = 0 >= 0 = c2() c3() = 1 >= 0 = c4() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() c1() -> c2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 1 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() c1() = 1 >= 0 = c2() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 4, [b2] = 4, [c6] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 1 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 4 >= 4 = b2() b2() = 4 >= 1 = b3() b3() = 1 >= 0 = b4() b4() = 0 >= 0 = b5() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() b4() -> b5() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [b5] = 0, [b4] = 1, [c5] = 0 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b4() = 1 >= 0 = b5() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() b1() -> b2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 1, [b2] = 0, [c6] = 0, [b5] = 0, [c5] = 0 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 0 >= 0 = c6() c6() = 0 >= 0 = b7() b1() = 1 >= 0 = b2() problem: b5() -> b6() b6() -> b7() c5() -> c6() c6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c6] = 4, [b5] = 0, [c5] = 4 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 4 >= 4 = c6() c6() = 4 >= 0 = b7() problem: b5() -> b6() b6() -> b7() c5() -> c6() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [c6] = 0, [b5] = 0, [c5] = 1 orientation: b5() = 0 >= 0 = b6() b6() = 0 >= 0 = b7() c5() = 1 >= 0 = c6() problem: b5() -> b6() b6() -> b7() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 4, [b5] = 4 orientation: b5() = 4 >= 4 = b6() b6() = 4 >= 0 = b7() problem: b5() -> b6() Matrix Interpretation Processor: dim=1 interpretation: [b6] = 0, [b5] = 1 orientation: b5() = 1 >= 0 = b6() problem: Qed 5:b1() -> b2() c1() -> c2() b2() -> b3() c2() -> c3() b3() -> b4() c3() -> c4() b4() -> b5() c4() -> c5() b5() -> b6() c5() -> c6() a6() -> b6() a6() -> c6() b6() -> b7() c6() -> b7() b7() -> b1() b7() -> c1() Church Rosser Transformation Processor: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() c1() -> c2() c2() -> c3() c3() -> c4() c4() -> c5() c5() -> c6() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 0, [c3] = 4, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 4 orientation: b6() = 0 >= 0 = b7() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() c1() = 4 >= 4 = c2() c2() = 4 >= 4 = c3() c3() = 4 >= 0 = c4() c4() = 0 >= 0 = c5() c5() = 0 >= 0 = c6() problem: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() c1() -> c2() c2() -> c3() c4() -> c5() c5() -> c6() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 4, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 4, [b3] = 0, [c1] = 0 orientation: b6() = 0 >= 0 = b7() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() c1() = 0 >= 0 = c2() c2() = 0 >= 0 = c3() c4() = 4 >= 4 = c5() c5() = 4 >= 0 = c6() problem: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() c1() -> c2() c2() -> c3() c4() -> c5() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c4] = 1, [c3] = 0, [b5] = 0, [b4] = 0, [c5] = 0, [b3] = 0, [c1] = 0 orientation: b6() = 0 >= 0 = b7() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() c1() = 0 >= 0 = c2() c2() = 0 >= 0 = c3() c4() = 1 >= 0 = c5() problem: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() c1() -> c2() c2() -> c3() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 4, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [c3] = 0, [b5] = 0, [b4] = 0, [b3] = 0, [c1] = 4 orientation: b6() = 0 >= 0 = b7() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() c1() = 4 >= 4 = c2() c2() = 4 >= 0 = c3() problem: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() c1() -> c2() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [c2] = 0, [b6] = 0, [b1] = 0, [b2] = 0, [c6] = 0, [b5] = 0, [b4] = 0, [b3] = 0, [c1] = 1 orientation: b6() = 0 >= 0 = b7() c6() = 0 >= 0 = b7() b1() = 0 >= 0 = b2() b2() = 0 >= 0 = b3() b3() = 0 >= 0 = b4() b4() = 0 >= 0 = b5() b5() = 0 >= 0 = b6() c1() = 1 >= 0 = c2() problem: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b3() -> b4() b4() -> b5() b5() -> b6() Matrix Interpretation Processor: dim=1 interpretation: [b7] = 0, [b6] = 0, [b1] = 4, [b2] = 4, [c6] = 0, [b5] = 0, [b4] = 1, [b3] = 4 orientation: b6() = 0 >= 0 = b7() c6() = 0 >= 0 = b7() b1() = 4 >= 4 = b2() b2() = 4 >= 4 = b3() b3() = 4 >= 1 = b4() b4() = 1 >= 0 = b5() b5() = 0 >= 0 = b6() problem: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b5() -> b6() DP Processor: DPs: b1#() -> b2#() b5#() -> b6#() TRS: b6() -> b7() c6() -> b7() b1() -> b2() b2() -> b3() b5() -> b6() SCC Processor: #sccs: 0 #rules: 0 #arcs: 4/4