MAYBE 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 None of the processors succeeded. 809.57/297.06 809.57/297.06 Details of failed attempt(s): 809.57/297.06 ----------------------------- 809.57/297.06 1) 'empty' failed due to the following reason: 809.57/297.06 809.57/297.06 Empty strict component of the problem is NOT empty. 809.57/297.06 809.57/297.06 2) 'Best' failed due to the following reason: 809.57/297.06 809.57/297.06 None of the processors succeeded. 809.57/297.06 809.57/297.06 Details of failed attempt(s): 809.57/297.06 ----------------------------- 809.57/297.06 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 809.57/297.06 following reason: 809.57/297.06 809.57/297.06 Computation stopped due to timeout after 297.0 seconds. 809.57/297.06 809.57/297.06 2) 'Best' failed due to the following reason: 809.57/297.06 809.57/297.06 None of the processors succeeded. 809.57/297.06 809.57/297.06 Details of failed attempt(s): 809.57/297.06 ----------------------------- 809.57/297.06 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 809.57/297.06 seconds)' failed due to the following reason: 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [1] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [0] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [false] = [0] 809.57/297.06 809.57/297.06 [0] = [1] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [0] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [1] 809.57/297.06 > [1] x + [0] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [1] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [1] y + [0] 809.57/297.06 >= [1] x + [1] y + [0] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 >= [1] x + [1] y + [0] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] x + [1] y + [1] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Weak Trs: { minus(x, y) -> if(gt(x, y), x, y) } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [0] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [false] = [0] 809.57/297.06 809.57/297.06 [0] = [1] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [0] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [1] x2 + [4] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [1] y + [4] 809.57/297.06 > [1] x + [1] y + [0] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 >= [1] x + [1] y + [0] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] x + [1] y + [4] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Weak Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [1] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [1] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [false] = [0] 809.57/297.06 809.57/297.06 [0] = [1] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [0] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [1] x2 + [7] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [1] 809.57/297.06 >= [1] x + [1] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [1] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [1] 809.57/297.06 > [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [1] 809.57/297.06 > [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [1] y + [7] 809.57/297.06 > [1] x + [1] y + [0] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] x + [1] y + [1] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] x + [1] y + [8] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Weak Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [4] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [0] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [false] = [0] 809.57/297.06 809.57/297.06 [0] = [1] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [1] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [4] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [4] 809.57/297.06 > [1] x + [0] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [4] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [1] 809.57/297.06 > [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [1] 809.57/297.06 > [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [4] 809.57/297.06 > [1] x + [1] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [8] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Weak Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [4] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [4] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [4] 809.57/297.06 809.57/297.06 [false] = [0] 809.57/297.06 809.57/297.06 [0] = [5] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [0] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [1] x2 + [4] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [4] 809.57/297.06 >= [1] x + [4] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [8] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [0] 809.57/297.06 ? [5] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [4] 809.57/297.06 >= [4] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [4] 809.57/297.06 > [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [4] 809.57/297.06 > [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [4] 809.57/297.06 > [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [9] 809.57/297.06 > [5] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [1] y + [4] 809.57/297.06 > [1] x + [1] y + [0] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] x + [1] y + [4] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [5] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [1] x + [1] y + [8] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [1] y + [0] 809.57/297.06 ? [5] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Weak Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [1] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [1] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [false] = [1] 809.57/297.06 809.57/297.06 [0] = [0] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [1] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [4] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [1] 809.57/297.06 >= [1] x + [1] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [1] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [1] 809.57/297.06 > [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [1] 809.57/297.06 > [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [1] 809.57/297.06 > [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [1] 809.57/297.06 >= [1] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [4] 809.57/297.06 > [1] x + [1] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [1] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [1] 809.57/297.06 > [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [5] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [1] 809.57/297.06 > [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) } 809.57/297.06 Weak Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.06 MAYBE 809.57/297.06 809.57/297.06 The weightgap principle applies (using the following nonconstant 809.57/297.06 growth matrix-interpretation) 809.57/297.06 809.57/297.06 The following argument positions are usable: 809.57/297.06 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.06 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.06 809.57/297.06 TcT has computed the following matrix interpretation satisfying 809.57/297.06 not(EDA) and not(IDA(1)). 809.57/297.06 809.57/297.06 [minus](x1, x2) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [gt](x1, x2) = [0] 809.57/297.06 809.57/297.06 [true] = [0] 809.57/297.06 809.57/297.06 [s](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [p](x1) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [false] = [0] 809.57/297.06 809.57/297.06 [0] = [0] 809.57/297.06 809.57/297.06 [ge](x1, x2) = [0] 809.57/297.06 809.57/297.06 [div](x1, x2) = [1] x1 + [0] 809.57/297.06 809.57/297.06 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [0] 809.57/297.06 809.57/297.06 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] 809.57/297.06 809.57/297.06 The order satisfies the following ordering constraints: 809.57/297.06 809.57/297.06 [minus(x, y)] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [if(gt(x, y), x, y)] 809.57/297.06 809.57/297.06 [if(true(), x, y)] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [s(minus(p(x), y))] 809.57/297.06 809.57/297.06 [if(false(), x, y)] = [1] x + [0] 809.57/297.06 >= [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [gt(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [gt(x, y)] 809.57/297.06 809.57/297.06 [gt(s(x), 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [gt(0(), y)] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [p(s(x))] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [x] 809.57/297.06 809.57/297.06 [p(0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [ge(x, 0())] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [true()] 809.57/297.06 809.57/297.06 [ge(s(x), s(y))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [ge(x, y)] 809.57/297.06 809.57/297.06 [ge(0(), s(x))] = [0] 809.57/297.06 >= [0] 809.57/297.06 = [false()] 809.57/297.06 809.57/297.06 [div(x, y)] = [1] x + [0] 809.57/297.06 >= [1] x + [0] 809.57/297.06 = [if1(ge(x, y), x, y)] 809.57/297.06 809.57/297.06 [if1(true(), x, y)] = [1] x + [0] 809.57/297.06 ? [1] x + [1] 809.57/297.06 = [if2(gt(y, 0()), x, y)] 809.57/297.06 809.57/297.06 [if1(false(), x, y)] = [1] x + [0] 809.57/297.06 >= [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 [if2(true(), x, y)] = [1] x + [1] 809.57/297.06 > [1] x + [0] 809.57/297.06 = [s(div(minus(x, y), y))] 809.57/297.06 809.57/297.06 [if2(false(), x, y)] = [1] x + [1] 809.57/297.06 > [0] 809.57/297.06 = [0()] 809.57/297.06 809.57/297.06 809.57/297.06 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.06 809.57/297.06 We are left with following problem, upon which TcT provides the 809.57/297.06 certificate MAYBE. 809.57/297.06 809.57/297.06 Strict Trs: 809.57/297.06 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.06 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.06 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.06 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) } 809.57/297.06 Weak Trs: 809.57/297.06 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.06 , if(false(), x, y) -> 0() 809.57/297.06 , gt(s(x), 0()) -> true() 809.57/297.06 , gt(0(), y) -> false() 809.57/297.06 , p(s(x)) -> x 809.57/297.06 , p(0()) -> 0() 809.57/297.06 , ge(x, 0()) -> true() 809.57/297.06 , ge(0(), s(x)) -> false() 809.57/297.06 , div(x, y) -> if1(ge(x, y), x, y) 809.57/297.06 , if1(false(), x, y) -> 0() 809.57/297.06 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.06 , if2(false(), x, y) -> 0() } 809.57/297.06 Obligation: 809.57/297.06 innermost runtime complexity 809.57/297.06 Answer: 809.57/297.07 MAYBE 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'empty' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 2) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'empty' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 2) 'Fastest' failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'empty' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 2) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 The weightgap principle applies (using the following nonconstant 809.57/297.07 growth matrix-interpretation) 809.57/297.07 809.57/297.07 The following argument positions are usable: 809.57/297.07 Uargs(minus) = {1}, Uargs(if) = {1}, Uargs(s) = {1}, 809.57/297.07 Uargs(div) = {1}, Uargs(if1) = {1}, Uargs(if2) = {1} 809.57/297.07 809.57/297.07 TcT has computed the following matrix interpretation satisfying 809.57/297.07 not(EDA) and not(IDA(1)). 809.57/297.07 809.57/297.07 [minus](x1, x2) = [1 0] x1 + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 809.57/297.07 [if](x1, x2, x3) = [1 0] x1 + [1 0] x2 + [0] 809.57/297.07 [0 0] [0 0] [0] 809.57/297.07 809.57/297.07 [gt](x1, x2) = [0] 809.57/297.07 [4] 809.57/297.07 809.57/297.07 [true] = [0] 809.57/297.07 [2] 809.57/297.07 809.57/297.07 [s](x1) = [1 0] x1 + [0] 809.57/297.07 [0 1] [2] 809.57/297.07 809.57/297.07 [p](x1) = [1 0] x1 + [0] 809.57/297.07 [0 1] [0] 809.57/297.07 809.57/297.07 [false] = [0] 809.57/297.07 [0] 809.57/297.07 809.57/297.07 [0] = [0] 809.57/297.07 [0] 809.57/297.07 809.57/297.07 [ge](x1, x2) = [0 4] x1 + [0] 809.57/297.07 [0 0] [4] 809.57/297.07 809.57/297.07 [div](x1, x2) = [1 4] x1 + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 809.57/297.07 [if1](x1, x2, x3) = [1 0] x1 + [1 0] x2 + [0] 809.57/297.07 [0 0] [0 0] [0] 809.57/297.07 809.57/297.07 [if2](x1, x2, x3) = [1 0] x1 + [1 0] x2 + [0] 809.57/297.07 [0 1] [0 0] [6] 809.57/297.07 809.57/297.07 The order satisfies the following ordering constraints: 809.57/297.07 809.57/297.07 [minus(x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 >= [1 0] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 = [if(gt(x, y), x, y)] 809.57/297.07 809.57/297.07 [if(true(), x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 ? [1 0] x + [0] 809.57/297.07 [0 0] [2] 809.57/297.07 = [s(minus(p(x), y))] 809.57/297.07 809.57/297.07 [if(false(), x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 >= [0] 809.57/297.07 [0] 809.57/297.07 = [0()] 809.57/297.07 809.57/297.07 [gt(s(x), s(y))] = [0] 809.57/297.07 [4] 809.57/297.07 >= [0] 809.57/297.07 [4] 809.57/297.07 = [gt(x, y)] 809.57/297.07 809.57/297.07 [gt(s(x), 0())] = [0] 809.57/297.07 [4] 809.57/297.07 >= [0] 809.57/297.07 [2] 809.57/297.07 = [true()] 809.57/297.07 809.57/297.07 [gt(0(), y)] = [0] 809.57/297.07 [4] 809.57/297.07 >= [0] 809.57/297.07 [0] 809.57/297.07 = [false()] 809.57/297.07 809.57/297.07 [p(s(x))] = [1 0] x + [0] 809.57/297.07 [0 1] [2] 809.57/297.07 >= [1 0] x + [0] 809.57/297.07 [0 1] [0] 809.57/297.07 = [x] 809.57/297.07 809.57/297.07 [p(0())] = [0] 809.57/297.07 [0] 809.57/297.07 >= [0] 809.57/297.07 [0] 809.57/297.07 = [0()] 809.57/297.07 809.57/297.07 [ge(x, 0())] = [0 4] x + [0] 809.57/297.07 [0 0] [4] 809.57/297.07 >= [0] 809.57/297.07 [2] 809.57/297.07 = [true()] 809.57/297.07 809.57/297.07 [ge(s(x), s(y))] = [0 4] x + [8] 809.57/297.07 [0 0] [4] 809.57/297.07 > [0 4] x + [0] 809.57/297.07 [0 0] [4] 809.57/297.07 = [ge(x, y)] 809.57/297.07 809.57/297.07 [ge(0(), s(x))] = [0] 809.57/297.07 [4] 809.57/297.07 >= [0] 809.57/297.07 [0] 809.57/297.07 = [false()] 809.57/297.07 809.57/297.07 [div(x, y)] = [1 4] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 >= [1 4] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 = [if1(ge(x, y), x, y)] 809.57/297.07 809.57/297.07 [if1(true(), x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 ? [1 0] x + [0] 809.57/297.07 [0 0] [10] 809.57/297.07 = [if2(gt(y, 0()), x, y)] 809.57/297.07 809.57/297.07 [if1(false(), x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [0] 809.57/297.07 >= [0] 809.57/297.07 [0] 809.57/297.07 = [0()] 809.57/297.07 809.57/297.07 [if2(true(), x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [8] 809.57/297.07 >= [1 0] x + [0] 809.57/297.07 [0 0] [2] 809.57/297.07 = [s(div(minus(x, y), y))] 809.57/297.07 809.57/297.07 [if2(false(), x, y)] = [1 0] x + [0] 809.57/297.07 [0 0] [6] 809.57/297.07 >= [0] 809.57/297.07 [0] 809.57/297.07 = [0()] 809.57/297.07 809.57/297.07 809.57/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 809.57/297.07 809.57/297.07 We are left with following problem, upon which TcT provides the 809.57/297.07 certificate MAYBE. 809.57/297.07 809.57/297.07 Strict Trs: 809.57/297.07 { if(true(), x, y) -> s(minus(p(x), y)) 809.57/297.07 , gt(s(x), s(y)) -> gt(x, y) 809.57/297.07 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) } 809.57/297.07 Weak Trs: 809.57/297.07 { minus(x, y) -> if(gt(x, y), x, y) 809.57/297.07 , if(false(), x, y) -> 0() 809.57/297.07 , gt(s(x), 0()) -> true() 809.57/297.07 , gt(0(), y) -> false() 809.57/297.07 , p(s(x)) -> x 809.57/297.07 , p(0()) -> 0() 809.57/297.07 , ge(x, 0()) -> true() 809.57/297.07 , ge(s(x), s(y)) -> ge(x, y) 809.57/297.07 , ge(0(), s(x)) -> false() 809.57/297.07 , div(x, y) -> if1(ge(x, y), x, y) 809.57/297.07 , if1(false(), x, y) -> 0() 809.57/297.07 , if2(true(), x, y) -> s(div(minus(x, y), y)) 809.57/297.07 , if2(false(), x, y) -> 0() } 809.57/297.07 Obligation: 809.57/297.07 innermost runtime complexity 809.57/297.07 Answer: 809.57/297.07 MAYBE 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'empty' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 2) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'empty' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 2) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 2) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'empty' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 2) 'With Problem ...' failed due to the following reason: 809.57/297.07 809.57/297.07 Empty strict component of the problem is NOT empty. 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 2) 'Best' failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 809.57/297.07 following reason: 809.57/297.07 809.57/297.07 The input cannot be shown compatible 809.57/297.07 809.57/297.07 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 809.57/297.07 to the following reason: 809.57/297.07 809.57/297.07 The input cannot be shown compatible 809.57/297.07 809.57/297.07 809.57/297.07 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 809.57/297.07 failed due to the following reason: 809.57/297.07 809.57/297.07 None of the processors succeeded. 809.57/297.07 809.57/297.07 Details of failed attempt(s): 809.57/297.07 ----------------------------- 809.57/297.07 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 809.57/297.07 failed due to the following reason: 809.57/297.07 809.57/297.07 match-boundness of the problem could not be verified. 809.57/297.07 809.57/297.07 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 809.57/297.07 failed due to the following reason: 809.57/297.07 809.57/297.07 match-boundness of the problem could not be verified. 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 809.57/297.07 Arrrr.. 809.74/297.18 EOF