MAYBE 529.29/219.51 MAYBE 529.29/219.51 529.29/219.51 We are left with following problem, upon which TcT provides the 529.29/219.51 certificate MAYBE. 529.29/219.51 529.29/219.51 Strict Trs: 529.29/219.51 { f(x, f(y, z)) -> f(f(x, y), z) 529.29/219.51 , f(f(a(), b()), x) -> f(b(), f(a(), f(c(), f(b(), f(a(), x))))) } 529.29/219.51 Obligation: 529.29/219.51 derivational complexity 529.29/219.51 Answer: 529.29/219.51 MAYBE 529.29/219.51 529.29/219.51 None of the processors succeeded. 529.29/219.51 529.29/219.51 Details of failed attempt(s): 529.29/219.51 ----------------------------- 529.29/219.51 1) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 529.29/219.51 the following reason: 529.29/219.51 529.29/219.51 The weightgap principle applies (using the following nonconstant 529.29/219.51 growth matrix-interpretation) 529.29/219.51 529.29/219.51 TcT has computed the following triangular matrix interpretation. 529.29/219.51 Note that the diagonal of the component-wise maxima of 529.29/219.51 interpretation-entries contains no more than 1 non-zero entries. 529.29/219.51 529.29/219.51 [f](x1, x2) = [1 1] x1 + [1 0] x2 + [0] 529.29/219.51 [0 0] [0 0] [1] 529.29/219.51 529.29/219.51 [a] = [0] 529.29/219.51 [0] 529.29/219.51 529.29/219.51 [b] = [0] 529.29/219.51 [0] 529.29/219.51 529.29/219.51 [c] = [0] 529.29/219.51 [0] 529.29/219.51 529.29/219.51 The order satisfies the following ordering constraints: 529.29/219.51 529.29/219.51 [f(x, f(y, z))] = [1 1] x + [1 1] y + [1 0] z + [0] 529.29/219.51 [0 0] [0 0] [0 0] [1] 529.29/219.51 ? [1 1] x + [1 0] y + [1 0] z + [1] 529.29/219.51 [0 0] [0 0] [0 0] [1] 529.29/219.51 = [f(f(x, y), z)] 529.29/219.51 529.29/219.51 [f(f(a(), b()), x)] = [1 0] x + [1] 529.29/219.51 [0 0] [1] 529.29/219.51 > [1 0] x + [0] 529.29/219.51 [0 0] [1] 529.29/219.51 = [f(b(), f(a(), f(c(), f(b(), f(a(), x)))))] 529.29/219.51 529.29/219.51 529.29/219.51 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 529.29/219.51 529.29/219.51 We are left with following problem, upon which TcT provides the 529.29/219.51 certificate MAYBE. 529.29/219.51 529.29/219.51 Strict Trs: { f(x, f(y, z)) -> f(f(x, y), z) } 529.29/219.51 Weak Trs: 529.29/219.51 { f(f(a(), b()), x) -> f(b(), f(a(), f(c(), f(b(), f(a(), x))))) } 529.29/219.51 Obligation: 529.29/219.51 derivational complexity 529.29/219.51 Answer: 529.29/219.51 MAYBE 529.29/219.51 529.29/219.51 None of the processors succeeded. 529.29/219.51 529.29/219.51 Details of failed attempt(s): 529.29/219.51 ----------------------------- 529.29/219.51 1) 'empty' failed due to the following reason: 529.29/219.51 529.29/219.51 Empty strict component of the problem is NOT empty. 529.29/219.51 529.29/219.51 2) 'Fastest' failed due to the following reason: 529.29/219.51 529.29/219.51 None of the processors succeeded. 529.29/219.51 529.29/219.51 Details of failed attempt(s): 529.29/219.51 ----------------------------- 529.29/219.51 1) 'Fastest' failed due to the following reason: 529.29/219.51 529.29/219.51 None of the processors succeeded. 529.29/219.51 529.29/219.51 Details of failed attempt(s): 529.29/219.51 ----------------------------- 529.29/219.51 1) 'matrix interpretation of dimension 6' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 2) 'matrix interpretation of dimension 5' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 3) 'matrix interpretation of dimension 4' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 4) 'matrix interpretation of dimension 3' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 5) 'matrix interpretation of dimension 2' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 6) 'matrix interpretation of dimension 1' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 529.29/219.51 2) 'bsearch-matrix' failed due to the following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 3) 'iteProgress' failed due to the following reason: 529.29/219.51 529.29/219.51 Fail 529.29/219.51 529.29/219.51 4) 'Fastest (timeout of 30 seconds)' failed due to the following 529.29/219.51 reason: 529.29/219.51 529.29/219.51 Computation stopped due to timeout after 30.0 seconds. 529.29/219.51 529.29/219.51 529.29/219.51 529.29/219.51 2) 'iteProgress (timeout of 297 seconds)' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 Fail 529.29/219.51 529.29/219.51 3) 'Fastest (timeout of 60 seconds)' failed due to the following 529.29/219.51 reason: 529.29/219.51 529.29/219.51 Computation stopped due to timeout after 60.0 seconds. 529.29/219.51 529.29/219.51 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 529.29/219.51 following reason: 529.29/219.51 529.29/219.51 The input cannot be shown compatible 529.29/219.51 529.29/219.51 529.29/219.51 Arrrr.. 529.29/219.59 EOF