MAYBE 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 We are left with following problem, upon which TcT provides the 671.63/297.03 certificate MAYBE. 671.63/297.03 671.63/297.03 Strict Trs: 671.63/297.03 { p(p(s(x))) -> p(x) 671.63/297.03 , p(0()) -> s(s(0())) 671.63/297.03 , p(s(x)) -> x 671.63/297.03 , le(p(s(x)), x) -> le(x, x) 671.63/297.03 , le(0(), y) -> true() 671.63/297.03 , le(s(x), 0()) -> false() 671.63/297.03 , le(s(x), s(y)) -> le(x, y) 671.63/297.03 , minus(x, y) -> if(le(x, y), x, y) 671.63/297.03 , if(true(), x, y) -> 0() 671.63/297.03 , if(false(), x, y) -> s(minus(p(x), y)) } 671.63/297.03 Obligation: 671.63/297.03 innermost runtime complexity 671.63/297.03 Answer: 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 Arguments of following rules are not normal-forms: 671.63/297.03 671.63/297.03 { p(p(s(x))) -> p(x) 671.63/297.03 , le(p(s(x)), x) -> le(x, x) } 671.63/297.03 671.63/297.03 All above mentioned rules can be savely removed. 671.63/297.03 671.63/297.03 We are left with following problem, upon which TcT provides the 671.63/297.03 certificate MAYBE. 671.63/297.03 671.63/297.03 Strict Trs: 671.63/297.03 { p(0()) -> s(s(0())) 671.63/297.03 , p(s(x)) -> x 671.63/297.03 , le(0(), y) -> true() 671.63/297.03 , le(s(x), 0()) -> false() 671.63/297.03 , le(s(x), s(y)) -> le(x, y) 671.63/297.03 , minus(x, y) -> if(le(x, y), x, y) 671.63/297.03 , if(true(), x, y) -> 0() 671.63/297.03 , if(false(), x, y) -> s(minus(p(x), y)) } 671.63/297.03 Obligation: 671.63/297.03 innermost runtime complexity 671.63/297.03 Answer: 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'Best' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 671.63/297.03 following reason: 671.63/297.03 671.63/297.03 Computation stopped due to timeout after 297.0 seconds. 671.63/297.03 671.63/297.03 2) 'Best' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 671.63/297.03 seconds)' failed due to the following reason: 671.63/297.03 671.63/297.03 The weightgap principle applies (using the following nonconstant 671.63/297.03 growth matrix-interpretation) 671.63/297.03 671.63/297.03 The following argument positions are usable: 671.63/297.03 Uargs(s) = {1}, Uargs(minus) = {1}, Uargs(if) = {1} 671.63/297.03 671.63/297.03 TcT has computed the following matrix interpretation satisfying 671.63/297.03 not(EDA) and not(IDA(1)). 671.63/297.03 671.63/297.03 [p](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [0] = [0] 671.63/297.03 671.63/297.03 [s](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [le](x1, x2) = [1] 671.63/297.03 671.63/297.03 [true] = [0] 671.63/297.03 671.63/297.03 [false] = [1] 671.63/297.03 671.63/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [0] 671.63/297.03 671.63/297.03 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 671.63/297.03 671.63/297.03 The order satisfies the following ordering constraints: 671.63/297.03 671.63/297.03 [p(0())] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [s(s(0()))] 671.63/297.03 671.63/297.03 [p(s(x))] = [1] x + [0] 671.63/297.03 >= [1] x + [0] 671.63/297.03 = [x] 671.63/297.03 671.63/297.03 [le(0(), y)] = [1] 671.63/297.03 > [0] 671.63/297.03 = [true()] 671.63/297.03 671.63/297.03 [le(s(x), 0())] = [1] 671.63/297.03 >= [1] 671.63/297.03 = [false()] 671.63/297.03 671.63/297.03 [le(s(x), s(y))] = [1] 671.63/297.03 >= [1] 671.63/297.03 = [le(x, y)] 671.63/297.03 671.63/297.03 [minus(x, y)] = [1] x + [1] y + [0] 671.63/297.03 ? [1] x + [1] y + [1] 671.63/297.03 = [if(le(x, y), x, y)] 671.63/297.03 671.63/297.03 [if(true(), x, y)] = [1] x + [1] y + [0] 671.63/297.03 >= [0] 671.63/297.03 = [0()] 671.63/297.03 671.63/297.03 [if(false(), x, y)] = [1] x + [1] y + [1] 671.63/297.03 > [1] x + [1] y + [0] 671.63/297.03 = [s(minus(p(x), y))] 671.63/297.03 671.63/297.03 671.63/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 671.63/297.03 671.63/297.03 We are left with following problem, upon which TcT provides the 671.63/297.03 certificate MAYBE. 671.63/297.03 671.63/297.03 Strict Trs: 671.63/297.03 { p(0()) -> s(s(0())) 671.63/297.03 , p(s(x)) -> x 671.63/297.03 , le(s(x), 0()) -> false() 671.63/297.03 , le(s(x), s(y)) -> le(x, y) 671.63/297.03 , minus(x, y) -> if(le(x, y), x, y) 671.63/297.03 , if(true(), x, y) -> 0() } 671.63/297.03 Weak Trs: 671.63/297.03 { le(0(), y) -> true() 671.63/297.03 , if(false(), x, y) -> s(minus(p(x), y)) } 671.63/297.03 Obligation: 671.63/297.03 innermost runtime complexity 671.63/297.03 Answer: 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 The weightgap principle applies (using the following nonconstant 671.63/297.03 growth matrix-interpretation) 671.63/297.03 671.63/297.03 The following argument positions are usable: 671.63/297.03 Uargs(s) = {1}, Uargs(minus) = {1}, Uargs(if) = {1} 671.63/297.03 671.63/297.03 TcT has computed the following matrix interpretation satisfying 671.63/297.03 not(EDA) and not(IDA(1)). 671.63/297.03 671.63/297.03 [p](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [0] = [0] 671.63/297.03 671.63/297.03 [s](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [le](x1, x2) = [0] 671.63/297.03 671.63/297.03 [true] = [0] 671.63/297.03 671.63/297.03 [false] = [4] 671.63/297.03 671.63/297.03 [minus](x1, x2) = [1] x1 + [1] 671.63/297.03 671.63/297.03 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 671.63/297.03 671.63/297.03 The order satisfies the following ordering constraints: 671.63/297.03 671.63/297.03 [p(0())] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [s(s(0()))] 671.63/297.03 671.63/297.03 [p(s(x))] = [1] x + [0] 671.63/297.03 >= [1] x + [0] 671.63/297.03 = [x] 671.63/297.03 671.63/297.03 [le(0(), y)] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [true()] 671.63/297.03 671.63/297.03 [le(s(x), 0())] = [0] 671.63/297.03 ? [4] 671.63/297.03 = [false()] 671.63/297.03 671.63/297.03 [le(s(x), s(y))] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [le(x, y)] 671.63/297.03 671.63/297.03 [minus(x, y)] = [1] x + [1] 671.63/297.03 > [1] x + [0] 671.63/297.03 = [if(le(x, y), x, y)] 671.63/297.03 671.63/297.03 [if(true(), x, y)] = [1] x + [0] 671.63/297.03 >= [0] 671.63/297.03 = [0()] 671.63/297.03 671.63/297.03 [if(false(), x, y)] = [1] x + [4] 671.63/297.03 > [1] x + [1] 671.63/297.03 = [s(minus(p(x), y))] 671.63/297.03 671.63/297.03 671.63/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 671.63/297.03 671.63/297.03 We are left with following problem, upon which TcT provides the 671.63/297.03 certificate MAYBE. 671.63/297.03 671.63/297.03 Strict Trs: 671.63/297.03 { p(0()) -> s(s(0())) 671.63/297.03 , p(s(x)) -> x 671.63/297.03 , le(s(x), 0()) -> false() 671.63/297.03 , le(s(x), s(y)) -> le(x, y) 671.63/297.03 , if(true(), x, y) -> 0() } 671.63/297.03 Weak Trs: 671.63/297.03 { le(0(), y) -> true() 671.63/297.03 , minus(x, y) -> if(le(x, y), x, y) 671.63/297.03 , if(false(), x, y) -> s(minus(p(x), y)) } 671.63/297.03 Obligation: 671.63/297.03 innermost runtime complexity 671.63/297.03 Answer: 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 The weightgap principle applies (using the following nonconstant 671.63/297.03 growth matrix-interpretation) 671.63/297.03 671.63/297.03 The following argument positions are usable: 671.63/297.03 Uargs(s) = {1}, Uargs(minus) = {1}, Uargs(if) = {1} 671.63/297.03 671.63/297.03 TcT has computed the following matrix interpretation satisfying 671.63/297.03 not(EDA) and not(IDA(1)). 671.63/297.03 671.63/297.03 [p](x1) = [1] x1 + [1] 671.63/297.03 671.63/297.03 [0] = [0] 671.63/297.03 671.63/297.03 [s](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [le](x1, x2) = [0] 671.63/297.03 671.63/297.03 [true] = [0] 671.63/297.03 671.63/297.03 [false] = [5] 671.63/297.03 671.63/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [4] 671.63/297.03 671.63/297.03 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 671.63/297.03 671.63/297.03 The order satisfies the following ordering constraints: 671.63/297.03 671.63/297.03 [p(0())] = [1] 671.63/297.03 > [0] 671.63/297.03 = [s(s(0()))] 671.63/297.03 671.63/297.03 [p(s(x))] = [1] x + [1] 671.63/297.03 > [1] x + [0] 671.63/297.03 = [x] 671.63/297.03 671.63/297.03 [le(0(), y)] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [true()] 671.63/297.03 671.63/297.03 [le(s(x), 0())] = [0] 671.63/297.03 ? [5] 671.63/297.03 = [false()] 671.63/297.03 671.63/297.03 [le(s(x), s(y))] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [le(x, y)] 671.63/297.03 671.63/297.03 [minus(x, y)] = [1] x + [1] y + [4] 671.63/297.03 > [1] x + [1] y + [0] 671.63/297.03 = [if(le(x, y), x, y)] 671.63/297.03 671.63/297.03 [if(true(), x, y)] = [1] x + [1] y + [0] 671.63/297.03 >= [0] 671.63/297.03 = [0()] 671.63/297.03 671.63/297.03 [if(false(), x, y)] = [1] x + [1] y + [5] 671.63/297.03 >= [1] x + [1] y + [5] 671.63/297.03 = [s(minus(p(x), y))] 671.63/297.03 671.63/297.03 671.63/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 671.63/297.03 671.63/297.03 We are left with following problem, upon which TcT provides the 671.63/297.03 certificate MAYBE. 671.63/297.03 671.63/297.03 Strict Trs: 671.63/297.03 { le(s(x), 0()) -> false() 671.63/297.03 , le(s(x), s(y)) -> le(x, y) 671.63/297.03 , if(true(), x, y) -> 0() } 671.63/297.03 Weak Trs: 671.63/297.03 { p(0()) -> s(s(0())) 671.63/297.03 , p(s(x)) -> x 671.63/297.03 , le(0(), y) -> true() 671.63/297.03 , minus(x, y) -> if(le(x, y), x, y) 671.63/297.03 , if(false(), x, y) -> s(minus(p(x), y)) } 671.63/297.03 Obligation: 671.63/297.03 innermost runtime complexity 671.63/297.03 Answer: 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 The weightgap principle applies (using the following nonconstant 671.63/297.03 growth matrix-interpretation) 671.63/297.03 671.63/297.03 The following argument positions are usable: 671.63/297.03 Uargs(s) = {1}, Uargs(minus) = {1}, Uargs(if) = {1} 671.63/297.03 671.63/297.03 TcT has computed the following matrix interpretation satisfying 671.63/297.03 not(EDA) and not(IDA(1)). 671.63/297.03 671.63/297.03 [p](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [0] = [0] 671.63/297.03 671.63/297.03 [s](x1) = [1] x1 + [0] 671.63/297.03 671.63/297.03 [le](x1, x2) = [1] 671.63/297.03 671.63/297.03 [true] = [1] 671.63/297.03 671.63/297.03 [false] = [1] 671.63/297.03 671.63/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [1] 671.63/297.03 671.63/297.03 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 671.63/297.03 671.63/297.03 The order satisfies the following ordering constraints: 671.63/297.03 671.63/297.03 [p(0())] = [0] 671.63/297.03 >= [0] 671.63/297.03 = [s(s(0()))] 671.63/297.03 671.63/297.03 [p(s(x))] = [1] x + [0] 671.63/297.03 >= [1] x + [0] 671.63/297.03 = [x] 671.63/297.03 671.63/297.03 [le(0(), y)] = [1] 671.63/297.03 >= [1] 671.63/297.03 = [true()] 671.63/297.03 671.63/297.03 [le(s(x), 0())] = [1] 671.63/297.03 >= [1] 671.63/297.03 = [false()] 671.63/297.03 671.63/297.03 [le(s(x), s(y))] = [1] 671.63/297.03 >= [1] 671.63/297.03 = [le(x, y)] 671.63/297.03 671.63/297.03 [minus(x, y)] = [1] x + [1] y + [1] 671.63/297.03 >= [1] x + [1] y + [1] 671.63/297.03 = [if(le(x, y), x, y)] 671.63/297.03 671.63/297.03 [if(true(), x, y)] = [1] x + [1] y + [1] 671.63/297.03 > [0] 671.63/297.03 = [0()] 671.63/297.03 671.63/297.03 [if(false(), x, y)] = [1] x + [1] y + [1] 671.63/297.03 >= [1] x + [1] y + [1] 671.63/297.03 = [s(minus(p(x), y))] 671.63/297.03 671.63/297.03 671.63/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 671.63/297.03 671.63/297.03 We are left with following problem, upon which TcT provides the 671.63/297.03 certificate MAYBE. 671.63/297.03 671.63/297.03 Strict Trs: 671.63/297.03 { le(s(x), 0()) -> false() 671.63/297.03 , le(s(x), s(y)) -> le(x, y) } 671.63/297.03 Weak Trs: 671.63/297.03 { p(0()) -> s(s(0())) 671.63/297.03 , p(s(x)) -> x 671.63/297.03 , le(0(), y) -> true() 671.63/297.03 , minus(x, y) -> if(le(x, y), x, y) 671.63/297.03 , if(true(), x, y) -> 0() 671.63/297.03 , if(false(), x, y) -> s(minus(p(x), y)) } 671.63/297.03 Obligation: 671.63/297.03 innermost runtime complexity 671.63/297.03 Answer: 671.63/297.03 MAYBE 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'Fastest' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 2) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'empty' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 2) 'With Problem ...' failed due to the following reason: 671.63/297.03 671.63/297.03 Empty strict component of the problem is NOT empty. 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 2) 'Best' failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 671.63/297.03 following reason: 671.63/297.03 671.63/297.03 The input cannot be shown compatible 671.63/297.03 671.63/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 671.63/297.03 to the following reason: 671.63/297.03 671.63/297.03 The input cannot be shown compatible 671.63/297.03 671.63/297.03 671.63/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 671.63/297.03 failed due to the following reason: 671.63/297.03 671.63/297.03 None of the processors succeeded. 671.63/297.03 671.63/297.03 Details of failed attempt(s): 671.63/297.03 ----------------------------- 671.63/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 671.63/297.03 failed due to the following reason: 671.63/297.03 671.63/297.03 match-boundness of the problem could not be verified. 671.63/297.03 671.63/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 671.63/297.03 failed due to the following reason: 671.63/297.03 671.63/297.03 match-boundness of the problem could not be verified. 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 671.63/297.03 Arrrr.. 671.75/297.19 EOF