MAYBE 453.00/297.12 MAYBE 453.00/297.12 453.00/297.12 We are left with following problem, upon which TcT provides the 453.00/297.12 certificate MAYBE. 453.00/297.12 453.00/297.12 Strict Trs: 453.00/297.12 { f(s(x)) -> f(id_inc(c(x, x))) 453.00/297.12 , f(c(s(x), y)) -> g(c(x, y)) 453.00/297.12 , id_inc(s(x)) -> s(id_inc(x)) 453.00/297.12 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 453.00/297.12 , id_inc(0()) -> s(0()) 453.00/297.12 , id_inc(0()) -> 0() 453.00/297.12 , g(c(x, x)) -> f(x) 453.00/297.12 , g(c(x, s(y))) -> g(c(y, x)) 453.00/297.12 , g(c(s(x), y)) -> g(c(y, x)) } 453.00/297.12 Obligation: 453.00/297.12 innermost runtime complexity 453.00/297.12 Answer: 453.00/297.12 MAYBE 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 2) 'Best' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 453.00/297.12 following reason: 453.00/297.12 453.00/297.12 Computation stopped due to timeout after 297.0 seconds. 453.00/297.12 453.00/297.12 2) 'Best' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 453.00/297.12 seconds)' failed due to the following reason: 453.00/297.12 453.00/297.12 The weightgap principle applies (using the following nonconstant 453.00/297.12 growth matrix-interpretation) 453.00/297.12 453.00/297.12 The following argument positions are usable: 453.00/297.12 Uargs(f) = {1}, Uargs(s) = {1}, Uargs(c) = {1, 2} 453.00/297.12 453.00/297.12 TcT has computed the following matrix interpretation satisfying 453.00/297.12 not(EDA) and not(IDA(1)). 453.00/297.12 453.00/297.12 [f](x1) = [1] x1 + [4] 453.00/297.12 453.00/297.12 [s](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [id_inc](x1) = [0] 453.00/297.12 453.00/297.12 [c](x1, x2) = [1] x1 + [1] x2 + [0] 453.00/297.12 453.00/297.12 [g](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [0] = [4] 453.00/297.12 453.00/297.12 The order satisfies the following ordering constraints: 453.00/297.12 453.00/297.12 [f(s(x))] = [1] x + [4] 453.00/297.12 >= [4] 453.00/297.12 = [f(id_inc(c(x, x)))] 453.00/297.12 453.00/297.12 [f(c(s(x), y))] = [1] x + [1] y + [4] 453.00/297.12 > [1] x + [1] y + [0] 453.00/297.12 = [g(c(x, y))] 453.00/297.12 453.00/297.12 [id_inc(s(x))] = [0] 453.00/297.12 >= [0] 453.00/297.12 = [s(id_inc(x))] 453.00/297.12 453.00/297.12 [id_inc(c(x, y))] = [0] 453.00/297.12 >= [0] 453.00/297.12 = [c(id_inc(x), id_inc(y))] 453.00/297.12 453.00/297.12 [id_inc(0())] = [0] 453.00/297.12 ? [4] 453.00/297.12 = [s(0())] 453.00/297.12 453.00/297.12 [id_inc(0())] = [0] 453.00/297.12 ? [4] 453.00/297.12 = [0()] 453.00/297.12 453.00/297.12 [g(c(x, x))] = [2] x + [0] 453.00/297.12 ? [1] x + [4] 453.00/297.12 = [f(x)] 453.00/297.12 453.00/297.12 [g(c(x, s(y)))] = [1] x + [1] y + [0] 453.00/297.12 >= [1] x + [1] y + [0] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 [g(c(s(x), y))] = [1] x + [1] y + [0] 453.00/297.12 >= [1] x + [1] y + [0] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 453.00/297.12 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 453.00/297.12 453.00/297.12 We are left with following problem, upon which TcT provides the 453.00/297.12 certificate MAYBE. 453.00/297.12 453.00/297.12 Strict Trs: 453.00/297.12 { f(s(x)) -> f(id_inc(c(x, x))) 453.00/297.12 , id_inc(s(x)) -> s(id_inc(x)) 453.00/297.12 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 453.00/297.12 , id_inc(0()) -> s(0()) 453.00/297.12 , id_inc(0()) -> 0() 453.00/297.12 , g(c(x, x)) -> f(x) 453.00/297.12 , g(c(x, s(y))) -> g(c(y, x)) 453.00/297.12 , g(c(s(x), y)) -> g(c(y, x)) } 453.00/297.12 Weak Trs: { f(c(s(x), y)) -> g(c(x, y)) } 453.00/297.12 Obligation: 453.00/297.12 innermost runtime complexity 453.00/297.12 Answer: 453.00/297.12 MAYBE 453.00/297.12 453.00/297.12 The weightgap principle applies (using the following nonconstant 453.00/297.12 growth matrix-interpretation) 453.00/297.12 453.00/297.12 The following argument positions are usable: 453.00/297.12 Uargs(f) = {1}, Uargs(s) = {1}, Uargs(c) = {1, 2} 453.00/297.12 453.00/297.12 TcT has computed the following matrix interpretation satisfying 453.00/297.12 not(EDA) and not(IDA(1)). 453.00/297.12 453.00/297.12 [f](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [s](x1) = [1] x1 + [4] 453.00/297.12 453.00/297.12 [id_inc](x1) = [0] 453.00/297.12 453.00/297.12 [c](x1, x2) = [1] x1 + [1] x2 + [0] 453.00/297.12 453.00/297.12 [g](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [0] = [4] 453.00/297.12 453.00/297.12 The order satisfies the following ordering constraints: 453.00/297.12 453.00/297.12 [f(s(x))] = [1] x + [4] 453.00/297.12 > [0] 453.00/297.12 = [f(id_inc(c(x, x)))] 453.00/297.12 453.00/297.12 [f(c(s(x), y))] = [1] x + [1] y + [4] 453.00/297.12 > [1] x + [1] y + [0] 453.00/297.12 = [g(c(x, y))] 453.00/297.12 453.00/297.12 [id_inc(s(x))] = [0] 453.00/297.12 ? [4] 453.00/297.12 = [s(id_inc(x))] 453.00/297.12 453.00/297.12 [id_inc(c(x, y))] = [0] 453.00/297.12 >= [0] 453.00/297.12 = [c(id_inc(x), id_inc(y))] 453.00/297.12 453.00/297.12 [id_inc(0())] = [0] 453.00/297.12 ? [8] 453.00/297.12 = [s(0())] 453.00/297.12 453.00/297.12 [id_inc(0())] = [0] 453.00/297.12 ? [4] 453.00/297.12 = [0()] 453.00/297.12 453.00/297.12 [g(c(x, x))] = [2] x + [0] 453.00/297.12 >= [1] x + [0] 453.00/297.12 = [f(x)] 453.00/297.12 453.00/297.12 [g(c(x, s(y)))] = [1] x + [1] y + [4] 453.00/297.12 > [1] x + [1] y + [0] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 [g(c(s(x), y))] = [1] x + [1] y + [4] 453.00/297.12 > [1] x + [1] y + [0] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 453.00/297.12 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 453.00/297.12 453.00/297.12 We are left with following problem, upon which TcT provides the 453.00/297.12 certificate MAYBE. 453.00/297.12 453.00/297.12 Strict Trs: 453.00/297.12 { id_inc(s(x)) -> s(id_inc(x)) 453.00/297.12 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 453.00/297.12 , id_inc(0()) -> s(0()) 453.00/297.12 , id_inc(0()) -> 0() 453.00/297.12 , g(c(x, x)) -> f(x) } 453.00/297.12 Weak Trs: 453.00/297.12 { f(s(x)) -> f(id_inc(c(x, x))) 453.00/297.12 , f(c(s(x), y)) -> g(c(x, y)) 453.00/297.12 , g(c(x, s(y))) -> g(c(y, x)) 453.00/297.12 , g(c(s(x), y)) -> g(c(y, x)) } 453.00/297.12 Obligation: 453.00/297.12 innermost runtime complexity 453.00/297.12 Answer: 453.00/297.12 MAYBE 453.00/297.12 453.00/297.12 The weightgap principle applies (using the following nonconstant 453.00/297.12 growth matrix-interpretation) 453.00/297.12 453.00/297.12 The following argument positions are usable: 453.00/297.12 Uargs(f) = {1}, Uargs(s) = {1}, Uargs(c) = {1, 2} 453.00/297.12 453.00/297.12 TcT has computed the following matrix interpretation satisfying 453.00/297.12 not(EDA) and not(IDA(1)). 453.00/297.12 453.00/297.12 [f](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [s](x1) = [1] x1 + [4] 453.00/297.12 453.00/297.12 [id_inc](x1) = [0] 453.00/297.12 453.00/297.12 [c](x1, x2) = [1] x1 + [1] x2 + [0] 453.00/297.12 453.00/297.12 [g](x1) = [1] x1 + [1] 453.00/297.12 453.00/297.12 [0] = [4] 453.00/297.12 453.00/297.12 The order satisfies the following ordering constraints: 453.00/297.12 453.00/297.12 [f(s(x))] = [1] x + [4] 453.00/297.12 > [0] 453.00/297.12 = [f(id_inc(c(x, x)))] 453.00/297.12 453.00/297.12 [f(c(s(x), y))] = [1] x + [1] y + [4] 453.00/297.12 > [1] x + [1] y + [1] 453.00/297.12 = [g(c(x, y))] 453.00/297.12 453.00/297.12 [id_inc(s(x))] = [0] 453.00/297.12 ? [4] 453.00/297.12 = [s(id_inc(x))] 453.00/297.12 453.00/297.12 [id_inc(c(x, y))] = [0] 453.00/297.12 >= [0] 453.00/297.12 = [c(id_inc(x), id_inc(y))] 453.00/297.12 453.00/297.12 [id_inc(0())] = [0] 453.00/297.12 ? [8] 453.00/297.12 = [s(0())] 453.00/297.12 453.00/297.12 [id_inc(0())] = [0] 453.00/297.12 ? [4] 453.00/297.12 = [0()] 453.00/297.12 453.00/297.12 [g(c(x, x))] = [2] x + [1] 453.00/297.12 > [1] x + [0] 453.00/297.12 = [f(x)] 453.00/297.12 453.00/297.12 [g(c(x, s(y)))] = [1] x + [1] y + [5] 453.00/297.12 > [1] x + [1] y + [1] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 [g(c(s(x), y))] = [1] x + [1] y + [5] 453.00/297.12 > [1] x + [1] y + [1] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 453.00/297.12 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 453.00/297.12 453.00/297.12 We are left with following problem, upon which TcT provides the 453.00/297.12 certificate MAYBE. 453.00/297.12 453.00/297.12 Strict Trs: 453.00/297.12 { id_inc(s(x)) -> s(id_inc(x)) 453.00/297.12 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 453.00/297.12 , id_inc(0()) -> s(0()) 453.00/297.12 , id_inc(0()) -> 0() } 453.00/297.12 Weak Trs: 453.00/297.12 { f(s(x)) -> f(id_inc(c(x, x))) 453.00/297.12 , f(c(s(x), y)) -> g(c(x, y)) 453.00/297.12 , g(c(x, x)) -> f(x) 453.00/297.12 , g(c(x, s(y))) -> g(c(y, x)) 453.00/297.12 , g(c(s(x), y)) -> g(c(y, x)) } 453.00/297.12 Obligation: 453.00/297.12 innermost runtime complexity 453.00/297.12 Answer: 453.00/297.12 MAYBE 453.00/297.12 453.00/297.12 The weightgap principle applies (using the following nonconstant 453.00/297.12 growth matrix-interpretation) 453.00/297.12 453.00/297.12 The following argument positions are usable: 453.00/297.12 Uargs(f) = {1}, Uargs(s) = {1}, Uargs(c) = {1, 2} 453.00/297.12 453.00/297.12 TcT has computed the following matrix interpretation satisfying 453.00/297.12 not(EDA) and not(IDA(1)). 453.00/297.12 453.00/297.12 [f](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [s](x1) = [1] x1 + [4] 453.00/297.12 453.00/297.12 [id_inc](x1) = [4] 453.00/297.12 453.00/297.12 [c](x1, x2) = [1] x1 + [1] x2 + [4] 453.00/297.12 453.00/297.12 [g](x1) = [1] x1 + [0] 453.00/297.12 453.00/297.12 [0] = [0] 453.00/297.12 453.00/297.12 The order satisfies the following ordering constraints: 453.00/297.12 453.00/297.12 [f(s(x))] = [1] x + [4] 453.00/297.12 >= [4] 453.00/297.12 = [f(id_inc(c(x, x)))] 453.00/297.12 453.00/297.12 [f(c(s(x), y))] = [1] x + [1] y + [8] 453.00/297.12 > [1] x + [1] y + [4] 453.00/297.12 = [g(c(x, y))] 453.00/297.12 453.00/297.12 [id_inc(s(x))] = [4] 453.00/297.12 ? [8] 453.00/297.12 = [s(id_inc(x))] 453.00/297.12 453.00/297.12 [id_inc(c(x, y))] = [4] 453.00/297.12 ? [12] 453.00/297.12 = [c(id_inc(x), id_inc(y))] 453.00/297.12 453.00/297.12 [id_inc(0())] = [4] 453.00/297.12 >= [4] 453.00/297.12 = [s(0())] 453.00/297.12 453.00/297.12 [id_inc(0())] = [4] 453.00/297.12 > [0] 453.00/297.12 = [0()] 453.00/297.12 453.00/297.12 [g(c(x, x))] = [2] x + [4] 453.00/297.12 > [1] x + [0] 453.00/297.12 = [f(x)] 453.00/297.12 453.00/297.12 [g(c(x, s(y)))] = [1] x + [1] y + [8] 453.00/297.12 > [1] x + [1] y + [4] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 [g(c(s(x), y))] = [1] x + [1] y + [8] 453.00/297.12 > [1] x + [1] y + [4] 453.00/297.12 = [g(c(y, x))] 453.00/297.12 453.00/297.12 453.00/297.12 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 453.00/297.12 453.00/297.12 We are left with following problem, upon which TcT provides the 453.00/297.12 certificate MAYBE. 453.00/297.12 453.00/297.12 Strict Trs: 453.00/297.12 { id_inc(s(x)) -> s(id_inc(x)) 453.00/297.12 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 453.00/297.12 , id_inc(0()) -> s(0()) } 453.00/297.12 Weak Trs: 453.00/297.12 { f(s(x)) -> f(id_inc(c(x, x))) 453.00/297.12 , f(c(s(x), y)) -> g(c(x, y)) 453.00/297.12 , id_inc(0()) -> 0() 453.00/297.12 , g(c(x, x)) -> f(x) 453.00/297.12 , g(c(x, s(y))) -> g(c(y, x)) 453.00/297.12 , g(c(s(x), y)) -> g(c(y, x)) } 453.00/297.12 Obligation: 453.00/297.12 innermost runtime complexity 453.00/297.12 Answer: 453.00/297.12 MAYBE 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 2) 'With Problem ...' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 2) 'Fastest' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'With Problem ...' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 2) 'With Problem ...' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 453.00/297.12 2) 'With Problem ...' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 2) 'With Problem ...' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.12 453.00/297.12 Empty strict component of the problem is NOT empty. 453.00/297.12 453.00/297.12 2) 'With Problem ...' failed due to the following reason: 453.00/297.12 453.00/297.12 None of the processors succeeded. 453.00/297.12 453.00/297.12 Details of failed attempt(s): 453.00/297.12 ----------------------------- 453.00/297.12 1) 'empty' failed due to the following reason: 453.00/297.13 453.00/297.13 Empty strict component of the problem is NOT empty. 453.00/297.13 453.00/297.13 2) 'With Problem ...' failed due to the following reason: 453.00/297.13 453.00/297.13 Empty strict component of the problem is NOT empty. 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 2) 'Best' failed due to the following reason: 453.00/297.13 453.00/297.13 None of the processors succeeded. 453.00/297.13 453.00/297.13 Details of failed attempt(s): 453.00/297.13 ----------------------------- 453.00/297.13 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 453.00/297.13 to the following reason: 453.00/297.13 453.00/297.13 The input cannot be shown compatible 453.00/297.13 453.00/297.13 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 453.00/297.13 following reason: 453.00/297.13 453.00/297.13 The input cannot be shown compatible 453.00/297.13 453.00/297.13 453.00/297.13 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 453.00/297.13 failed due to the following reason: 453.00/297.13 453.00/297.13 None of the processors succeeded. 453.00/297.13 453.00/297.13 Details of failed attempt(s): 453.00/297.13 ----------------------------- 453.00/297.13 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 453.00/297.13 failed due to the following reason: 453.00/297.13 453.00/297.13 match-boundness of the problem could not be verified. 453.00/297.13 453.00/297.13 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 453.00/297.13 failed due to the following reason: 453.00/297.13 453.00/297.13 match-boundness of the problem could not be verified. 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 453.00/297.13 Arrrr.. 453.00/297.16 EOF