MAYBE 204.84/60.02 MAYBE 204.84/60.02 204.84/60.02 We are left with following problem, upon which TcT provides the 204.84/60.02 certificate MAYBE. 204.84/60.02 204.84/60.02 Strict Trs: 204.84/60.02 { f(s(x)) -> s(s(f(p(s(x))))) 204.84/60.02 , f(0()) -> 0() 204.84/60.02 , p(s(x)) -> x } 204.84/60.02 Obligation: 204.84/60.02 derivational complexity 204.84/60.02 Answer: 204.84/60.02 MAYBE 204.84/60.02 204.84/60.02 None of the processors succeeded. 204.84/60.02 204.84/60.02 Details of failed attempt(s): 204.84/60.02 ----------------------------- 204.84/60.02 1) 'Fastest (timeout of 60 seconds)' failed due to the following 204.84/60.02 reason: 204.84/60.02 204.84/60.02 Computation stopped due to timeout after 60.0 seconds. 204.84/60.02 204.84/60.02 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 204.84/60.02 the following reason: 204.84/60.02 204.84/60.02 We use the processor 'matrix interpretation of dimension 1' to 204.84/60.02 orient following rules strictly. 204.84/60.02 204.84/60.02 Trs: { f(0()) -> 0() } 204.84/60.02 204.84/60.02 The induced complexity on above rules (modulo remaining rules) is 204.84/60.02 YES(?,O(n^1)) . These rules are moved into the corresponding weak 204.84/60.02 component(s). 204.84/60.02 204.84/60.02 Sub-proof: 204.84/60.02 ---------- 204.84/60.02 TcT has computed the following triangular matrix interpretation. 204.84/60.02 204.84/60.02 [f](x1) = [1] x1 + [1] 204.84/60.02 204.84/60.02 [s](x1) = [1] x1 + [0] 204.84/60.02 204.84/60.02 [p](x1) = [1] x1 + [0] 204.84/60.02 204.84/60.02 [0] = [1] 204.84/60.02 204.84/60.02 The order satisfies the following ordering constraints: 204.84/60.02 204.84/60.02 [f(s(x))] = [1] x + [1] 204.84/60.02 >= [1] x + [1] 204.84/60.02 = [s(s(f(p(s(x)))))] 204.84/60.02 204.84/60.02 [f(0())] = [2] 204.84/60.02 > [1] 204.84/60.02 = [0()] 204.84/60.02 204.84/60.02 [p(s(x))] = [1] x + [0] 204.84/60.02 >= [1] x + [0] 204.84/60.02 = [x] 204.84/60.02 204.84/60.02 204.84/60.02 We return to the main proof. 204.84/60.02 204.84/60.02 We are left with following problem, upon which TcT provides the 204.84/60.02 certificate MAYBE. 204.84/60.02 204.84/60.02 Strict Trs: 204.84/60.02 { f(s(x)) -> s(s(f(p(s(x))))) 204.84/60.02 , p(s(x)) -> x } 204.84/60.02 Weak Trs: { f(0()) -> 0() } 204.84/60.02 Obligation: 204.84/60.02 derivational complexity 204.84/60.02 Answer: 204.84/60.02 MAYBE 204.84/60.02 204.84/60.02 The weightgap principle applies (using the following nonconstant 204.84/60.02 growth matrix-interpretation) 204.84/60.02 204.84/60.02 TcT has computed the following triangular matrix interpretation. 204.84/60.02 Note that the diagonal of the component-wise maxima of 204.84/60.02 interpretation-entries contains no more than 1 non-zero entries. 204.84/60.02 204.84/60.02 [f](x1) = [1] x1 + [0] 204.84/60.02 204.84/60.02 [s](x1) = [1] x1 + [0] 204.84/60.02 204.84/60.02 [p](x1) = [1] x1 + [1] 204.84/60.02 204.84/60.02 [0] = [2] 204.84/60.02 204.84/60.02 The order satisfies the following ordering constraints: 204.84/60.02 204.84/60.02 [f(s(x))] = [1] x + [0] 204.84/60.02 ? [1] x + [1] 204.84/60.02 = [s(s(f(p(s(x)))))] 204.84/60.02 204.84/60.02 [f(0())] = [2] 204.84/60.02 >= [2] 204.84/60.02 = [0()] 204.84/60.02 204.84/60.02 [p(s(x))] = [1] x + [1] 204.84/60.02 > [1] x + [0] 204.84/60.02 = [x] 204.84/60.02 204.84/60.02 204.84/60.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 204.84/60.02 204.84/60.02 We are left with following problem, upon which TcT provides the 204.84/60.02 certificate MAYBE. 204.84/60.02 204.84/60.02 Strict Trs: { f(s(x)) -> s(s(f(p(s(x))))) } 204.84/60.02 Weak Trs: 204.84/60.02 { f(0()) -> 0() 204.84/60.02 , p(s(x)) -> x } 204.84/60.02 Obligation: 204.84/60.02 derivational complexity 204.84/60.02 Answer: 204.84/60.02 MAYBE 204.84/60.02 204.84/60.02 None of the processors succeeded. 204.84/60.02 204.84/60.02 Details of failed attempt(s): 204.84/60.02 ----------------------------- 204.84/60.02 1) 'empty' failed due to the following reason: 204.84/60.02 204.84/60.02 Empty strict component of the problem is NOT empty. 204.84/60.02 204.84/60.02 2) 'Fastest' failed due to the following reason: 204.84/60.02 204.84/60.02 None of the processors succeeded. 204.84/60.02 204.84/60.02 Details of failed attempt(s): 204.84/60.02 ----------------------------- 204.84/60.02 1) 'bsearch-matrix' failed due to the following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 2) 'Fastest (timeout of 30 seconds)' failed due to the following 204.84/60.02 reason: 204.84/60.02 204.84/60.02 Computation stopped due to timeout after 30.0 seconds. 204.84/60.02 204.84/60.02 3) 'iteProgress' failed due to the following reason: 204.84/60.02 204.84/60.02 Fail 204.84/60.02 204.84/60.02 4) 'Fastest' failed due to the following reason: 204.84/60.02 204.84/60.02 None of the processors succeeded. 204.84/60.02 204.84/60.02 Details of failed attempt(s): 204.84/60.02 ----------------------------- 204.84/60.02 1) 'matrix interpretation of dimension 6' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 2) 'matrix interpretation of dimension 5' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 3) 'matrix interpretation of dimension 4' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 4) 'matrix interpretation of dimension 3' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 5) 'matrix interpretation of dimension 2' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 6) 'matrix interpretation of dimension 1' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 204.84/60.02 204.84/60.02 204.84/60.02 3) 'iteProgress (timeout of 297 seconds)' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 Fail 204.84/60.02 204.84/60.02 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 204.84/60.02 following reason: 204.84/60.02 204.84/60.02 The input cannot be shown compatible 204.84/60.02 204.84/60.02 204.84/60.02 Arrrr.. 204.84/60.03 EOF