MAYBE 228.05/60.08 MAYBE 228.05/60.08 228.05/60.08 We are left with following problem, upon which TcT provides the 228.05/60.08 certificate MAYBE. 228.05/60.08 228.05/60.08 Strict Trs: 228.05/60.08 { g(x, x) -> g(a(), b()) 228.05/60.08 , g(c(), g(c(), x)) -> g(e(), g(d(), x)) 228.05/60.08 , g(e(), g(e(), x)) -> g(d(), g(c(), x)) 228.05/60.08 , g(d(), g(d(), x)) -> g(c(), g(e(), x)) 228.05/60.08 , f(g(x, y)) -> g(y, g(f(f(x)), a())) } 228.05/60.08 Obligation: 228.05/60.08 derivational complexity 228.05/60.08 Answer: 228.05/60.08 MAYBE 228.05/60.08 228.05/60.08 None of the processors succeeded. 228.05/60.08 228.05/60.08 Details of failed attempt(s): 228.05/60.08 ----------------------------- 228.05/60.08 1) 'Fastest (timeout of 60 seconds)' failed due to the following 228.05/60.08 reason: 228.05/60.08 228.05/60.08 Computation stopped due to timeout after 60.0 seconds. 228.05/60.08 228.05/60.08 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 228.05/60.08 the following reason: 228.05/60.08 228.05/60.08 The weightgap principle applies (using the following nonconstant 228.05/60.08 growth matrix-interpretation) 228.05/60.08 228.05/60.08 TcT has computed the following triangular matrix interpretation. 228.05/60.08 Note that the diagonal of the component-wise maxima of 228.05/60.08 interpretation-entries contains no more than 1 non-zero entries. 228.05/60.08 228.05/60.08 [g](x1, x2) = [1] x1 + [1] x2 + [0] 228.05/60.08 228.05/60.08 [a] = [0] 228.05/60.08 228.05/60.08 [b] = [1] 228.05/60.08 228.05/60.08 [c] = [0] 228.05/60.08 228.05/60.08 [e] = [0] 228.05/60.08 228.05/60.08 [d] = [1] 228.05/60.08 228.05/60.08 [f](x1) = [1] x1 + [0] 228.05/60.08 228.05/60.08 The order satisfies the following ordering constraints: 228.05/60.08 228.05/60.08 [g(x, x)] = [2] x + [0] 228.05/60.08 ? [1] 228.05/60.08 = [g(a(), b())] 228.05/60.08 228.05/60.08 [g(c(), g(c(), x))] = [1] x + [0] 228.05/60.08 ? [1] x + [1] 228.05/60.08 = [g(e(), g(d(), x))] 228.05/60.08 228.05/60.08 [g(e(), g(e(), x))] = [1] x + [0] 228.05/60.08 ? [1] x + [1] 228.05/60.08 = [g(d(), g(c(), x))] 228.05/60.08 228.05/60.08 [g(d(), g(d(), x))] = [1] x + [2] 228.05/60.08 > [1] x + [0] 228.05/60.08 = [g(c(), g(e(), x))] 228.05/60.08 228.05/60.08 [f(g(x, y))] = [1] x + [1] y + [0] 228.05/60.08 >= [1] x + [1] y + [0] 228.05/60.08 = [g(y, g(f(f(x)), a()))] 228.05/60.08 228.05/60.08 228.05/60.08 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 228.05/60.08 228.05/60.08 We are left with following problem, upon which TcT provides the 228.05/60.08 certificate MAYBE. 228.05/60.08 228.05/60.08 Strict Trs: 228.05/60.08 { g(x, x) -> g(a(), b()) 228.05/60.08 , g(c(), g(c(), x)) -> g(e(), g(d(), x)) 228.05/60.08 , g(e(), g(e(), x)) -> g(d(), g(c(), x)) 228.05/60.08 , f(g(x, y)) -> g(y, g(f(f(x)), a())) } 228.05/60.08 Weak Trs: { g(d(), g(d(), x)) -> g(c(), g(e(), x)) } 228.05/60.08 Obligation: 228.05/60.08 derivational complexity 228.05/60.08 Answer: 228.05/60.08 MAYBE 228.05/60.08 228.05/60.08 The weightgap principle applies (using the following nonconstant 228.05/60.08 growth matrix-interpretation) 228.05/60.08 228.05/60.08 TcT has computed the following triangular matrix interpretation. 228.05/60.08 Note that the diagonal of the component-wise maxima of 228.05/60.08 interpretation-entries contains no more than 1 non-zero entries. 228.05/60.08 228.05/60.08 [g](x1, x2) = [1] x1 + [1] x2 + [0] 228.05/60.08 228.05/60.08 [a] = [0] 228.05/60.08 228.05/60.08 [b] = [1] 228.05/60.08 228.05/60.08 [c] = [2] 228.05/60.08 228.05/60.08 [e] = [0] 228.05/60.08 228.05/60.08 [d] = [2] 228.05/60.08 228.05/60.08 [f](x1) = [1] x1 + [0] 228.05/60.08 228.05/60.08 The order satisfies the following ordering constraints: 228.05/60.08 228.05/60.08 [g(x, x)] = [2] x + [0] 228.05/60.08 ? [1] 228.05/60.08 = [g(a(), b())] 228.05/60.08 228.05/60.08 [g(c(), g(c(), x))] = [1] x + [4] 228.05/60.08 > [1] x + [2] 228.05/60.08 = [g(e(), g(d(), x))] 228.05/60.08 228.05/60.08 [g(e(), g(e(), x))] = [1] x + [0] 228.05/60.08 ? [1] x + [4] 228.05/60.08 = [g(d(), g(c(), x))] 228.05/60.08 228.05/60.08 [g(d(), g(d(), x))] = [1] x + [4] 228.05/60.08 > [1] x + [2] 228.05/60.08 = [g(c(), g(e(), x))] 228.05/60.08 228.05/60.08 [f(g(x, y))] = [1] x + [1] y + [0] 228.05/60.08 >= [1] x + [1] y + [0] 228.05/60.08 = [g(y, g(f(f(x)), a()))] 228.05/60.08 228.05/60.08 228.05/60.08 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 228.05/60.08 228.05/60.08 We are left with following problem, upon which TcT provides the 228.05/60.08 certificate MAYBE. 228.05/60.08 228.05/60.08 Strict Trs: 228.05/60.08 { g(x, x) -> g(a(), b()) 228.05/60.08 , g(e(), g(e(), x)) -> g(d(), g(c(), x)) 228.05/60.08 , f(g(x, y)) -> g(y, g(f(f(x)), a())) } 228.05/60.08 Weak Trs: 228.05/60.08 { g(c(), g(c(), x)) -> g(e(), g(d(), x)) 228.05/60.08 , g(d(), g(d(), x)) -> g(c(), g(e(), x)) } 228.05/60.08 Obligation: 228.05/60.08 derivational complexity 228.05/60.08 Answer: 228.05/60.08 MAYBE 228.05/60.08 228.05/60.08 None of the processors succeeded. 228.05/60.08 228.05/60.08 Details of failed attempt(s): 228.05/60.08 ----------------------------- 228.05/60.08 1) 'empty' failed due to the following reason: 228.05/60.08 228.05/60.08 Empty strict component of the problem is NOT empty. 228.05/60.08 228.05/60.08 2) 'Fastest' failed due to the following reason: 228.05/60.08 228.05/60.08 None of the processors succeeded. 228.05/60.08 228.05/60.08 Details of failed attempt(s): 228.05/60.08 ----------------------------- 228.05/60.08 1) 'Fastest (timeout of 30 seconds)' failed due to the following 228.05/60.08 reason: 228.05/60.08 228.05/60.08 Computation stopped due to timeout after 30.0 seconds. 228.05/60.08 228.05/60.08 2) 'Fastest' failed due to the following reason: 228.05/60.08 228.05/60.08 None of the processors succeeded. 228.05/60.08 228.05/60.08 Details of failed attempt(s): 228.05/60.08 ----------------------------- 228.05/60.08 1) 'matrix interpretation of dimension 6' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 2) 'matrix interpretation of dimension 5' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 3) 'matrix interpretation of dimension 4' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 4) 'matrix interpretation of dimension 3' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 5) 'matrix interpretation of dimension 2' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 6) 'matrix interpretation of dimension 1' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 228.05/60.08 3) 'iteProgress' failed due to the following reason: 228.05/60.08 228.05/60.08 Fail 228.05/60.08 228.05/60.08 4) 'bsearch-matrix' failed due to the following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 228.05/60.08 228.05/60.08 3) 'iteProgress (timeout of 297 seconds)' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 Fail 228.05/60.08 228.05/60.08 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 228.05/60.08 following reason: 228.05/60.08 228.05/60.08 The input cannot be shown compatible 228.05/60.08 228.05/60.08 228.05/60.08 Arrrr.. 228.05/60.09 EOF