MAYBE 751.46/297.02 MAYBE 751.46/297.02 751.46/297.02 We are left with following problem, upon which TcT provides the 751.46/297.02 certificate MAYBE. 751.46/297.02 751.46/297.02 Strict Trs: 751.46/297.02 { cond(true(), x, y) -> cond(gr(x, y), x, add(x, y)) 751.46/297.02 , gr(0(), x) -> false() 751.46/297.02 , gr(s(x), 0()) -> true() 751.46/297.02 , gr(s(x), s(y)) -> gr(x, y) 751.46/297.02 , add(0(), x) -> x 751.46/297.02 , add(s(x), y) -> s(add(x, y)) } 751.46/297.02 Obligation: 751.46/297.02 innermost runtime complexity 751.46/297.02 Answer: 751.46/297.02 MAYBE 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'Best' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 751.46/297.02 following reason: 751.46/297.02 751.46/297.02 Computation stopped due to timeout after 297.0 seconds. 751.46/297.02 751.46/297.02 2) 'Best' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 751.46/297.02 seconds)' failed due to the following reason: 751.46/297.02 751.46/297.02 The weightgap principle applies (using the following nonconstant 751.46/297.02 growth matrix-interpretation) 751.46/297.02 751.46/297.02 The following argument positions are usable: 751.46/297.02 Uargs(cond) = {1, 3}, Uargs(s) = {1} 751.46/297.02 751.46/297.02 TcT has computed the following matrix interpretation satisfying 751.46/297.02 not(EDA) and not(IDA(1)). 751.46/297.02 751.46/297.02 [cond](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [3] 751.46/297.02 751.46/297.02 [true] = [3] 751.46/297.02 751.46/297.02 [gr](x1, x2) = [5] 751.46/297.02 751.46/297.02 [add](x1, x2) = [1] x2 + [6] 751.46/297.02 751.46/297.02 [0] = [7] 751.46/297.02 751.46/297.02 [false] = [4] 751.46/297.02 751.46/297.02 [s](x1) = [1] x1 + [1] 751.46/297.02 751.46/297.02 The order satisfies the following ordering constraints: 751.46/297.02 751.46/297.02 [cond(true(), x, y)] = [1] x + [1] y + [6] 751.46/297.02 ? [1] x + [1] y + [14] 751.46/297.02 = [cond(gr(x, y), x, add(x, y))] 751.46/297.02 751.46/297.02 [gr(0(), x)] = [5] 751.46/297.02 > [4] 751.46/297.02 = [false()] 751.46/297.02 751.46/297.02 [gr(s(x), 0())] = [5] 751.46/297.02 > [3] 751.46/297.02 = [true()] 751.46/297.02 751.46/297.02 [gr(s(x), s(y))] = [5] 751.46/297.02 >= [5] 751.46/297.02 = [gr(x, y)] 751.46/297.02 751.46/297.02 [add(0(), x)] = [1] x + [6] 751.46/297.02 > [1] x + [0] 751.46/297.02 = [x] 751.46/297.02 751.46/297.02 [add(s(x), y)] = [1] y + [6] 751.46/297.02 ? [1] y + [7] 751.46/297.02 = [s(add(x, y))] 751.46/297.02 751.46/297.02 751.46/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 751.46/297.02 751.46/297.02 We are left with following problem, upon which TcT provides the 751.46/297.02 certificate MAYBE. 751.46/297.02 751.46/297.02 Strict Trs: 751.46/297.02 { cond(true(), x, y) -> cond(gr(x, y), x, add(x, y)) 751.46/297.02 , gr(s(x), s(y)) -> gr(x, y) 751.46/297.02 , add(s(x), y) -> s(add(x, y)) } 751.46/297.02 Weak Trs: 751.46/297.02 { gr(0(), x) -> false() 751.46/297.02 , gr(s(x), 0()) -> true() 751.46/297.02 , add(0(), x) -> x } 751.46/297.02 Obligation: 751.46/297.02 innermost runtime complexity 751.46/297.02 Answer: 751.46/297.02 MAYBE 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'Fastest' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 751.46/297.02 2) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'empty' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 2) 'With Problem ...' failed due to the following reason: 751.46/297.02 751.46/297.02 Empty strict component of the problem is NOT empty. 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 2) 'Best' failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 751.46/297.02 following reason: 751.46/297.02 751.46/297.02 The input cannot be shown compatible 751.46/297.02 751.46/297.02 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 751.46/297.02 to the following reason: 751.46/297.02 751.46/297.02 The input cannot be shown compatible 751.46/297.02 751.46/297.02 751.46/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 751.46/297.02 failed due to the following reason: 751.46/297.02 751.46/297.02 None of the processors succeeded. 751.46/297.02 751.46/297.02 Details of failed attempt(s): 751.46/297.02 ----------------------------- 751.46/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 751.46/297.02 failed due to the following reason: 751.46/297.02 751.46/297.02 match-boundness of the problem could not be verified. 751.46/297.02 751.46/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 751.46/297.02 failed due to the following reason: 751.46/297.02 751.46/297.02 match-boundness of the problem could not be verified. 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 751.46/297.02 Arrrr.. 751.67/297.22 EOF