MAYBE 786.61/297.02 MAYBE 786.61/297.02 786.61/297.02 We are left with following problem, upon which TcT provides the 786.61/297.02 certificate MAYBE. 786.61/297.02 786.61/297.02 Strict Trs: 786.61/297.02 { lt(x, 0()) -> false() 786.61/297.02 , lt(0(), s(y)) -> true() 786.61/297.02 , lt(s(x), s(y)) -> lt(x, y) 786.61/297.02 , plus(x, 0()) -> x 786.61/297.02 , plus(x, s(y)) -> s(plus(x, y)) 786.61/297.02 , quot(x, s(y)) -> help(x, s(y), 0()) 786.61/297.02 , help(x, s(y), c) -> if(lt(c, x), x, s(y), c) 786.61/297.02 , if(false(), x, s(y), c) -> 0() 786.61/297.02 , if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } 786.61/297.02 Obligation: 786.61/297.02 innermost runtime complexity 786.61/297.02 Answer: 786.61/297.02 MAYBE 786.61/297.02 786.61/297.02 None of the processors succeeded. 786.61/297.02 786.61/297.02 Details of failed attempt(s): 786.61/297.02 ----------------------------- 786.61/297.02 1) 'empty' failed due to the following reason: 786.61/297.02 786.61/297.02 Empty strict component of the problem is NOT empty. 786.61/297.02 786.61/297.02 2) 'Best' failed due to the following reason: 786.61/297.02 786.61/297.02 None of the processors succeeded. 786.61/297.02 786.61/297.02 Details of failed attempt(s): 786.61/297.02 ----------------------------- 786.61/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 786.61/297.02 following reason: 786.61/297.02 786.61/297.02 Computation stopped due to timeout after 297.0 seconds. 786.61/297.02 786.61/297.02 2) 'Best' failed due to the following reason: 786.61/297.02 786.61/297.02 None of the processors succeeded. 786.61/297.02 786.61/297.02 Details of failed attempt(s): 786.61/297.02 ----------------------------- 786.61/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 786.61/297.02 seconds)' failed due to the following reason: 786.61/297.02 786.61/297.02 The weightgap principle applies (using the following nonconstant 786.61/297.02 growth matrix-interpretation) 786.61/297.02 786.61/297.02 The following argument positions are usable: 786.61/297.02 Uargs(s) = {1}, Uargs(help) = {3}, Uargs(if) = {1} 786.61/297.02 786.61/297.02 TcT has computed the following matrix interpretation satisfying 786.61/297.02 not(EDA) and not(IDA(1)). 786.61/297.02 786.61/297.02 [lt](x1, x2) = [1] 786.61/297.02 786.61/297.02 [0] = [0] 786.61/297.02 786.61/297.02 [false] = [0] 786.61/297.02 786.61/297.03 [s](x1) = [1] x1 + [0] 786.61/297.03 786.61/297.03 [true] = [0] 786.61/297.03 786.61/297.03 [plus](x1, x2) = [1] x1 + [0] 786.61/297.03 786.61/297.03 [quot](x1, x2) = [1] x1 + [1] x2 + [3] 786.61/297.03 786.61/297.03 [help](x1, x2, x3) = [1] x1 + [1] x3 + [0] 786.61/297.03 786.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 786.61/297.03 786.61/297.03 The order satisfies the following ordering constraints: 786.61/297.03 786.61/297.03 [lt(x, 0())] = [1] 786.61/297.03 > [0] 786.61/297.03 = [false()] 786.61/297.03 786.61/297.03 [lt(0(), s(y))] = [1] 786.61/297.03 > [0] 786.61/297.03 = [true()] 786.61/297.03 786.61/297.03 [lt(s(x), s(y))] = [1] 786.61/297.03 >= [1] 786.61/297.03 = [lt(x, y)] 786.61/297.03 786.61/297.03 [plus(x, 0())] = [1] x + [0] 786.61/297.03 >= [1] x + [0] 786.61/297.03 = [x] 786.61/297.03 786.61/297.03 [plus(x, s(y))] = [1] x + [0] 786.61/297.03 >= [1] x + [0] 786.61/297.03 = [s(plus(x, y))] 786.61/297.03 786.61/297.03 [quot(x, s(y))] = [1] x + [1] y + [3] 786.61/297.03 > [1] x + [0] 786.61/297.03 = [help(x, s(y), 0())] 786.61/297.03 786.61/297.03 [help(x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 ? [1] x + [1] c + [1] 786.61/297.03 = [if(lt(c, x), x, s(y), c)] 786.61/297.03 786.61/297.03 [if(false(), x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 >= [0] 786.61/297.03 = [0()] 786.61/297.03 786.61/297.03 [if(true(), x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 >= [1] x + [1] c + [0] 786.61/297.03 = [s(help(x, s(y), plus(c, s(y))))] 786.61/297.03 786.61/297.03 786.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 786.61/297.03 786.61/297.03 We are left with following problem, upon which TcT provides the 786.61/297.03 certificate MAYBE. 786.61/297.03 786.61/297.03 Strict Trs: 786.61/297.03 { lt(s(x), s(y)) -> lt(x, y) 786.61/297.03 , plus(x, 0()) -> x 786.61/297.03 , plus(x, s(y)) -> s(plus(x, y)) 786.61/297.03 , help(x, s(y), c) -> if(lt(c, x), x, s(y), c) 786.61/297.03 , if(false(), x, s(y), c) -> 0() 786.61/297.03 , if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } 786.61/297.03 Weak Trs: 786.61/297.03 { lt(x, 0()) -> false() 786.61/297.03 , lt(0(), s(y)) -> true() 786.61/297.03 , quot(x, s(y)) -> help(x, s(y), 0()) } 786.61/297.03 Obligation: 786.61/297.03 innermost runtime complexity 786.61/297.03 Answer: 786.61/297.03 MAYBE 786.61/297.03 786.61/297.03 The weightgap principle applies (using the following nonconstant 786.61/297.03 growth matrix-interpretation) 786.61/297.03 786.61/297.03 The following argument positions are usable: 786.61/297.03 Uargs(s) = {1}, Uargs(help) = {3}, Uargs(if) = {1} 786.61/297.03 786.61/297.03 TcT has computed the following matrix interpretation satisfying 786.61/297.03 not(EDA) and not(IDA(1)). 786.61/297.03 786.61/297.03 [lt](x1, x2) = [4] 786.61/297.03 786.61/297.03 [0] = [0] 786.61/297.03 786.61/297.03 [false] = [1] 786.61/297.03 786.61/297.03 [s](x1) = [1] x1 + [0] 786.61/297.03 786.61/297.03 [true] = [0] 786.61/297.03 786.61/297.03 [plus](x1, x2) = [1] x1 + [0] 786.61/297.03 786.61/297.03 [quot](x1, x2) = [1] x1 + [1] x2 + [7] 786.61/297.03 786.61/297.03 [help](x1, x2, x3) = [1] x1 + [1] x3 + [0] 786.61/297.03 786.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 786.61/297.03 786.61/297.03 The order satisfies the following ordering constraints: 786.61/297.03 786.61/297.03 [lt(x, 0())] = [4] 786.61/297.03 > [1] 786.61/297.03 = [false()] 786.61/297.03 786.61/297.03 [lt(0(), s(y))] = [4] 786.61/297.03 > [0] 786.61/297.03 = [true()] 786.61/297.03 786.61/297.03 [lt(s(x), s(y))] = [4] 786.61/297.03 >= [4] 786.61/297.03 = [lt(x, y)] 786.61/297.03 786.61/297.03 [plus(x, 0())] = [1] x + [0] 786.61/297.03 >= [1] x + [0] 786.61/297.03 = [x] 786.61/297.03 786.61/297.03 [plus(x, s(y))] = [1] x + [0] 786.61/297.03 >= [1] x + [0] 786.61/297.03 = [s(plus(x, y))] 786.61/297.03 786.61/297.03 [quot(x, s(y))] = [1] x + [1] y + [7] 786.61/297.03 > [1] x + [0] 786.61/297.03 = [help(x, s(y), 0())] 786.61/297.03 786.61/297.03 [help(x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 ? [1] x + [1] c + [4] 786.61/297.03 = [if(lt(c, x), x, s(y), c)] 786.61/297.03 786.61/297.03 [if(false(), x, s(y), c)] = [1] x + [1] c + [1] 786.61/297.03 > [0] 786.61/297.03 = [0()] 786.61/297.03 786.61/297.03 [if(true(), x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 >= [1] x + [1] c + [0] 786.61/297.03 = [s(help(x, s(y), plus(c, s(y))))] 786.61/297.03 786.61/297.03 786.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 786.61/297.03 786.61/297.03 We are left with following problem, upon which TcT provides the 786.61/297.03 certificate MAYBE. 786.61/297.03 786.61/297.03 Strict Trs: 786.61/297.03 { lt(s(x), s(y)) -> lt(x, y) 786.61/297.03 , plus(x, 0()) -> x 786.61/297.03 , plus(x, s(y)) -> s(plus(x, y)) 786.61/297.03 , help(x, s(y), c) -> if(lt(c, x), x, s(y), c) 786.61/297.03 , if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } 786.61/297.03 Weak Trs: 786.61/297.03 { lt(x, 0()) -> false() 786.61/297.03 , lt(0(), s(y)) -> true() 786.61/297.03 , quot(x, s(y)) -> help(x, s(y), 0()) 786.61/297.03 , if(false(), x, s(y), c) -> 0() } 786.61/297.03 Obligation: 786.61/297.03 innermost runtime complexity 786.61/297.03 Answer: 786.61/297.03 MAYBE 786.61/297.03 786.61/297.03 The weightgap principle applies (using the following nonconstant 786.61/297.03 growth matrix-interpretation) 786.61/297.03 786.61/297.03 The following argument positions are usable: 786.61/297.03 Uargs(s) = {1}, Uargs(help) = {3}, Uargs(if) = {1} 786.61/297.03 786.61/297.03 TcT has computed the following matrix interpretation satisfying 786.61/297.03 not(EDA) and not(IDA(1)). 786.61/297.03 786.61/297.03 [lt](x1, x2) = [1] 786.61/297.03 786.61/297.03 [0] = [0] 786.61/297.03 786.61/297.03 [false] = [0] 786.61/297.03 786.61/297.03 [s](x1) = [1] x1 + [0] 786.61/297.03 786.61/297.03 [true] = [1] 786.61/297.03 786.61/297.03 [plus](x1, x2) = [1] x1 + [0] 786.61/297.03 786.61/297.03 [quot](x1, x2) = [1] x1 + [1] x2 + [7] 786.61/297.03 786.61/297.03 [help](x1, x2, x3) = [1] x1 + [1] x3 + [0] 786.61/297.03 786.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 786.61/297.03 786.61/297.03 The order satisfies the following ordering constraints: 786.61/297.03 786.61/297.03 [lt(x, 0())] = [1] 786.61/297.03 > [0] 786.61/297.03 = [false()] 786.61/297.03 786.61/297.03 [lt(0(), s(y))] = [1] 786.61/297.03 >= [1] 786.61/297.03 = [true()] 786.61/297.03 786.61/297.03 [lt(s(x), s(y))] = [1] 786.61/297.03 >= [1] 786.61/297.03 = [lt(x, y)] 786.61/297.03 786.61/297.03 [plus(x, 0())] = [1] x + [0] 786.61/297.03 >= [1] x + [0] 786.61/297.03 = [x] 786.61/297.03 786.61/297.03 [plus(x, s(y))] = [1] x + [0] 786.61/297.03 >= [1] x + [0] 786.61/297.03 = [s(plus(x, y))] 786.61/297.03 786.61/297.03 [quot(x, s(y))] = [1] x + [1] y + [7] 786.61/297.03 > [1] x + [0] 786.61/297.03 = [help(x, s(y), 0())] 786.61/297.03 786.61/297.03 [help(x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 ? [1] x + [1] c + [1] 786.61/297.03 = [if(lt(c, x), x, s(y), c)] 786.61/297.03 786.61/297.03 [if(false(), x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 >= [0] 786.61/297.03 = [0()] 786.61/297.03 786.61/297.03 [if(true(), x, s(y), c)] = [1] x + [1] c + [1] 786.61/297.03 > [1] x + [1] c + [0] 786.61/297.03 = [s(help(x, s(y), plus(c, s(y))))] 786.61/297.03 786.61/297.03 786.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 786.61/297.03 786.61/297.03 We are left with following problem, upon which TcT provides the 786.61/297.03 certificate MAYBE. 786.61/297.03 786.61/297.03 Strict Trs: 786.61/297.03 { lt(s(x), s(y)) -> lt(x, y) 786.61/297.03 , plus(x, 0()) -> x 786.61/297.03 , plus(x, s(y)) -> s(plus(x, y)) 786.61/297.03 , help(x, s(y), c) -> if(lt(c, x), x, s(y), c) } 786.61/297.03 Weak Trs: 786.61/297.03 { lt(x, 0()) -> false() 786.61/297.03 , lt(0(), s(y)) -> true() 786.61/297.03 , quot(x, s(y)) -> help(x, s(y), 0()) 786.61/297.03 , if(false(), x, s(y), c) -> 0() 786.61/297.03 , if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } 786.61/297.03 Obligation: 786.61/297.03 innermost runtime complexity 786.61/297.03 Answer: 786.61/297.03 MAYBE 786.61/297.03 786.61/297.03 The weightgap principle applies (using the following nonconstant 786.61/297.03 growth matrix-interpretation) 786.61/297.03 786.61/297.03 The following argument positions are usable: 786.61/297.03 Uargs(s) = {1}, Uargs(help) = {3}, Uargs(if) = {1} 786.61/297.03 786.61/297.03 TcT has computed the following matrix interpretation satisfying 786.61/297.03 not(EDA) and not(IDA(1)). 786.61/297.03 786.61/297.03 [lt](x1, x2) = [1] 786.61/297.03 786.61/297.03 [0] = [0] 786.61/297.03 786.61/297.03 [false] = [0] 786.61/297.03 786.61/297.03 [s](x1) = [1] x1 + [4] 786.61/297.03 786.61/297.03 [true] = [1] 786.61/297.03 786.61/297.03 [plus](x1, x2) = [1] x1 + [4] 786.61/297.03 786.61/297.03 [quot](x1, x2) = [1] x1 + [7] 786.61/297.03 786.61/297.03 [help](x1, x2, x3) = [1] x1 + [1] x3 + [0] 786.61/297.03 786.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [7] 786.61/297.03 786.61/297.03 The order satisfies the following ordering constraints: 786.61/297.03 786.61/297.03 [lt(x, 0())] = [1] 786.61/297.03 > [0] 786.61/297.03 = [false()] 786.61/297.03 786.61/297.03 [lt(0(), s(y))] = [1] 786.61/297.03 >= [1] 786.61/297.03 = [true()] 786.61/297.03 786.61/297.03 [lt(s(x), s(y))] = [1] 786.61/297.03 >= [1] 786.61/297.03 = [lt(x, y)] 786.61/297.03 786.61/297.03 [plus(x, 0())] = [1] x + [4] 786.61/297.03 > [1] x + [0] 786.61/297.03 = [x] 786.61/297.03 786.61/297.03 [plus(x, s(y))] = [1] x + [4] 786.61/297.03 ? [1] x + [8] 786.61/297.03 = [s(plus(x, y))] 786.61/297.03 786.61/297.03 [quot(x, s(y))] = [1] x + [7] 786.61/297.03 > [1] x + [0] 786.61/297.03 = [help(x, s(y), 0())] 786.61/297.03 786.61/297.03 [help(x, s(y), c)] = [1] x + [1] c + [0] 786.61/297.03 ? [1] x + [1] c + [8] 786.61/297.03 = [if(lt(c, x), x, s(y), c)] 786.61/297.03 786.61/297.03 [if(false(), x, s(y), c)] = [1] x + [1] c + [7] 786.61/297.03 > [0] 786.61/297.03 = [0()] 786.61/297.03 786.61/297.03 [if(true(), x, s(y), c)] = [1] x + [1] c + [8] 786.61/297.03 >= [1] x + [1] c + [8] 786.61/297.03 = [s(help(x, s(y), plus(c, s(y))))] 786.61/297.03 786.61/297.03 786.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 786.61/297.03 786.61/297.03 We are left with following problem, upon which TcT provides the 786.61/297.03 certificate MAYBE. 786.61/297.03 786.61/297.03 Strict Trs: 786.61/297.03 { lt(s(x), s(y)) -> lt(x, y) 786.61/297.03 , plus(x, s(y)) -> s(plus(x, y)) 786.61/297.03 , help(x, s(y), c) -> if(lt(c, x), x, s(y), c) } 786.61/297.03 Weak Trs: 786.61/297.03 { lt(x, 0()) -> false() 786.61/297.03 , lt(0(), s(y)) -> true() 786.61/297.03 , plus(x, 0()) -> x 786.61/297.03 , quot(x, s(y)) -> help(x, s(y), 0()) 786.61/297.03 , if(false(), x, s(y), c) -> 0() 786.61/297.03 , if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } 786.61/297.03 Obligation: 786.61/297.03 innermost runtime complexity 786.61/297.03 Answer: 786.61/297.03 MAYBE 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'empty' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 2) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'empty' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 2) 'Fastest' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'empty' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 2) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 786.61/297.03 2) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'empty' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 2) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'empty' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 2) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'empty' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 2) 'With Problem ...' failed due to the following reason: 786.61/297.03 786.61/297.03 Empty strict component of the problem is NOT empty. 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 2) 'Best' failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 786.61/297.03 to the following reason: 786.61/297.03 786.61/297.03 The input cannot be shown compatible 786.61/297.03 786.61/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 786.61/297.03 following reason: 786.61/297.03 786.61/297.03 The input cannot be shown compatible 786.61/297.03 786.61/297.03 786.61/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 786.61/297.03 failed due to the following reason: 786.61/297.03 786.61/297.03 None of the processors succeeded. 786.61/297.03 786.61/297.03 Details of failed attempt(s): 786.61/297.03 ----------------------------- 786.61/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 786.61/297.03 failed due to the following reason: 786.61/297.03 786.61/297.03 match-boundness of the problem could not be verified. 786.61/297.03 786.61/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 786.61/297.03 failed due to the following reason: 786.61/297.03 786.61/297.03 match-boundness of the problem could not be verified. 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 786.61/297.03 Arrrr.. 786.73/297.16 EOF