MAYBE 897.57/297.21 MAYBE 897.57/297.21 897.57/297.21 We are left with following problem, upon which TcT provides the 897.57/297.21 certificate MAYBE. 897.57/297.21 897.57/297.21 Strict Trs: 897.57/297.21 { f(true(), x, y, z) -> g(gt(x, y), x, y, z) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) 897.57/297.21 , gt(s(u), s(v)) -> gt(u, v) 897.57/297.21 , gt(s(u), 0()) -> true() 897.57/297.21 , gt(0(), v) -> false() } 897.57/297.21 Obligation: 897.57/297.21 runtime complexity 897.57/297.21 Answer: 897.57/297.21 MAYBE 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 897.57/297.21 following reason: 897.57/297.21 897.57/297.21 Computation stopped due to timeout after 297.0 seconds. 897.57/297.21 897.57/297.21 2) 'Best' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 897.57/297.21 seconds)' failed due to the following reason: 897.57/297.21 897.57/297.21 The weightgap principle applies (using the following nonconstant 897.57/297.21 growth matrix-interpretation) 897.57/297.21 897.57/297.21 The following argument positions are usable: 897.57/297.21 Uargs(f) = {1}, Uargs(g) = {1} 897.57/297.21 897.57/297.21 TcT has computed the following matrix interpretation satisfying 897.57/297.21 not(EDA) and not(IDA(1)). 897.57/297.21 897.57/297.21 [f](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 897.57/297.21 897.57/297.21 [true] = [4] 897.57/297.21 897.57/297.21 [g](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 897.57/297.21 897.57/297.21 [gt](x1, x2) = [0] 897.57/297.21 897.57/297.21 [s](x1) = [1] x1 + [0] 897.57/297.21 897.57/297.21 [0] = [7] 897.57/297.21 897.57/297.21 [false] = [7] 897.57/297.21 897.57/297.21 The order satisfies the following ordering constraints: 897.57/297.21 897.57/297.21 [f(true(), x, y, z)] = [1] x + [1] y + [1] z + [4] 897.57/297.21 > [1] x + [1] y + [1] z + [0] 897.57/297.21 = [g(gt(x, y), x, y, z)] 897.57/297.21 897.57/297.21 [g(true(), x, y, z)] = [1] x + [1] y + [1] z + [4] 897.57/297.21 > [1] x + [1] y + [1] z + [0] 897.57/297.21 = [f(gt(x, z), x, y, s(z))] 897.57/297.21 897.57/297.21 [g(true(), x, y, z)] = [1] x + [1] y + [1] z + [4] 897.57/297.21 > [1] x + [1] y + [1] z + [0] 897.57/297.21 = [f(gt(x, z), x, s(y), z)] 897.57/297.21 897.57/297.21 [gt(s(u), s(v))] = [0] 897.57/297.21 >= [0] 897.57/297.21 = [gt(u, v)] 897.57/297.21 897.57/297.21 [gt(s(u), 0())] = [0] 897.57/297.21 ? [4] 897.57/297.21 = [true()] 897.57/297.21 897.57/297.21 [gt(0(), v)] = [0] 897.57/297.21 ? [7] 897.57/297.21 = [false()] 897.57/297.21 897.57/297.21 897.57/297.21 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 897.57/297.21 897.57/297.21 We are left with following problem, upon which TcT provides the 897.57/297.21 certificate MAYBE. 897.57/297.21 897.57/297.21 Strict Trs: 897.57/297.21 { gt(s(u), s(v)) -> gt(u, v) 897.57/297.21 , gt(s(u), 0()) -> true() 897.57/297.21 , gt(0(), v) -> false() } 897.57/297.21 Weak Trs: 897.57/297.21 { f(true(), x, y, z) -> g(gt(x, y), x, y, z) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) } 897.57/297.21 Obligation: 897.57/297.21 runtime complexity 897.57/297.21 Answer: 897.57/297.21 MAYBE 897.57/297.21 897.57/297.21 The weightgap principle applies (using the following nonconstant 897.57/297.21 growth matrix-interpretation) 897.57/297.21 897.57/297.21 The following argument positions are usable: 897.57/297.21 Uargs(f) = {1}, Uargs(g) = {1} 897.57/297.21 897.57/297.21 TcT has computed the following matrix interpretation satisfying 897.57/297.21 not(EDA) and not(IDA(1)). 897.57/297.21 897.57/297.21 [f](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 897.57/297.21 897.57/297.21 [true] = [4] 897.57/297.21 897.57/297.21 [g](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 897.57/297.21 897.57/297.21 [gt](x1, x2) = [1] 897.57/297.21 897.57/297.21 [s](x1) = [0] 897.57/297.21 897.57/297.21 [0] = [7] 897.57/297.21 897.57/297.21 [false] = [0] 897.57/297.21 897.57/297.21 The order satisfies the following ordering constraints: 897.57/297.21 897.57/297.21 [f(true(), x, y, z)] = [1] x + [1] y + [1] z + [4] 897.57/297.21 > [1] x + [1] y + [1] z + [1] 897.57/297.21 = [g(gt(x, y), x, y, z)] 897.57/297.21 897.57/297.21 [g(true(), x, y, z)] = [1] x + [1] y + [1] z + [4] 897.57/297.21 > [1] x + [1] y + [1] 897.57/297.21 = [f(gt(x, z), x, y, s(z))] 897.57/297.21 897.57/297.21 [g(true(), x, y, z)] = [1] x + [1] y + [1] z + [4] 897.57/297.21 > [1] x + [1] z + [1] 897.57/297.21 = [f(gt(x, z), x, s(y), z)] 897.57/297.21 897.57/297.21 [gt(s(u), s(v))] = [1] 897.57/297.21 >= [1] 897.57/297.21 = [gt(u, v)] 897.57/297.21 897.57/297.21 [gt(s(u), 0())] = [1] 897.57/297.21 ? [4] 897.57/297.21 = [true()] 897.57/297.21 897.57/297.21 [gt(0(), v)] = [1] 897.57/297.21 > [0] 897.57/297.21 = [false()] 897.57/297.21 897.57/297.21 897.57/297.21 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 897.57/297.21 897.57/297.21 We are left with following problem, upon which TcT provides the 897.57/297.21 certificate MAYBE. 897.57/297.21 897.57/297.21 Strict Trs: 897.57/297.21 { gt(s(u), s(v)) -> gt(u, v) 897.57/297.21 , gt(s(u), 0()) -> true() } 897.57/297.21 Weak Trs: 897.57/297.21 { f(true(), x, y, z) -> g(gt(x, y), x, y, z) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) 897.57/297.21 , gt(0(), v) -> false() } 897.57/297.21 Obligation: 897.57/297.21 runtime complexity 897.57/297.21 Answer: 897.57/297.21 MAYBE 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'empty' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 2) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'empty' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 2) 'Fastest' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'empty' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 2) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 897.57/297.21 2) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'empty' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 2) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'empty' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 2) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'empty' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 2) 'With Problem ...' failed due to the following reason: 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 897.57/297.21 897.57/297.21 897.57/297.21 897.57/297.21 897.57/297.21 897.57/297.21 2) 'Best' failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 897.57/297.21 following reason: 897.57/297.21 897.57/297.21 The processor is inapplicable, reason: 897.57/297.21 Processor only applicable for innermost runtime complexity analysis 897.57/297.21 897.57/297.21 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 897.57/297.21 to the following reason: 897.57/297.21 897.57/297.21 The processor is inapplicable, reason: 897.57/297.21 Processor only applicable for innermost runtime complexity analysis 897.57/297.21 897.57/297.21 897.57/297.21 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 897.57/297.21 failed due to the following reason: 897.57/297.21 897.57/297.21 None of the processors succeeded. 897.57/297.21 897.57/297.21 Details of failed attempt(s): 897.57/297.21 ----------------------------- 897.57/297.21 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 897.57/297.21 failed due to the following reason: 897.57/297.21 897.57/297.21 match-boundness of the problem could not be verified. 897.57/297.21 897.57/297.21 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 897.57/297.21 failed due to the following reason: 897.57/297.21 897.57/297.21 match-boundness of the problem could not be verified. 897.57/297.21 897.57/297.21 897.57/297.21 897.57/297.21 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 897.57/297.21 the following reason: 897.57/297.21 897.57/297.21 We add the following weak dependency pairs: 897.57/297.21 897.57/297.21 Strict DPs: 897.57/297.21 { f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) 897.57/297.21 , g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) 897.57/297.21 , g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) 897.57/297.21 , gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) 897.57/297.21 , gt^#(s(u), 0()) -> c_5() 897.57/297.21 , gt^#(0(), v) -> c_6() } 897.57/297.21 897.57/297.21 and mark the set of starting terms. 897.57/297.21 897.57/297.21 We are left with following problem, upon which TcT provides the 897.57/297.21 certificate MAYBE. 897.57/297.21 897.57/297.21 Strict DPs: 897.57/297.21 { f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) 897.57/297.21 , g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) 897.57/297.21 , g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) 897.57/297.21 , gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) 897.57/297.21 , gt^#(s(u), 0()) -> c_5() 897.57/297.21 , gt^#(0(), v) -> c_6() } 897.57/297.21 Strict Trs: 897.57/297.21 { f(true(), x, y, z) -> g(gt(x, y), x, y, z) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) 897.57/297.21 , gt(s(u), s(v)) -> gt(u, v) 897.57/297.21 , gt(s(u), 0()) -> true() 897.57/297.21 , gt(0(), v) -> false() } 897.57/297.21 Obligation: 897.57/297.21 runtime complexity 897.57/297.21 Answer: 897.57/297.21 MAYBE 897.57/297.21 897.57/297.21 We estimate the number of application of {5,6} by applications of 897.57/297.21 Pre({5,6}) = {4}. Here rules are labeled as follows: 897.57/297.21 897.57/297.21 DPs: 897.57/297.21 { 1: f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) 897.57/297.21 , 2: g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) 897.57/297.21 , 3: g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) 897.57/297.21 , 4: gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) 897.57/297.21 , 5: gt^#(s(u), 0()) -> c_5() 897.57/297.21 , 6: gt^#(0(), v) -> c_6() } 897.57/297.21 897.57/297.21 We are left with following problem, upon which TcT provides the 897.57/297.21 certificate MAYBE. 897.57/297.21 897.57/297.21 Strict DPs: 897.57/297.21 { f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) 897.57/297.21 , g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) 897.57/297.21 , g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) 897.57/297.21 , gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) } 897.57/297.21 Strict Trs: 897.57/297.21 { f(true(), x, y, z) -> g(gt(x, y), x, y, z) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) 897.57/297.21 , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) 897.57/297.21 , gt(s(u), s(v)) -> gt(u, v) 897.57/297.21 , gt(s(u), 0()) -> true() 897.57/297.21 , gt(0(), v) -> false() } 897.57/297.21 Weak DPs: 897.57/297.21 { gt^#(s(u), 0()) -> c_5() 897.57/297.21 , gt^#(0(), v) -> c_6() } 897.57/297.21 Obligation: 897.57/297.21 runtime complexity 897.57/297.21 Answer: 897.57/297.21 MAYBE 897.57/297.21 897.57/297.21 Empty strict component of the problem is NOT empty. 897.57/297.21 897.57/297.21 897.57/297.21 Arrrr.. 897.82/297.44 EOF