MAYBE 204.20/60.04 MAYBE 204.20/60.04 204.20/60.04 We are left with following problem, upon which TcT provides the 204.20/60.04 certificate MAYBE. 204.20/60.04 204.20/60.04 Strict Trs: 204.20/60.04 { f(s(x1)) -> s(s(f(p(s(x1))))) 204.20/60.04 , f(0(x1)) -> 0(x1) 204.20/60.04 , p(s(x1)) -> x1 } 204.20/60.04 Obligation: 204.20/60.04 derivational complexity 204.20/60.04 Answer: 204.20/60.04 MAYBE 204.20/60.04 204.20/60.04 None of the processors succeeded. 204.20/60.04 204.20/60.04 Details of failed attempt(s): 204.20/60.04 ----------------------------- 204.20/60.04 1) 'Fastest (timeout of 60 seconds)' failed due to the following 204.20/60.04 reason: 204.20/60.04 204.20/60.04 Computation stopped due to timeout after 60.0 seconds. 204.20/60.04 204.20/60.04 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 204.20/60.04 the following reason: 204.20/60.04 204.20/60.04 We use the processor 'matrix interpretation of dimension 1' to 204.20/60.04 orient following rules strictly. 204.20/60.04 204.20/60.04 Trs: { f(0(x1)) -> 0(x1) } 204.20/60.04 204.20/60.04 The induced complexity on above rules (modulo remaining rules) is 204.20/60.04 YES(?,O(n^1)) . These rules are moved into the corresponding weak 204.20/60.04 component(s). 204.20/60.04 204.20/60.04 Sub-proof: 204.20/60.04 ---------- 204.20/60.04 TcT has computed the following triangular matrix interpretation. 204.20/60.04 204.20/60.04 [f](x1) = [1] x1 + [1] 204.20/60.04 204.20/60.04 [s](x1) = [1] x1 + [0] 204.20/60.04 204.20/60.04 [p](x1) = [1] x1 + [0] 204.20/60.04 204.20/60.04 [0](x1) = [1] x1 + [1] 204.20/60.04 204.20/60.04 The order satisfies the following ordering constraints: 204.20/60.04 204.20/60.04 [f(s(x1))] = [1] x1 + [1] 204.20/60.04 >= [1] x1 + [1] 204.20/60.04 = [s(s(f(p(s(x1)))))] 204.20/60.04 204.20/60.04 [f(0(x1))] = [1] x1 + [2] 204.20/60.04 > [1] x1 + [1] 204.20/60.04 = [0(x1)] 204.20/60.04 204.20/60.04 [p(s(x1))] = [1] x1 + [0] 204.20/60.04 >= [1] x1 + [0] 204.20/60.04 = [x1] 204.20/60.04 204.20/60.04 204.20/60.04 We return to the main proof. 204.20/60.04 204.20/60.04 We are left with following problem, upon which TcT provides the 204.20/60.04 certificate MAYBE. 204.20/60.04 204.20/60.04 Strict Trs: 204.20/60.04 { f(s(x1)) -> s(s(f(p(s(x1))))) 204.20/60.04 , p(s(x1)) -> x1 } 204.20/60.04 Weak Trs: { f(0(x1)) -> 0(x1) } 204.20/60.04 Obligation: 204.20/60.04 derivational complexity 204.20/60.04 Answer: 204.20/60.04 MAYBE 204.20/60.04 204.20/60.04 The weightgap principle applies (using the following nonconstant 204.20/60.04 growth matrix-interpretation) 204.20/60.04 204.20/60.04 TcT has computed the following triangular matrix interpretation. 204.20/60.04 Note that the diagonal of the component-wise maxima of 204.20/60.04 interpretation-entries contains no more than 1 non-zero entries. 204.20/60.04 204.20/60.04 [f](x1) = [1] x1 + [0] 204.20/60.04 204.20/60.04 [s](x1) = [1] x1 + [0] 204.20/60.04 204.20/60.04 [p](x1) = [1] x1 + [1] 204.20/60.04 204.20/60.04 [0](x1) = [1] x1 + [2] 204.20/60.04 204.20/60.04 The order satisfies the following ordering constraints: 204.20/60.04 204.20/60.04 [f(s(x1))] = [1] x1 + [0] 204.20/60.04 ? [1] x1 + [1] 204.20/60.04 = [s(s(f(p(s(x1)))))] 204.20/60.04 204.20/60.04 [f(0(x1))] = [1] x1 + [2] 204.20/60.04 >= [1] x1 + [2] 204.20/60.04 = [0(x1)] 204.20/60.04 204.20/60.04 [p(s(x1))] = [1] x1 + [1] 204.20/60.04 > [1] x1 + [0] 204.20/60.04 = [x1] 204.20/60.04 204.20/60.04 204.20/60.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 204.20/60.04 204.20/60.04 We are left with following problem, upon which TcT provides the 204.20/60.04 certificate MAYBE. 204.20/60.04 204.20/60.04 Strict Trs: { f(s(x1)) -> s(s(f(p(s(x1))))) } 204.20/60.04 Weak Trs: 204.20/60.04 { f(0(x1)) -> 0(x1) 204.20/60.04 , p(s(x1)) -> x1 } 204.20/60.04 Obligation: 204.20/60.04 derivational complexity 204.20/60.04 Answer: 204.20/60.04 MAYBE 204.20/60.04 204.20/60.04 None of the processors succeeded. 204.20/60.04 204.20/60.04 Details of failed attempt(s): 204.20/60.04 ----------------------------- 204.20/60.04 1) 'empty' failed due to the following reason: 204.20/60.04 204.20/60.04 Empty strict component of the problem is NOT empty. 204.20/60.04 204.20/60.04 2) 'Fastest' failed due to the following reason: 204.20/60.04 204.20/60.04 None of the processors succeeded. 204.20/60.04 204.20/60.04 Details of failed attempt(s): 204.20/60.04 ----------------------------- 204.20/60.04 1) 'Fastest' failed due to the following reason: 204.20/60.04 204.20/60.04 None of the processors succeeded. 204.20/60.04 204.20/60.04 Details of failed attempt(s): 204.20/60.04 ----------------------------- 204.20/60.04 1) 'matrix interpretation of dimension 6' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 2) 'matrix interpretation of dimension 5' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 3) 'matrix interpretation of dimension 4' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 4) 'matrix interpretation of dimension 3' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 5) 'matrix interpretation of dimension 2' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 6) 'matrix interpretation of dimension 1' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 204.20/60.04 2) 'Fastest (timeout of 30 seconds)' failed due to the following 204.20/60.04 reason: 204.20/60.04 204.20/60.04 Computation stopped due to timeout after 30.0 seconds. 204.20/60.04 204.20/60.04 3) 'bsearch-matrix' failed due to the following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 4) 'iteProgress' failed due to the following reason: 204.20/60.04 204.20/60.04 Fail 204.20/60.04 204.20/60.04 204.20/60.04 204.20/60.04 3) 'iteProgress (timeout of 297 seconds)' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 Fail 204.20/60.04 204.20/60.04 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 204.20/60.04 following reason: 204.20/60.04 204.20/60.04 The input cannot be shown compatible 204.20/60.04 204.20/60.04 204.20/60.04 Arrrr.. 204.20/60.05 EOF