MAYBE 672.39/297.02 MAYBE 672.39/297.02 672.39/297.02 We are left with following problem, upon which TcT provides the 672.39/297.02 certificate MAYBE. 672.39/297.02 672.39/297.02 Strict Trs: 672.39/297.02 { le(0(), y) -> true() 672.39/297.02 , le(s(x), 0()) -> false() 672.39/297.02 , le(s(x), s(y)) -> le(x, y) 672.39/297.02 , int(x, y) -> if(le(x, y), x, y) 672.39/297.02 , if(true(), x, y) -> cons(x, int(s(x), y)) 672.39/297.02 , if(false(), x, y) -> nil() } 672.39/297.02 Obligation: 672.39/297.02 innermost runtime complexity 672.39/297.02 Answer: 672.39/297.02 MAYBE 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'empty' failed due to the following reason: 672.39/297.02 672.39/297.02 Empty strict component of the problem is NOT empty. 672.39/297.02 672.39/297.02 2) 'Best' failed due to the following reason: 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 672.39/297.02 following reason: 672.39/297.02 672.39/297.02 Computation stopped due to timeout after 297.0 seconds. 672.39/297.02 672.39/297.02 2) 'Best' failed due to the following reason: 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 672.39/297.02 seconds)' failed due to the following reason: 672.39/297.02 672.39/297.02 The weightgap principle applies (using the following nonconstant 672.39/297.02 growth matrix-interpretation) 672.39/297.02 672.39/297.02 The following argument positions are usable: 672.39/297.02 Uargs(if) = {1}, Uargs(cons) = {2} 672.39/297.02 672.39/297.02 TcT has computed the following matrix interpretation satisfying 672.39/297.02 not(EDA) and not(IDA(1)). 672.39/297.02 672.39/297.02 [le](x1, x2) = [4] 672.39/297.02 672.39/297.02 [0] = [7] 672.39/297.02 672.39/297.02 [true] = [1] 672.39/297.02 672.39/297.02 [s](x1) = [1] x1 + [0] 672.39/297.02 672.39/297.02 [false] = [1] 672.39/297.02 672.39/297.02 [int](x1, x2) = [1] x1 + [1] x2 + [5] 672.39/297.02 672.39/297.02 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 672.39/297.02 672.39/297.02 [cons](x1, x2) = [1] x2 + [2] 672.39/297.02 672.39/297.02 [nil] = [0] 672.39/297.02 672.39/297.02 The order satisfies the following ordering constraints: 672.39/297.02 672.39/297.02 [le(0(), y)] = [4] 672.39/297.02 > [1] 672.39/297.02 = [true()] 672.39/297.02 672.39/297.02 [le(s(x), 0())] = [4] 672.39/297.02 > [1] 672.39/297.02 = [false()] 672.39/297.02 672.39/297.02 [le(s(x), s(y))] = [4] 672.39/297.02 >= [4] 672.39/297.02 = [le(x, y)] 672.39/297.02 672.39/297.02 [int(x, y)] = [1] y + [1] x + [5] 672.39/297.02 > [1] y + [1] x + [4] 672.39/297.02 = [if(le(x, y), x, y)] 672.39/297.02 672.39/297.02 [if(true(), x, y)] = [1] y + [1] x + [1] 672.39/297.02 ? [1] y + [1] x + [7] 672.39/297.02 = [cons(x, int(s(x), y))] 672.39/297.02 672.39/297.02 [if(false(), x, y)] = [1] y + [1] x + [1] 672.39/297.02 > [0] 672.39/297.02 = [nil()] 672.39/297.02 672.39/297.02 672.39/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 672.39/297.02 672.39/297.02 We are left with following problem, upon which TcT provides the 672.39/297.02 certificate MAYBE. 672.39/297.02 672.39/297.02 Strict Trs: 672.39/297.02 { le(s(x), s(y)) -> le(x, y) 672.39/297.02 , if(true(), x, y) -> cons(x, int(s(x), y)) } 672.39/297.02 Weak Trs: 672.39/297.02 { le(0(), y) -> true() 672.39/297.02 , le(s(x), 0()) -> false() 672.39/297.02 , int(x, y) -> if(le(x, y), x, y) 672.39/297.02 , if(false(), x, y) -> nil() } 672.39/297.02 Obligation: 672.39/297.02 innermost runtime complexity 672.39/297.02 Answer: 672.39/297.02 MAYBE 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'empty' failed due to the following reason: 672.39/297.02 672.39/297.02 Empty strict component of the problem is NOT empty. 672.39/297.02 672.39/297.02 2) 'With Problem ...' failed due to the following reason: 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'empty' failed due to the following reason: 672.39/297.02 672.39/297.02 Empty strict component of the problem is NOT empty. 672.39/297.02 672.39/297.02 2) 'Fastest' failed due to the following reason: 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'With Problem ...' failed due to the following reason: 672.39/297.02 672.39/297.02 None of the processors succeeded. 672.39/297.02 672.39/297.02 Details of failed attempt(s): 672.39/297.02 ----------------------------- 672.39/297.02 1) 'empty' failed due to the following reason: 672.39/297.02 672.39/297.02 Empty strict component of the problem is NOT empty. 672.39/297.02 672.39/297.02 2) 'With Problem ...' failed due to the following reason: 672.39/297.02 672.39/297.02 The weightgap principle applies (using the following nonconstant 672.39/297.02 growth matrix-interpretation) 672.39/297.02 672.39/297.02 The following argument positions are usable: 672.39/297.02 Uargs(if) = {1}, Uargs(cons) = {2} 672.39/297.02 672.39/297.02 TcT has computed the following matrix interpretation satisfying 672.39/297.02 not(EDA) and not(IDA(1)). 672.39/297.02 672.39/297.02 [le](x1, x2) = [0 0] x1 + [0] 672.39/297.02 [1 0] [1] 672.39/297.02 672.39/297.02 [0] = [3] 672.39/297.02 [0] 672.39/297.02 672.39/297.02 [true] = [0] 672.39/297.02 [4] 672.39/297.02 672.39/297.02 [s](x1) = [0] 672.39/297.02 [0] 672.39/297.02 672.39/297.02 [false] = [0] 672.39/297.02 [0] 672.39/297.02 672.39/297.02 [int](x1, x2) = [1 0] x1 + [1] 672.39/297.02 [0 0] [4] 672.39/297.02 672.39/297.02 [if](x1, x2, x3) = [1 1] x1 + [0] 672.39/297.02 [0 0] [0] 672.39/297.02 672.39/297.02 [cons](x1, x2) = [1 0] x2 + [1] 672.39/297.02 [0 0] [0] 672.39/297.02 672.39/297.02 [nil] = [0] 672.39/297.02 [0] 672.39/297.02 672.39/297.02 The order satisfies the following ordering constraints: 672.39/297.03 672.39/297.03 [le(0(), y)] = [0] 672.39/297.03 [4] 672.39/297.03 >= [0] 672.39/297.03 [4] 672.39/297.03 = [true()] 672.39/297.03 672.39/297.03 [le(s(x), 0())] = [0] 672.39/297.03 [1] 672.39/297.03 >= [0] 672.39/297.03 [0] 672.39/297.03 = [false()] 672.39/297.03 672.39/297.03 [le(s(x), s(y))] = [0] 672.39/297.03 [1] 672.39/297.03 ? [0 0] x + [0] 672.39/297.03 [1 0] [1] 672.39/297.03 = [le(x, y)] 672.39/297.03 672.39/297.03 [int(x, y)] = [1 0] x + [1] 672.39/297.03 [0 0] [4] 672.39/297.03 >= [1 0] x + [1] 672.39/297.03 [0 0] [0] 672.39/297.03 = [if(le(x, y), x, y)] 672.39/297.03 672.39/297.03 [if(true(), x, y)] = [4] 672.39/297.03 [0] 672.39/297.03 > [2] 672.39/297.03 [0] 672.39/297.03 = [cons(x, int(s(x), y))] 672.39/297.03 672.39/297.03 [if(false(), x, y)] = [0] 672.39/297.03 [0] 672.39/297.03 >= [0] 672.39/297.03 [0] 672.39/297.03 = [nil()] 672.39/297.03 672.39/297.03 672.39/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 672.39/297.03 672.39/297.03 We are left with following problem, upon which TcT provides the 672.39/297.03 certificate MAYBE. 672.39/297.03 672.39/297.03 Strict Trs: { le(s(x), s(y)) -> le(x, y) } 672.39/297.03 Weak Trs: 672.39/297.03 { le(0(), y) -> true() 672.39/297.03 , le(s(x), 0()) -> false() 672.39/297.03 , int(x, y) -> if(le(x, y), x, y) 672.39/297.03 , if(true(), x, y) -> cons(x, int(s(x), y)) 672.39/297.03 , if(false(), x, y) -> nil() } 672.39/297.03 Obligation: 672.39/297.03 innermost runtime complexity 672.39/297.03 Answer: 672.39/297.03 MAYBE 672.39/297.03 672.39/297.03 None of the processors succeeded. 672.39/297.03 672.39/297.03 Details of failed attempt(s): 672.39/297.03 ----------------------------- 672.39/297.03 1) 'empty' failed due to the following reason: 672.39/297.03 672.39/297.03 Empty strict component of the problem is NOT empty. 672.39/297.03 672.39/297.03 2) 'With Problem ...' failed due to the following reason: 672.39/297.03 672.39/297.03 None of the processors succeeded. 672.39/297.03 672.39/297.03 Details of failed attempt(s): 672.39/297.03 ----------------------------- 672.39/297.03 1) 'empty' failed due to the following reason: 672.39/297.03 672.39/297.03 Empty strict component of the problem is NOT empty. 672.39/297.03 672.39/297.03 2) 'With Problem ...' failed due to the following reason: 672.39/297.03 672.39/297.03 Empty strict component of the problem is NOT empty. 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 2) 'With Problem ...' failed due to the following reason: 672.39/297.03 672.39/297.03 None of the processors succeeded. 672.39/297.03 672.39/297.03 Details of failed attempt(s): 672.39/297.03 ----------------------------- 672.39/297.03 1) 'empty' failed due to the following reason: 672.39/297.03 672.39/297.03 Empty strict component of the problem is NOT empty. 672.39/297.03 672.39/297.03 2) 'With Problem ...' failed due to the following reason: 672.39/297.03 672.39/297.03 Empty strict component of the problem is NOT empty. 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 2) 'Best' failed due to the following reason: 672.39/297.03 672.39/297.03 None of the processors succeeded. 672.39/297.03 672.39/297.03 Details of failed attempt(s): 672.39/297.03 ----------------------------- 672.39/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 672.39/297.03 following reason: 672.39/297.03 672.39/297.03 The input cannot be shown compatible 672.39/297.03 672.39/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 672.39/297.03 to the following reason: 672.39/297.03 672.39/297.03 The input cannot be shown compatible 672.39/297.03 672.39/297.03 672.39/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 672.39/297.03 failed due to the following reason: 672.39/297.03 672.39/297.03 None of the processors succeeded. 672.39/297.03 672.39/297.03 Details of failed attempt(s): 672.39/297.03 ----------------------------- 672.39/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 672.39/297.03 failed due to the following reason: 672.39/297.03 672.39/297.03 match-boundness of the problem could not be verified. 672.39/297.03 672.39/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 672.39/297.03 failed due to the following reason: 672.39/297.03 672.39/297.03 match-boundness of the problem could not be verified. 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 672.39/297.03 Arrrr.. 672.51/297.18 EOF