MAYBE 251.88/82.37 MAYBE 251.88/82.37 251.88/82.37 We are left with following problem, upon which TcT provides the 251.88/82.37 certificate MAYBE. 251.88/82.37 251.88/82.37 Strict Trs: 251.88/82.37 { f(x, f(y, z)) -> f(f(x, y), z) 251.88/82.37 , f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x))) } 251.88/82.37 Obligation: 251.88/82.37 derivational complexity 251.88/82.37 Answer: 251.88/82.37 MAYBE 251.88/82.37 251.88/82.37 None of the processors succeeded. 251.88/82.37 251.88/82.37 Details of failed attempt(s): 251.88/82.37 ----------------------------- 251.88/82.37 1) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 251.88/82.37 the following reason: 251.88/82.37 251.88/82.37 The weightgap principle applies (using the following nonconstant 251.88/82.37 growth matrix-interpretation) 251.88/82.37 251.88/82.37 TcT has computed the following triangular matrix interpretation. 251.88/82.37 Note that the diagonal of the component-wise maxima of 251.88/82.37 interpretation-entries contains no more than 1 non-zero entries. 251.88/82.37 251.88/82.37 [f](x1, x2) = [1 1] x1 + [1 0] x2 + [0] 251.88/82.37 [0 0] [0 0] [1] 251.88/82.37 251.88/82.37 [a] = [0] 251.88/82.37 [0] 251.88/82.37 251.88/82.37 [b] = [0] 251.88/82.37 [0] 251.88/82.37 251.88/82.37 The order satisfies the following ordering constraints: 251.88/82.37 251.88/82.37 [f(x, f(y, z))] = [1 1] x + [1 1] y + [1 0] z + [0] 251.88/82.37 [0 0] [0 0] [0 0] [1] 251.88/82.37 ? [1 1] x + [1 0] y + [1 0] z + [1] 251.88/82.37 [0 0] [0 0] [0 0] [1] 251.88/82.37 = [f(f(x, y), z)] 251.88/82.37 251.88/82.37 [f(f(a(), a()), x)] = [1 0] x + [1] 251.88/82.37 [0 0] [1] 251.88/82.37 > [1 0] x + [0] 251.88/82.37 [0 0] [1] 251.88/82.37 = [f(a(), f(b(), f(a(), x)))] 251.88/82.37 251.88/82.37 251.88/82.37 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 251.88/82.37 251.88/82.37 We are left with following problem, upon which TcT provides the 251.88/82.37 certificate MAYBE. 251.88/82.37 251.88/82.37 Strict Trs: { f(x, f(y, z)) -> f(f(x, y), z) } 251.88/82.37 Weak Trs: { f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x))) } 251.88/82.37 Obligation: 251.88/82.37 derivational complexity 251.88/82.37 Answer: 251.88/82.37 MAYBE 251.88/82.37 251.88/82.37 None of the processors succeeded. 251.88/82.37 251.88/82.37 Details of failed attempt(s): 251.88/82.37 ----------------------------- 251.88/82.37 1) 'empty' failed due to the following reason: 251.88/82.37 251.88/82.37 Empty strict component of the problem is NOT empty. 251.88/82.37 251.88/82.37 2) 'Fastest' failed due to the following reason: 251.88/82.37 251.88/82.37 None of the processors succeeded. 251.88/82.37 251.88/82.37 Details of failed attempt(s): 251.88/82.37 ----------------------------- 251.88/82.37 1) 'Fastest' failed due to the following reason: 251.88/82.37 251.88/82.37 None of the processors succeeded. 251.88/82.37 251.88/82.37 Details of failed attempt(s): 251.88/82.37 ----------------------------- 251.88/82.37 1) 'matrix interpretation of dimension 6' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 2) 'matrix interpretation of dimension 5' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 3) 'matrix interpretation of dimension 4' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 4) 'matrix interpretation of dimension 3' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 5) 'matrix interpretation of dimension 2' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 6) 'matrix interpretation of dimension 1' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 251.88/82.37 2) 'Fastest (timeout of 30 seconds)' failed due to the following 251.88/82.37 reason: 251.88/82.37 251.88/82.37 Computation stopped due to timeout after 30.0 seconds. 251.88/82.37 251.88/82.37 3) 'iteProgress' failed due to the following reason: 251.88/82.37 251.88/82.37 Fail 251.88/82.37 251.88/82.37 4) 'bsearch-matrix' failed due to the following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 251.88/82.37 251.88/82.37 2) 'Fastest (timeout of 60 seconds)' failed due to the following 251.88/82.37 reason: 251.88/82.37 251.88/82.37 Computation stopped due to timeout after 60.0 seconds. 251.88/82.37 251.88/82.37 3) 'iteProgress (timeout of 297 seconds)' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 Fail 251.88/82.37 251.88/82.37 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 251.88/82.37 following reason: 251.88/82.37 251.88/82.37 The input cannot be shown compatible 251.88/82.37 251.88/82.37 251.88/82.37 Arrrr.. 251.88/82.39 EOF