MAYBE 834.61/297.03 MAYBE 834.61/297.03 834.61/297.03 We are left with following problem, upon which TcT provides the 834.61/297.03 certificate MAYBE. 834.61/297.03 834.61/297.03 Strict Trs: 834.61/297.03 { minus(x, 0()) -> x 834.61/297.03 , minus(0(), y) -> 0() 834.61/297.03 , minus(s(x), s(y)) -> minus(x, y) 834.61/297.03 , plus(0(), y) -> y 834.61/297.03 , plus(s(x), y) -> plus(x, s(y)) 834.61/297.03 , zero(0()) -> true() 834.61/297.03 , zero(s(x)) -> false() 834.61/297.03 , p(s(x)) -> x 834.61/297.03 , div(x, y) -> quot(x, y, 0()) 834.61/297.03 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.03 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) 834.61/297.03 , if(true(), x, y, z) -> p(z) } 834.61/297.03 Obligation: 834.61/297.03 innermost runtime complexity 834.61/297.03 Answer: 834.61/297.03 MAYBE 834.61/297.03 834.61/297.03 None of the processors succeeded. 834.61/297.03 834.61/297.03 Details of failed attempt(s): 834.61/297.03 ----------------------------- 834.61/297.03 1) 'empty' failed due to the following reason: 834.61/297.03 834.61/297.03 Empty strict component of the problem is NOT empty. 834.61/297.03 834.61/297.03 2) 'Best' failed due to the following reason: 834.61/297.03 834.61/297.03 None of the processors succeeded. 834.61/297.03 834.61/297.03 Details of failed attempt(s): 834.61/297.03 ----------------------------- 834.61/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 834.61/297.03 following reason: 834.61/297.03 834.61/297.03 Computation stopped due to timeout after 297.0 seconds. 834.61/297.03 834.61/297.03 2) 'Best' failed due to the following reason: 834.61/297.03 834.61/297.03 None of the processors succeeded. 834.61/297.03 834.61/297.03 Details of failed attempt(s): 834.61/297.03 ----------------------------- 834.61/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 834.61/297.03 seconds)' failed due to the following reason: 834.61/297.03 834.61/297.03 The weightgap principle applies (using the following nonconstant 834.61/297.03 growth matrix-interpretation) 834.61/297.03 834.61/297.03 The following argument positions are usable: 834.61/297.03 Uargs(quot) = {1}, Uargs(if) = {1, 4} 834.61/297.03 834.61/297.03 TcT has computed the following matrix interpretation satisfying 834.61/297.03 not(EDA) and not(IDA(1)). 834.61/297.03 834.61/297.03 [minus](x1, x2) = [1] x1 + [1] 834.61/297.03 834.61/297.03 [0] = [0] 834.61/297.03 834.61/297.03 [s](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [plus](x1, x2) = [1] x2 + [0] 834.61/297.03 834.61/297.03 [zero](x1) = [0] 834.61/297.03 834.61/297.03 [false] = [0] 834.61/297.03 834.61/297.03 [true] = [1] 834.61/297.03 834.61/297.03 [p](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [div](x1, x2) = [1] x1 + [1] x2 + [7] 834.61/297.03 834.61/297.03 [quot](x1, x2, x3) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 834.61/297.03 834.61/297.03 The order satisfies the following ordering constraints: 834.61/297.03 834.61/297.03 [minus(x, 0())] = [1] x + [1] 834.61/297.03 > [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [minus(0(), y)] = [1] 834.61/297.03 > [0] 834.61/297.03 = [0()] 834.61/297.03 834.61/297.03 [minus(s(x), s(y))] = [1] x + [1] 834.61/297.03 >= [1] x + [1] 834.61/297.03 = [minus(x, y)] 834.61/297.03 834.61/297.03 [plus(0(), y)] = [1] y + [0] 834.61/297.03 >= [1] y + [0] 834.61/297.03 = [y] 834.61/297.03 834.61/297.03 [plus(s(x), y)] = [1] y + [0] 834.61/297.03 >= [1] y + [0] 834.61/297.03 = [plus(x, s(y))] 834.61/297.03 834.61/297.03 [zero(0())] = [0] 834.61/297.03 ? [1] 834.61/297.03 = [true()] 834.61/297.03 834.61/297.03 [zero(s(x))] = [0] 834.61/297.03 >= [0] 834.61/297.03 = [false()] 834.61/297.03 834.61/297.03 [p(s(x))] = [1] x + [0] 834.61/297.03 >= [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [div(x, y)] = [1] y + [1] x + [7] 834.61/297.03 > [1] x + [0] 834.61/297.03 = [quot(x, y, 0())] 834.61/297.03 834.61/297.03 [quot(x, y, z)] = [1] x + [0] 834.61/297.03 >= [1] x + [0] 834.61/297.03 = [if(zero(x), x, y, plus(z, s(0())))] 834.61/297.03 834.61/297.03 [if(false(), x, s(y), z)] = [1] x + [1] z + [0] 834.61/297.03 ? [1] x + [1] 834.61/297.03 = [quot(minus(x, s(y)), s(y), z)] 834.61/297.03 834.61/297.03 [if(true(), x, y, z)] = [1] x + [1] z + [1] 834.61/297.03 > [1] z + [0] 834.61/297.03 = [p(z)] 834.61/297.03 834.61/297.03 834.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 834.61/297.03 834.61/297.03 We are left with following problem, upon which TcT provides the 834.61/297.03 certificate MAYBE. 834.61/297.03 834.61/297.03 Strict Trs: 834.61/297.03 { minus(s(x), s(y)) -> minus(x, y) 834.61/297.03 , plus(0(), y) -> y 834.61/297.03 , plus(s(x), y) -> plus(x, s(y)) 834.61/297.03 , zero(0()) -> true() 834.61/297.03 , zero(s(x)) -> false() 834.61/297.03 , p(s(x)) -> x 834.61/297.03 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.03 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) } 834.61/297.03 Weak Trs: 834.61/297.03 { minus(x, 0()) -> x 834.61/297.03 , minus(0(), y) -> 0() 834.61/297.03 , div(x, y) -> quot(x, y, 0()) 834.61/297.03 , if(true(), x, y, z) -> p(z) } 834.61/297.03 Obligation: 834.61/297.03 innermost runtime complexity 834.61/297.03 Answer: 834.61/297.03 MAYBE 834.61/297.03 834.61/297.03 The weightgap principle applies (using the following nonconstant 834.61/297.03 growth matrix-interpretation) 834.61/297.03 834.61/297.03 The following argument positions are usable: 834.61/297.03 Uargs(quot) = {1}, Uargs(if) = {1, 4} 834.61/297.03 834.61/297.03 TcT has computed the following matrix interpretation satisfying 834.61/297.03 not(EDA) and not(IDA(1)). 834.61/297.03 834.61/297.03 [minus](x1, x2) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [0] = [0] 834.61/297.03 834.61/297.03 [s](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [plus](x1, x2) = [1] x2 + [0] 834.61/297.03 834.61/297.03 [zero](x1) = [5] 834.61/297.03 834.61/297.03 [false] = [0] 834.61/297.03 834.61/297.03 [true] = [4] 834.61/297.03 834.61/297.03 [p](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [div](x1, x2) = [1] x1 + [1] x2 + [7] 834.61/297.03 834.61/297.03 [quot](x1, x2, x3) = [1] x1 + [1] x3 + [0] 834.61/297.03 834.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 834.61/297.03 834.61/297.03 The order satisfies the following ordering constraints: 834.61/297.03 834.61/297.03 [minus(x, 0())] = [1] x + [0] 834.61/297.03 >= [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [minus(0(), y)] = [0] 834.61/297.03 >= [0] 834.61/297.03 = [0()] 834.61/297.03 834.61/297.03 [minus(s(x), s(y))] = [1] x + [0] 834.61/297.03 >= [1] x + [0] 834.61/297.03 = [minus(x, y)] 834.61/297.03 834.61/297.03 [plus(0(), y)] = [1] y + [0] 834.61/297.03 >= [1] y + [0] 834.61/297.03 = [y] 834.61/297.03 834.61/297.03 [plus(s(x), y)] = [1] y + [0] 834.61/297.03 >= [1] y + [0] 834.61/297.03 = [plus(x, s(y))] 834.61/297.03 834.61/297.03 [zero(0())] = [5] 834.61/297.03 > [4] 834.61/297.03 = [true()] 834.61/297.03 834.61/297.03 [zero(s(x))] = [5] 834.61/297.03 > [0] 834.61/297.03 = [false()] 834.61/297.03 834.61/297.03 [p(s(x))] = [1] x + [0] 834.61/297.03 >= [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [div(x, y)] = [1] y + [1] x + [7] 834.61/297.03 > [1] x + [0] 834.61/297.03 = [quot(x, y, 0())] 834.61/297.03 834.61/297.03 [quot(x, y, z)] = [1] x + [1] z + [0] 834.61/297.03 ? [1] x + [5] 834.61/297.03 = [if(zero(x), x, y, plus(z, s(0())))] 834.61/297.03 834.61/297.03 [if(false(), x, s(y), z)] = [1] x + [1] z + [0] 834.61/297.03 >= [1] x + [1] z + [0] 834.61/297.03 = [quot(minus(x, s(y)), s(y), z)] 834.61/297.03 834.61/297.03 [if(true(), x, y, z)] = [1] x + [1] z + [4] 834.61/297.03 > [1] z + [0] 834.61/297.03 = [p(z)] 834.61/297.03 834.61/297.03 834.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 834.61/297.03 834.61/297.03 We are left with following problem, upon which TcT provides the 834.61/297.03 certificate MAYBE. 834.61/297.03 834.61/297.03 Strict Trs: 834.61/297.03 { minus(s(x), s(y)) -> minus(x, y) 834.61/297.03 , plus(0(), y) -> y 834.61/297.03 , plus(s(x), y) -> plus(x, s(y)) 834.61/297.03 , p(s(x)) -> x 834.61/297.03 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.03 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) } 834.61/297.03 Weak Trs: 834.61/297.03 { minus(x, 0()) -> x 834.61/297.03 , minus(0(), y) -> 0() 834.61/297.03 , zero(0()) -> true() 834.61/297.03 , zero(s(x)) -> false() 834.61/297.03 , div(x, y) -> quot(x, y, 0()) 834.61/297.03 , if(true(), x, y, z) -> p(z) } 834.61/297.03 Obligation: 834.61/297.03 innermost runtime complexity 834.61/297.03 Answer: 834.61/297.03 MAYBE 834.61/297.03 834.61/297.03 The weightgap principle applies (using the following nonconstant 834.61/297.03 growth matrix-interpretation) 834.61/297.03 834.61/297.03 The following argument positions are usable: 834.61/297.03 Uargs(quot) = {1}, Uargs(if) = {1, 4} 834.61/297.03 834.61/297.03 TcT has computed the following matrix interpretation satisfying 834.61/297.03 not(EDA) and not(IDA(1)). 834.61/297.03 834.61/297.03 [minus](x1, x2) = [1] x1 + [2] 834.61/297.03 834.61/297.03 [0] = [0] 834.61/297.03 834.61/297.03 [s](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [plus](x1, x2) = [1] x2 + [0] 834.61/297.03 834.61/297.03 [zero](x1) = [4] 834.61/297.03 834.61/297.03 [false] = [0] 834.61/297.03 834.61/297.03 [true] = [4] 834.61/297.03 834.61/297.03 [p](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [div](x1, x2) = [1] x1 + [1] x2 + [7] 834.61/297.03 834.61/297.03 [quot](x1, x2, x3) = [1] x1 + [1] x3 + [6] 834.61/297.03 834.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 834.61/297.03 834.61/297.03 The order satisfies the following ordering constraints: 834.61/297.03 834.61/297.03 [minus(x, 0())] = [1] x + [2] 834.61/297.03 > [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [minus(0(), y)] = [2] 834.61/297.03 > [0] 834.61/297.03 = [0()] 834.61/297.03 834.61/297.03 [minus(s(x), s(y))] = [1] x + [2] 834.61/297.03 >= [1] x + [2] 834.61/297.03 = [minus(x, y)] 834.61/297.03 834.61/297.03 [plus(0(), y)] = [1] y + [0] 834.61/297.03 >= [1] y + [0] 834.61/297.03 = [y] 834.61/297.03 834.61/297.03 [plus(s(x), y)] = [1] y + [0] 834.61/297.03 >= [1] y + [0] 834.61/297.03 = [plus(x, s(y))] 834.61/297.03 834.61/297.03 [zero(0())] = [4] 834.61/297.03 >= [4] 834.61/297.03 = [true()] 834.61/297.03 834.61/297.03 [zero(s(x))] = [4] 834.61/297.03 > [0] 834.61/297.03 = [false()] 834.61/297.03 834.61/297.03 [p(s(x))] = [1] x + [0] 834.61/297.03 >= [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [div(x, y)] = [1] y + [1] x + [7] 834.61/297.03 > [1] x + [6] 834.61/297.03 = [quot(x, y, 0())] 834.61/297.03 834.61/297.03 [quot(x, y, z)] = [1] x + [1] z + [6] 834.61/297.03 > [1] x + [4] 834.61/297.03 = [if(zero(x), x, y, plus(z, s(0())))] 834.61/297.03 834.61/297.03 [if(false(), x, s(y), z)] = [1] x + [1] z + [0] 834.61/297.03 ? [1] x + [1] z + [8] 834.61/297.03 = [quot(minus(x, s(y)), s(y), z)] 834.61/297.03 834.61/297.03 [if(true(), x, y, z)] = [1] x + [1] z + [4] 834.61/297.03 > [1] z + [0] 834.61/297.03 = [p(z)] 834.61/297.03 834.61/297.03 834.61/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 834.61/297.03 834.61/297.03 We are left with following problem, upon which TcT provides the 834.61/297.03 certificate MAYBE. 834.61/297.03 834.61/297.03 Strict Trs: 834.61/297.03 { minus(s(x), s(y)) -> minus(x, y) 834.61/297.03 , plus(0(), y) -> y 834.61/297.03 , plus(s(x), y) -> plus(x, s(y)) 834.61/297.03 , p(s(x)) -> x 834.61/297.03 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) } 834.61/297.03 Weak Trs: 834.61/297.03 { minus(x, 0()) -> x 834.61/297.03 , minus(0(), y) -> 0() 834.61/297.03 , zero(0()) -> true() 834.61/297.03 , zero(s(x)) -> false() 834.61/297.03 , div(x, y) -> quot(x, y, 0()) 834.61/297.03 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.03 , if(true(), x, y, z) -> p(z) } 834.61/297.03 Obligation: 834.61/297.03 innermost runtime complexity 834.61/297.03 Answer: 834.61/297.03 MAYBE 834.61/297.03 834.61/297.03 The weightgap principle applies (using the following nonconstant 834.61/297.03 growth matrix-interpretation) 834.61/297.03 834.61/297.03 The following argument positions are usable: 834.61/297.03 Uargs(quot) = {1}, Uargs(if) = {1, 4} 834.61/297.03 834.61/297.03 TcT has computed the following matrix interpretation satisfying 834.61/297.03 not(EDA) and not(IDA(1)). 834.61/297.03 834.61/297.03 [minus](x1, x2) = [1] x1 + [2] 834.61/297.03 834.61/297.03 [0] = [1] 834.61/297.03 834.61/297.03 [s](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [plus](x1, x2) = [1] x1 + [1] x2 + [0] 834.61/297.03 834.61/297.03 [zero](x1) = [4] 834.61/297.03 834.61/297.03 [false] = [0] 834.61/297.03 834.61/297.03 [true] = [4] 834.61/297.03 834.61/297.03 [p](x1) = [1] x1 + [0] 834.61/297.03 834.61/297.03 [div](x1, x2) = [1] x1 + [1] x2 + [7] 834.61/297.03 834.61/297.03 [quot](x1, x2, x3) = [1] x1 + [1] x3 + [6] 834.61/297.03 834.61/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 834.61/297.03 834.61/297.03 The order satisfies the following ordering constraints: 834.61/297.03 834.61/297.03 [minus(x, 0())] = [1] x + [2] 834.61/297.03 > [1] x + [0] 834.61/297.03 = [x] 834.61/297.03 834.61/297.03 [minus(0(), y)] = [3] 834.61/297.03 > [1] 834.61/297.03 = [0()] 834.61/297.03 834.61/297.03 [minus(s(x), s(y))] = [1] x + [2] 834.61/297.03 >= [1] x + [2] 834.61/297.03 = [minus(x, y)] 834.61/297.03 834.61/297.03 [plus(0(), y)] = [1] y + [1] 834.61/297.03 > [1] y + [0] 834.61/297.03 = [y] 834.61/297.03 834.61/297.03 [plus(s(x), y)] = [1] y + [1] x + [0] 834.61/297.03 >= [1] y + [1] x + [0] 834.61/297.03 = [plus(x, s(y))] 834.61/297.03 834.61/297.03 [zero(0())] = [4] 834.61/297.03 >= [4] 834.61/297.03 = [true()] 834.61/297.03 834.61/297.03 [zero(s(x))] = [4] 834.61/297.03 > [0] 834.61/297.04 = [false()] 834.61/297.04 834.61/297.04 [p(s(x))] = [1] x + [0] 834.61/297.04 >= [1] x + [0] 834.61/297.04 = [x] 834.61/297.04 834.61/297.04 [div(x, y)] = [1] y + [1] x + [7] 834.61/297.04 >= [1] x + [7] 834.61/297.04 = [quot(x, y, 0())] 834.61/297.04 834.61/297.04 [quot(x, y, z)] = [1] x + [1] z + [6] 834.61/297.04 > [1] x + [1] z + [5] 834.61/297.04 = [if(zero(x), x, y, plus(z, s(0())))] 834.61/297.04 834.61/297.04 [if(false(), x, s(y), z)] = [1] x + [1] z + [0] 834.61/297.04 ? [1] x + [1] z + [8] 834.61/297.04 = [quot(minus(x, s(y)), s(y), z)] 834.61/297.04 834.61/297.04 [if(true(), x, y, z)] = [1] x + [1] z + [4] 834.61/297.04 > [1] z + [0] 834.61/297.04 = [p(z)] 834.61/297.04 834.61/297.04 834.61/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 834.61/297.04 834.61/297.04 We are left with following problem, upon which TcT provides the 834.61/297.04 certificate MAYBE. 834.61/297.04 834.61/297.04 Strict Trs: 834.61/297.04 { minus(s(x), s(y)) -> minus(x, y) 834.61/297.04 , plus(s(x), y) -> plus(x, s(y)) 834.61/297.04 , p(s(x)) -> x 834.61/297.04 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) } 834.61/297.04 Weak Trs: 834.61/297.04 { minus(x, 0()) -> x 834.61/297.04 , minus(0(), y) -> 0() 834.61/297.04 , plus(0(), y) -> y 834.61/297.04 , zero(0()) -> true() 834.61/297.04 , zero(s(x)) -> false() 834.61/297.04 , div(x, y) -> quot(x, y, 0()) 834.61/297.04 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.04 , if(true(), x, y, z) -> p(z) } 834.61/297.04 Obligation: 834.61/297.04 innermost runtime complexity 834.61/297.04 Answer: 834.61/297.04 MAYBE 834.61/297.04 834.61/297.04 The weightgap principle applies (using the following nonconstant 834.61/297.04 growth matrix-interpretation) 834.61/297.04 834.61/297.04 The following argument positions are usable: 834.61/297.04 Uargs(quot) = {1}, Uargs(if) = {1, 4} 834.61/297.04 834.61/297.04 TcT has computed the following matrix interpretation satisfying 834.61/297.04 not(EDA) and not(IDA(1)). 834.61/297.04 834.61/297.04 [minus](x1, x2) = [1] x1 + [4] 834.61/297.04 834.61/297.04 [0] = [0] 834.61/297.04 834.61/297.04 [s](x1) = [1] x1 + [0] 834.61/297.04 834.61/297.04 [plus](x1, x2) = [1] x2 + [0] 834.61/297.04 834.61/297.04 [zero](x1) = [1] 834.61/297.04 834.61/297.04 [false] = [0] 834.61/297.04 834.61/297.04 [true] = [1] 834.61/297.04 834.61/297.04 [p](x1) = [1] x1 + [1] 834.61/297.04 834.61/297.04 [div](x1, x2) = [1] x1 + [1] x2 + [7] 834.61/297.04 834.61/297.04 [quot](x1, x2, x3) = [1] x1 + [1] x3 + [4] 834.61/297.04 834.61/297.04 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 834.61/297.04 834.61/297.04 The order satisfies the following ordering constraints: 834.61/297.04 834.61/297.04 [minus(x, 0())] = [1] x + [4] 834.61/297.04 > [1] x + [0] 834.61/297.04 = [x] 834.61/297.04 834.61/297.04 [minus(0(), y)] = [4] 834.61/297.04 > [0] 834.61/297.04 = [0()] 834.61/297.04 834.61/297.04 [minus(s(x), s(y))] = [1] x + [4] 834.61/297.04 >= [1] x + [4] 834.61/297.04 = [minus(x, y)] 834.61/297.04 834.61/297.04 [plus(0(), y)] = [1] y + [0] 834.61/297.04 >= [1] y + [0] 834.61/297.04 = [y] 834.61/297.04 834.61/297.04 [plus(s(x), y)] = [1] y + [0] 834.61/297.04 >= [1] y + [0] 834.61/297.04 = [plus(x, s(y))] 834.61/297.04 834.61/297.04 [zero(0())] = [1] 834.61/297.04 >= [1] 834.61/297.04 = [true()] 834.61/297.04 834.61/297.04 [zero(s(x))] = [1] 834.61/297.04 > [0] 834.61/297.04 = [false()] 834.61/297.04 834.61/297.04 [p(s(x))] = [1] x + [1] 834.61/297.04 > [1] x + [0] 834.61/297.04 = [x] 834.61/297.04 834.61/297.04 [div(x, y)] = [1] y + [1] x + [7] 834.61/297.04 > [1] x + [4] 834.61/297.04 = [quot(x, y, 0())] 834.61/297.04 834.61/297.04 [quot(x, y, z)] = [1] x + [1] z + [4] 834.61/297.04 > [1] x + [1] 834.61/297.04 = [if(zero(x), x, y, plus(z, s(0())))] 834.61/297.04 834.61/297.04 [if(false(), x, s(y), z)] = [1] x + [1] z + [0] 834.61/297.04 ? [1] x + [1] z + [8] 834.61/297.04 = [quot(minus(x, s(y)), s(y), z)] 834.61/297.04 834.61/297.04 [if(true(), x, y, z)] = [1] x + [1] z + [1] 834.61/297.04 >= [1] z + [1] 834.61/297.04 = [p(z)] 834.61/297.04 834.61/297.04 834.61/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 834.61/297.04 834.61/297.04 We are left with following problem, upon which TcT provides the 834.61/297.04 certificate MAYBE. 834.61/297.04 834.61/297.04 Strict Trs: 834.61/297.04 { minus(s(x), s(y)) -> minus(x, y) 834.61/297.04 , plus(s(x), y) -> plus(x, s(y)) 834.61/297.04 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) } 834.61/297.04 Weak Trs: 834.61/297.04 { minus(x, 0()) -> x 834.61/297.04 , minus(0(), y) -> 0() 834.61/297.04 , plus(0(), y) -> y 834.61/297.04 , zero(0()) -> true() 834.61/297.04 , zero(s(x)) -> false() 834.61/297.04 , p(s(x)) -> x 834.61/297.04 , div(x, y) -> quot(x, y, 0()) 834.61/297.04 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.04 , if(true(), x, y, z) -> p(z) } 834.61/297.04 Obligation: 834.61/297.04 innermost runtime complexity 834.61/297.04 Answer: 834.61/297.04 MAYBE 834.61/297.04 834.61/297.04 The weightgap principle applies (using the following nonconstant 834.61/297.04 growth matrix-interpretation) 834.61/297.04 834.61/297.04 The following argument positions are usable: 834.61/297.04 Uargs(quot) = {1}, Uargs(if) = {1, 4} 834.61/297.04 834.61/297.04 TcT has computed the following matrix interpretation satisfying 834.61/297.04 not(EDA) and not(IDA(1)). 834.61/297.04 834.61/297.04 [minus](x1, x2) = [1] x1 + [4] 834.61/297.04 834.61/297.04 [0] = [0] 834.61/297.04 834.61/297.04 [s](x1) = [1] x1 + [4] 834.61/297.04 834.61/297.04 [plus](x1, x2) = [1] x2 + [0] 834.61/297.04 834.61/297.04 [zero](x1) = [0] 834.61/297.04 834.61/297.04 [false] = [0] 834.61/297.04 834.61/297.04 [true] = [0] 834.61/297.04 834.61/297.04 [p](x1) = [1] x1 + [0] 834.61/297.04 834.61/297.04 [div](x1, x2) = [1] x1 + [1] x2 + [7] 834.61/297.04 834.61/297.04 [quot](x1, x2, x3) = [1] x1 + [1] x3 + [4] 834.61/297.04 834.61/297.04 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x4 + [0] 834.61/297.04 834.61/297.04 The order satisfies the following ordering constraints: 834.61/297.04 834.61/297.04 [minus(x, 0())] = [1] x + [4] 834.61/297.04 > [1] x + [0] 834.61/297.04 = [x] 834.61/297.04 834.61/297.04 [minus(0(), y)] = [4] 834.61/297.04 > [0] 834.61/297.04 = [0()] 834.61/297.04 834.61/297.04 [minus(s(x), s(y))] = [1] x + [8] 834.61/297.04 > [1] x + [4] 834.61/297.04 = [minus(x, y)] 834.61/297.04 834.61/297.04 [plus(0(), y)] = [1] y + [0] 834.61/297.04 >= [1] y + [0] 834.61/297.04 = [y] 834.61/297.04 834.61/297.04 [plus(s(x), y)] = [1] y + [0] 834.61/297.04 ? [1] y + [4] 834.61/297.04 = [plus(x, s(y))] 834.61/297.04 834.61/297.04 [zero(0())] = [0] 834.61/297.04 >= [0] 834.61/297.04 = [true()] 834.61/297.04 834.61/297.04 [zero(s(x))] = [0] 834.61/297.04 >= [0] 834.61/297.04 = [false()] 834.61/297.04 834.61/297.04 [p(s(x))] = [1] x + [4] 834.61/297.04 > [1] x + [0] 834.61/297.04 = [x] 834.61/297.04 834.61/297.04 [div(x, y)] = [1] y + [1] x + [7] 834.61/297.04 > [1] x + [4] 834.61/297.04 = [quot(x, y, 0())] 834.61/297.04 834.61/297.04 [quot(x, y, z)] = [1] x + [1] z + [4] 834.61/297.04 >= [1] x + [4] 834.61/297.04 = [if(zero(x), x, y, plus(z, s(0())))] 834.61/297.04 834.61/297.04 [if(false(), x, s(y), z)] = [1] x + [1] z + [0] 834.61/297.04 ? [1] x + [1] z + [8] 834.61/297.04 = [quot(minus(x, s(y)), s(y), z)] 834.61/297.04 834.61/297.04 [if(true(), x, y, z)] = [1] x + [1] z + [0] 834.61/297.04 >= [1] z + [0] 834.61/297.04 = [p(z)] 834.61/297.04 834.61/297.04 834.61/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 834.61/297.04 834.61/297.04 We are left with following problem, upon which TcT provides the 834.61/297.04 certificate MAYBE. 834.61/297.04 834.61/297.04 Strict Trs: 834.61/297.04 { plus(s(x), y) -> plus(x, s(y)) 834.61/297.04 , if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z) } 834.61/297.04 Weak Trs: 834.61/297.04 { minus(x, 0()) -> x 834.61/297.04 , minus(0(), y) -> 0() 834.61/297.04 , minus(s(x), s(y)) -> minus(x, y) 834.61/297.04 , plus(0(), y) -> y 834.61/297.04 , zero(0()) -> true() 834.61/297.04 , zero(s(x)) -> false() 834.61/297.04 , p(s(x)) -> x 834.61/297.04 , div(x, y) -> quot(x, y, 0()) 834.61/297.04 , quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))) 834.61/297.04 , if(true(), x, y, z) -> p(z) } 834.61/297.04 Obligation: 834.61/297.04 innermost runtime complexity 834.61/297.04 Answer: 834.61/297.04 MAYBE 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'empty' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 2) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'empty' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 2) 'Fastest' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'empty' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 2) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 834.61/297.04 2) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'empty' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 2) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'empty' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 2) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'empty' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 2) 'With Problem ...' failed due to the following reason: 834.61/297.04 834.61/297.04 Empty strict component of the problem is NOT empty. 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 2) 'Best' failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 834.61/297.04 to the following reason: 834.61/297.04 834.61/297.04 The input cannot be shown compatible 834.61/297.04 834.61/297.04 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 834.61/297.04 following reason: 834.61/297.04 834.61/297.04 The input cannot be shown compatible 834.61/297.04 834.61/297.04 834.61/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 834.61/297.04 failed due to the following reason: 834.61/297.04 834.61/297.04 None of the processors succeeded. 834.61/297.04 834.61/297.04 Details of failed attempt(s): 834.61/297.04 ----------------------------- 834.61/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 834.61/297.04 failed due to the following reason: 834.61/297.04 834.61/297.04 match-boundness of the problem could not be verified. 834.61/297.04 834.61/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 834.61/297.04 failed due to the following reason: 834.61/297.04 834.61/297.04 match-boundness of the problem could not be verified. 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 834.61/297.04 Arrrr.. 834.74/297.18 EOF