MAYBE 826.26/297.02 MAYBE 826.26/297.02 826.26/297.02 We are left with following problem, upon which TcT provides the 826.26/297.02 certificate MAYBE. 826.26/297.02 826.26/297.02 Strict Trs: 826.26/297.02 { f(t(), x, y) -> f(g(x, y), x, s(y)) 826.26/297.02 , g(s(x), s(y)) -> g(x, y) 826.26/297.02 , g(s(x), 0()) -> t() } 826.26/297.02 Obligation: 826.26/297.02 runtime complexity 826.26/297.02 Answer: 826.26/297.02 MAYBE 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 826.26/297.02 following reason: 826.26/297.02 826.26/297.02 Computation stopped due to timeout after 297.0 seconds. 826.26/297.02 826.26/297.02 2) 'Best' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 826.26/297.02 seconds)' failed due to the following reason: 826.26/297.02 826.26/297.02 The weightgap principle applies (using the following nonconstant 826.26/297.02 growth matrix-interpretation) 826.26/297.02 826.26/297.02 The following argument positions are usable: 826.26/297.02 Uargs(f) = {1} 826.26/297.02 826.26/297.02 TcT has computed the following matrix interpretation satisfying 826.26/297.02 not(EDA) and not(IDA(1)). 826.26/297.02 826.26/297.02 [f](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [7] 826.26/297.02 826.26/297.02 [t] = [3] 826.26/297.02 826.26/297.02 [g](x1, x2) = [7] 826.26/297.02 826.26/297.02 [s](x1) = [0] 826.26/297.02 826.26/297.02 [0] = [7] 826.26/297.02 826.26/297.02 The order satisfies the following ordering constraints: 826.26/297.02 826.26/297.02 [f(t(), x, y)] = [1] x + [1] y + [10] 826.26/297.02 ? [1] x + [14] 826.26/297.02 = [f(g(x, y), x, s(y))] 826.26/297.02 826.26/297.02 [g(s(x), s(y))] = [7] 826.26/297.02 >= [7] 826.26/297.02 = [g(x, y)] 826.26/297.02 826.26/297.02 [g(s(x), 0())] = [7] 826.26/297.02 > [3] 826.26/297.02 = [t()] 826.26/297.02 826.26/297.02 826.26/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 826.26/297.02 826.26/297.02 We are left with following problem, upon which TcT provides the 826.26/297.02 certificate MAYBE. 826.26/297.02 826.26/297.02 Strict Trs: 826.26/297.02 { f(t(), x, y) -> f(g(x, y), x, s(y)) 826.26/297.02 , g(s(x), s(y)) -> g(x, y) } 826.26/297.02 Weak Trs: { g(s(x), 0()) -> t() } 826.26/297.02 Obligation: 826.26/297.02 runtime complexity 826.26/297.02 Answer: 826.26/297.02 MAYBE 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'empty' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 2) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'empty' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 2) 'Fastest' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'empty' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 2) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 The weightgap principle applies (using the following nonconstant 826.26/297.02 growth matrix-interpretation) 826.26/297.02 826.26/297.02 The following argument positions are usable: 826.26/297.02 Uargs(f) = {1} 826.26/297.02 826.26/297.02 TcT has computed the following matrix interpretation satisfying 826.26/297.02 not(EDA) and not(IDA(1)). 826.26/297.02 826.26/297.02 [f](x1, x2, x3) = [1 1] x1 + [1 0] x3 + [0] 826.26/297.02 [0 0] [0 0] [1] 826.26/297.02 826.26/297.02 [t] = [0] 826.26/297.02 [4] 826.26/297.02 826.26/297.02 [g](x1, x2) = [0 0] x2 + [0] 826.26/297.02 [1 0] [0] 826.26/297.02 826.26/297.02 [s](x1) = [0] 826.26/297.02 [0] 826.26/297.02 826.26/297.02 [0] = [4] 826.26/297.02 [0] 826.26/297.02 826.26/297.02 The order satisfies the following ordering constraints: 826.26/297.02 826.26/297.02 [f(t(), x, y)] = [1 0] y + [4] 826.26/297.02 [0 0] [1] 826.26/297.02 > [1 0] y + [0] 826.26/297.02 [0 0] [1] 826.26/297.02 = [f(g(x, y), x, s(y))] 826.26/297.02 826.26/297.02 [g(s(x), s(y))] = [0] 826.26/297.02 [0] 826.26/297.02 ? [0 0] y + [0] 826.26/297.02 [1 0] [0] 826.26/297.02 = [g(x, y)] 826.26/297.02 826.26/297.02 [g(s(x), 0())] = [0] 826.26/297.02 [4] 826.26/297.02 >= [0] 826.26/297.02 [4] 826.26/297.02 = [t()] 826.26/297.02 826.26/297.02 826.26/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 826.26/297.02 826.26/297.02 We are left with following problem, upon which TcT provides the 826.26/297.02 certificate MAYBE. 826.26/297.02 826.26/297.02 Strict Trs: { g(s(x), s(y)) -> g(x, y) } 826.26/297.02 Weak Trs: 826.26/297.02 { f(t(), x, y) -> f(g(x, y), x, s(y)) 826.26/297.02 , g(s(x), 0()) -> t() } 826.26/297.02 Obligation: 826.26/297.02 runtime complexity 826.26/297.02 Answer: 826.26/297.02 MAYBE 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'empty' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 2) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'empty' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 2) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 826.26/297.02 826.26/297.02 826.26/297.02 2) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'empty' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 2) 'With Problem ...' failed due to the following reason: 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 826.26/297.02 826.26/297.02 826.26/297.02 826.26/297.02 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 826.26/297.02 failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 826.26/297.02 failed due to the following reason: 826.26/297.02 826.26/297.02 match-boundness of the problem could not be verified. 826.26/297.02 826.26/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 826.26/297.02 failed due to the following reason: 826.26/297.02 826.26/297.02 match-boundness of the problem could not be verified. 826.26/297.02 826.26/297.02 826.26/297.02 3) 'Best' failed due to the following reason: 826.26/297.02 826.26/297.02 None of the processors succeeded. 826.26/297.02 826.26/297.02 Details of failed attempt(s): 826.26/297.02 ----------------------------- 826.26/297.02 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 826.26/297.02 following reason: 826.26/297.02 826.26/297.02 The processor is inapplicable, reason: 826.26/297.02 Processor only applicable for innermost runtime complexity analysis 826.26/297.02 826.26/297.02 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 826.26/297.02 to the following reason: 826.26/297.02 826.26/297.02 The processor is inapplicable, reason: 826.26/297.02 Processor only applicable for innermost runtime complexity analysis 826.26/297.02 826.26/297.02 826.26/297.02 826.26/297.02 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 826.26/297.02 the following reason: 826.26/297.02 826.26/297.02 We add the following weak dependency pairs: 826.26/297.02 826.26/297.02 Strict DPs: 826.26/297.02 { f^#(t(), x, y) -> c_1(f^#(g(x, y), x, s(y))) 826.26/297.02 , g^#(s(x), s(y)) -> c_2(g^#(x, y)) 826.26/297.02 , g^#(s(x), 0()) -> c_3() } 826.26/297.02 826.26/297.02 and mark the set of starting terms. 826.26/297.02 826.26/297.02 We are left with following problem, upon which TcT provides the 826.26/297.02 certificate MAYBE. 826.26/297.02 826.26/297.02 Strict DPs: 826.26/297.02 { f^#(t(), x, y) -> c_1(f^#(g(x, y), x, s(y))) 826.26/297.02 , g^#(s(x), s(y)) -> c_2(g^#(x, y)) 826.26/297.02 , g^#(s(x), 0()) -> c_3() } 826.26/297.02 Strict Trs: 826.26/297.02 { f(t(), x, y) -> f(g(x, y), x, s(y)) 826.26/297.02 , g(s(x), s(y)) -> g(x, y) 826.26/297.02 , g(s(x), 0()) -> t() } 826.26/297.02 Obligation: 826.26/297.02 runtime complexity 826.26/297.02 Answer: 826.26/297.02 MAYBE 826.26/297.02 826.26/297.02 We estimate the number of application of {3} by applications of 826.26/297.02 Pre({3}) = {2}. Here rules are labeled as follows: 826.26/297.02 826.26/297.02 DPs: 826.26/297.02 { 1: f^#(t(), x, y) -> c_1(f^#(g(x, y), x, s(y))) 826.26/297.02 , 2: g^#(s(x), s(y)) -> c_2(g^#(x, y)) 826.26/297.02 , 3: g^#(s(x), 0()) -> c_3() } 826.26/297.02 826.26/297.02 We are left with following problem, upon which TcT provides the 826.26/297.02 certificate MAYBE. 826.26/297.02 826.26/297.02 Strict DPs: 826.26/297.02 { f^#(t(), x, y) -> c_1(f^#(g(x, y), x, s(y))) 826.26/297.02 , g^#(s(x), s(y)) -> c_2(g^#(x, y)) } 826.26/297.02 Strict Trs: 826.26/297.02 { f(t(), x, y) -> f(g(x, y), x, s(y)) 826.26/297.02 , g(s(x), s(y)) -> g(x, y) 826.26/297.02 , g(s(x), 0()) -> t() } 826.26/297.02 Weak DPs: { g^#(s(x), 0()) -> c_3() } 826.26/297.02 Obligation: 826.26/297.02 runtime complexity 826.26/297.02 Answer: 826.26/297.02 MAYBE 826.26/297.02 826.26/297.02 Empty strict component of the problem is NOT empty. 826.26/297.02 826.26/297.02 826.26/297.02 Arrrr.. 826.68/297.44 EOF