MAYBE 202.39/60.02 MAYBE 202.39/60.02 202.39/60.02 We are left with following problem, upon which TcT provides the 202.39/60.02 certificate MAYBE. 202.39/60.02 202.39/60.02 Strict Trs: 202.39/60.02 { R(x1) -> r(x1) 202.39/60.02 , R(r(x1)) -> x1 202.39/60.02 , r(R(x1)) -> x1 202.39/60.02 , r(r(x1)) -> x1 202.39/60.02 , r(p(x1)) -> p(p(r(P(x1)))) 202.39/60.02 , r(P(P(x1))) -> P(P(r(x1))) 202.39/60.02 , p(P(x1)) -> x1 202.39/60.02 , P(p(x1)) -> x1 } 202.39/60.02 Obligation: 202.39/60.02 derivational complexity 202.39/60.02 Answer: 202.39/60.02 MAYBE 202.39/60.02 202.39/60.02 None of the processors succeeded. 202.39/60.02 202.39/60.02 Details of failed attempt(s): 202.39/60.02 ----------------------------- 202.39/60.02 1) 'Fastest (timeout of 60 seconds)' failed due to the following 202.39/60.02 reason: 202.39/60.02 202.39/60.02 Computation stopped due to timeout after 60.0 seconds. 202.39/60.02 202.39/60.02 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 202.39/60.02 the following reason: 202.39/60.02 202.39/60.02 The weightgap principle applies (using the following nonconstant 202.39/60.02 growth matrix-interpretation) 202.39/60.02 202.39/60.02 TcT has computed the following triangular matrix interpretation. 202.39/60.02 Note that the diagonal of the component-wise maxima of 202.39/60.02 interpretation-entries contains no more than 1 non-zero entries. 202.39/60.02 202.39/60.02 [R](x1) = [1] x1 + [1] 202.39/60.02 202.39/60.02 [r](x1) = [1] x1 + [1] 202.39/60.02 202.39/60.02 [p](x1) = [1] x1 + [1] 202.39/60.02 202.39/60.02 [P](x1) = [1] x1 + [1] 202.39/60.02 202.39/60.02 The order satisfies the following ordering constraints: 202.39/60.02 202.39/60.02 [R(x1)] = [1] x1 + [1] 202.39/60.02 >= [1] x1 + [1] 202.39/60.02 = [r(x1)] 202.39/60.02 202.39/60.02 [R(r(x1))] = [1] x1 + [2] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [r(R(x1))] = [1] x1 + [2] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [r(r(x1))] = [1] x1 + [2] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [r(p(x1))] = [1] x1 + [2] 202.39/60.02 ? [1] x1 + [4] 202.39/60.02 = [p(p(r(P(x1))))] 202.39/60.02 202.39/60.02 [r(P(P(x1)))] = [1] x1 + [3] 202.39/60.02 >= [1] x1 + [3] 202.39/60.02 = [P(P(r(x1)))] 202.39/60.02 202.39/60.02 [p(P(x1))] = [1] x1 + [2] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [P(p(x1))] = [1] x1 + [2] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 202.39/60.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 202.39/60.02 202.39/60.02 We are left with following problem, upon which TcT provides the 202.39/60.02 certificate MAYBE. 202.39/60.02 202.39/60.02 Strict Trs: 202.39/60.02 { R(x1) -> r(x1) 202.39/60.02 , r(p(x1)) -> p(p(r(P(x1)))) 202.39/60.02 , r(P(P(x1))) -> P(P(r(x1))) } 202.39/60.02 Weak Trs: 202.39/60.02 { R(r(x1)) -> x1 202.39/60.02 , r(R(x1)) -> x1 202.39/60.02 , r(r(x1)) -> x1 202.39/60.02 , p(P(x1)) -> x1 202.39/60.02 , P(p(x1)) -> x1 } 202.39/60.02 Obligation: 202.39/60.02 derivational complexity 202.39/60.02 Answer: 202.39/60.02 MAYBE 202.39/60.02 202.39/60.02 We use the processor 'matrix interpretation of dimension 1' to 202.39/60.02 orient following rules strictly. 202.39/60.02 202.39/60.02 Trs: { R(x1) -> r(x1) } 202.39/60.02 202.39/60.02 The induced complexity on above rules (modulo remaining rules) is 202.39/60.02 YES(?,O(n^1)) . These rules are moved into the corresponding weak 202.39/60.02 component(s). 202.39/60.02 202.39/60.02 Sub-proof: 202.39/60.02 ---------- 202.39/60.02 TcT has computed the following triangular matrix interpretation. 202.39/60.02 202.39/60.02 [R](x1) = [1] x1 + [1] 202.39/60.02 202.39/60.02 [r](x1) = [1] x1 + [0] 202.39/60.02 202.39/60.02 [p](x1) = [1] x1 + [0] 202.39/60.02 202.39/60.02 [P](x1) = [1] x1 + [0] 202.39/60.02 202.39/60.02 The order satisfies the following ordering constraints: 202.39/60.02 202.39/60.02 [R(x1)] = [1] x1 + [1] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [r(x1)] 202.39/60.02 202.39/60.02 [R(r(x1))] = [1] x1 + [1] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [r(R(x1))] = [1] x1 + [1] 202.39/60.02 > [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [r(r(x1))] = [1] x1 + [0] 202.39/60.02 >= [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [r(p(x1))] = [1] x1 + [0] 202.39/60.02 >= [1] x1 + [0] 202.39/60.02 = [p(p(r(P(x1))))] 202.39/60.02 202.39/60.02 [r(P(P(x1)))] = [1] x1 + [0] 202.39/60.02 >= [1] x1 + [0] 202.39/60.02 = [P(P(r(x1)))] 202.39/60.02 202.39/60.02 [p(P(x1))] = [1] x1 + [0] 202.39/60.02 >= [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 [P(p(x1))] = [1] x1 + [0] 202.39/60.02 >= [1] x1 + [0] 202.39/60.02 = [x1] 202.39/60.02 202.39/60.02 202.39/60.02 We return to the main proof. 202.39/60.02 202.39/60.02 We are left with following problem, upon which TcT provides the 202.39/60.02 certificate MAYBE. 202.39/60.02 202.39/60.02 Strict Trs: 202.39/60.02 { r(p(x1)) -> p(p(r(P(x1)))) 202.39/60.02 , r(P(P(x1))) -> P(P(r(x1))) } 202.39/60.02 Weak Trs: 202.39/60.02 { R(x1) -> r(x1) 202.39/60.02 , R(r(x1)) -> x1 202.39/60.02 , r(R(x1)) -> x1 202.39/60.02 , r(r(x1)) -> x1 202.39/60.02 , p(P(x1)) -> x1 202.39/60.02 , P(p(x1)) -> x1 } 202.39/60.02 Obligation: 202.39/60.02 derivational complexity 202.39/60.02 Answer: 202.39/60.02 MAYBE 202.39/60.02 202.39/60.02 None of the processors succeeded. 202.39/60.02 202.39/60.02 Details of failed attempt(s): 202.39/60.02 ----------------------------- 202.39/60.02 1) 'empty' failed due to the following reason: 202.39/60.02 202.39/60.02 Empty strict component of the problem is NOT empty. 202.39/60.02 202.39/60.02 2) 'Fastest' failed due to the following reason: 202.39/60.02 202.39/60.02 None of the processors succeeded. 202.39/60.02 202.39/60.02 Details of failed attempt(s): 202.39/60.02 ----------------------------- 202.39/60.02 1) 'Fastest (timeout of 30 seconds)' failed due to the following 202.39/60.02 reason: 202.39/60.02 202.39/60.02 Computation stopped due to timeout after 30.0 seconds. 202.39/60.02 202.39/60.02 2) 'Fastest' failed due to the following reason: 202.39/60.02 202.39/60.02 None of the processors succeeded. 202.39/60.02 202.39/60.02 Details of failed attempt(s): 202.39/60.02 ----------------------------- 202.39/60.02 1) 'matrix interpretation of dimension 6' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 2) 'matrix interpretation of dimension 5' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 3) 'matrix interpretation of dimension 4' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 4) 'matrix interpretation of dimension 3' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 5) 'matrix interpretation of dimension 2' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 6) 'matrix interpretation of dimension 1' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 202.39/60.02 3) 'iteProgress' failed due to the following reason: 202.39/60.02 202.39/60.02 Fail 202.39/60.02 202.39/60.02 4) 'bsearch-matrix' failed due to the following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 202.39/60.02 202.39/60.02 3) 'iteProgress (timeout of 297 seconds)' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 Fail 202.39/60.02 202.39/60.02 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 202.39/60.02 following reason: 202.39/60.02 202.39/60.02 The input cannot be shown compatible 202.39/60.02 202.39/60.02 202.39/60.02 Arrrr.. 202.39/60.03 EOF