MAYBE 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 We are left with following problem, upon which TcT provides the 821.30/297.04 certificate MAYBE. 821.30/297.04 821.30/297.04 Strict Trs: 821.30/297.04 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.04 , if(true(), x, y) -> s(minus(x, y)) 821.30/297.04 , if(false(), x, y) -> 0() 821.30/297.04 , gt(s(x), s(y)) -> gt(x, y) 821.30/297.04 , gt(s(x), 0()) -> true() 821.30/297.04 , gt(0(), y) -> false() 821.30/297.04 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.04 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.04 , if1(false(), x, y) -> gcd(y, x) 821.30/297.04 , ge(x, 0()) -> true() 821.30/297.04 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.04 , ge(0(), s(x)) -> false() 821.30/297.04 , if2(true(), x, y) -> gcd(minus(x, y), y) 821.30/297.04 , if2(false(), x, y) -> x } 821.30/297.04 Obligation: 821.30/297.04 innermost runtime complexity 821.30/297.04 Answer: 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 None of the processors succeeded. 821.30/297.04 821.30/297.04 Details of failed attempt(s): 821.30/297.04 ----------------------------- 821.30/297.04 1) 'empty' failed due to the following reason: 821.30/297.04 821.30/297.04 Empty strict component of the problem is NOT empty. 821.30/297.04 821.30/297.04 2) 'Best' failed due to the following reason: 821.30/297.04 821.30/297.04 None of the processors succeeded. 821.30/297.04 821.30/297.04 Details of failed attempt(s): 821.30/297.04 ----------------------------- 821.30/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 821.30/297.04 following reason: 821.30/297.04 821.30/297.04 Computation stopped due to timeout after 297.0 seconds. 821.30/297.04 821.30/297.04 2) 'Best' failed due to the following reason: 821.30/297.04 821.30/297.04 None of the processors succeeded. 821.30/297.04 821.30/297.04 Details of failed attempt(s): 821.30/297.04 ----------------------------- 821.30/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 821.30/297.04 seconds)' failed due to the following reason: 821.30/297.04 821.30/297.04 The weightgap principle applies (using the following nonconstant 821.30/297.04 growth matrix-interpretation) 821.30/297.04 821.30/297.04 The following argument positions are usable: 821.30/297.04 Uargs(s) = {1}, Uargs(if) = {1}, Uargs(gcd) = {1}, 821.30/297.04 Uargs(if1) = {1}, Uargs(if2) = {1} 821.30/297.04 821.30/297.04 TcT has computed the following matrix interpretation satisfying 821.30/297.04 not(EDA) and not(IDA(1)). 821.30/297.04 821.30/297.04 [minus](x1, x2) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [s](x1) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [gt](x1, x2) = [0] 821.30/297.04 821.30/297.04 [true] = [4] 821.30/297.04 821.30/297.04 [false] = [0] 821.30/297.04 821.30/297.04 [0] = [7] 821.30/297.04 821.30/297.04 [gcd](x1, x2) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 [ge](x1, x2) = [0] 821.30/297.04 821.30/297.04 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 The order satisfies the following ordering constraints: 821.30/297.04 821.30/297.04 [minus(s(x), y)] = [1] x + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [if(gt(s(x), y), x, y)] 821.30/297.04 821.30/297.04 [if(true(), x, y)] = [1] x + [4] 821.30/297.04 > [1] x + [0] 821.30/297.04 = [s(minus(x, y))] 821.30/297.04 821.30/297.04 [if(false(), x, y)] = [1] x + [0] 821.30/297.04 ? [7] 821.30/297.04 = [0()] 821.30/297.04 821.30/297.04 [gt(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [gt(x, y)] 821.30/297.04 821.30/297.04 [gt(s(x), 0())] = [0] 821.30/297.04 ? [4] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [gt(0(), y)] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [gcd(x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [if1(ge(x, y), x, y)] 821.30/297.04 821.30/297.04 [if1(true(), x, y)] = [1] x + [1] y + [4] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [if2(gt(y, 0()), x, y)] 821.30/297.04 821.30/297.04 [if1(false(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [gcd(y, x)] 821.30/297.04 821.30/297.04 [ge(x, 0())] = [0] 821.30/297.04 ? [4] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [ge(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [ge(x, y)] 821.30/297.04 821.30/297.04 [ge(0(), s(x))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [if2(true(), x, y)] = [1] x + [1] y + [4] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [gcd(minus(x, y), y)] 821.30/297.04 821.30/297.04 [if2(false(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [x] 821.30/297.04 821.30/297.04 821.30/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 821.30/297.04 821.30/297.04 We are left with following problem, upon which TcT provides the 821.30/297.04 certificate MAYBE. 821.30/297.04 821.30/297.04 Strict Trs: 821.30/297.04 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.04 , if(false(), x, y) -> 0() 821.30/297.04 , gt(s(x), s(y)) -> gt(x, y) 821.30/297.04 , gt(s(x), 0()) -> true() 821.30/297.04 , gt(0(), y) -> false() 821.30/297.04 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.04 , if1(false(), x, y) -> gcd(y, x) 821.30/297.04 , ge(x, 0()) -> true() 821.30/297.04 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.04 , ge(0(), s(x)) -> false() 821.30/297.04 , if2(false(), x, y) -> x } 821.30/297.04 Weak Trs: 821.30/297.04 { if(true(), x, y) -> s(minus(x, y)) 821.30/297.04 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.04 , if2(true(), x, y) -> gcd(minus(x, y), y) } 821.30/297.04 Obligation: 821.30/297.04 innermost runtime complexity 821.30/297.04 Answer: 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 The weightgap principle applies (using the following nonconstant 821.30/297.04 growth matrix-interpretation) 821.30/297.04 821.30/297.04 The following argument positions are usable: 821.30/297.04 Uargs(s) = {1}, Uargs(if) = {1}, Uargs(gcd) = {1}, 821.30/297.04 Uargs(if1) = {1}, Uargs(if2) = {1} 821.30/297.04 821.30/297.04 TcT has computed the following matrix interpretation satisfying 821.30/297.04 not(EDA) and not(IDA(1)). 821.30/297.04 821.30/297.04 [minus](x1, x2) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [s](x1) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [gt](x1, x2) = [0] 821.30/297.04 821.30/297.04 [true] = [0] 821.30/297.04 821.30/297.04 [false] = [1] 821.30/297.04 821.30/297.04 [0] = [0] 821.30/297.04 821.30/297.04 [gcd](x1, x2) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 [ge](x1, x2) = [0] 821.30/297.04 821.30/297.04 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 The order satisfies the following ordering constraints: 821.30/297.04 821.30/297.04 [minus(s(x), y)] = [1] x + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [if(gt(s(x), y), x, y)] 821.30/297.04 821.30/297.04 [if(true(), x, y)] = [1] x + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [s(minus(x, y))] 821.30/297.04 821.30/297.04 [if(false(), x, y)] = [1] x + [1] 821.30/297.04 > [0] 821.30/297.04 = [0()] 821.30/297.04 821.30/297.04 [gt(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [gt(x, y)] 821.30/297.04 821.30/297.04 [gt(s(x), 0())] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [gt(0(), y)] = [0] 821.30/297.04 ? [1] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [gcd(x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [if1(ge(x, y), x, y)] 821.30/297.04 821.30/297.04 [if1(true(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [if2(gt(y, 0()), x, y)] 821.30/297.04 821.30/297.04 [if1(false(), x, y)] = [1] x + [1] y + [1] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [gcd(y, x)] 821.30/297.04 821.30/297.04 [ge(x, 0())] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [ge(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [ge(x, y)] 821.30/297.04 821.30/297.04 [ge(0(), s(x))] = [0] 821.30/297.04 ? [1] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [if2(true(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [gcd(minus(x, y), y)] 821.30/297.04 821.30/297.04 [if2(false(), x, y)] = [1] x + [1] y + [1] 821.30/297.04 > [1] x + [0] 821.30/297.04 = [x] 821.30/297.04 821.30/297.04 821.30/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 821.30/297.04 821.30/297.04 We are left with following problem, upon which TcT provides the 821.30/297.04 certificate MAYBE. 821.30/297.04 821.30/297.04 Strict Trs: 821.30/297.04 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.04 , gt(s(x), s(y)) -> gt(x, y) 821.30/297.04 , gt(s(x), 0()) -> true() 821.30/297.04 , gt(0(), y) -> false() 821.30/297.04 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.04 , ge(x, 0()) -> true() 821.30/297.04 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.04 , ge(0(), s(x)) -> false() } 821.30/297.04 Weak Trs: 821.30/297.04 { if(true(), x, y) -> s(minus(x, y)) 821.30/297.04 , if(false(), x, y) -> 0() 821.30/297.04 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.04 , if1(false(), x, y) -> gcd(y, x) 821.30/297.04 , if2(true(), x, y) -> gcd(minus(x, y), y) 821.30/297.04 , if2(false(), x, y) -> x } 821.30/297.04 Obligation: 821.30/297.04 innermost runtime complexity 821.30/297.04 Answer: 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 The weightgap principle applies (using the following nonconstant 821.30/297.04 growth matrix-interpretation) 821.30/297.04 821.30/297.04 The following argument positions are usable: 821.30/297.04 Uargs(s) = {1}, Uargs(if) = {1}, Uargs(gcd) = {1}, 821.30/297.04 Uargs(if1) = {1}, Uargs(if2) = {1} 821.30/297.04 821.30/297.04 TcT has computed the following matrix interpretation satisfying 821.30/297.04 not(EDA) and not(IDA(1)). 821.30/297.04 821.30/297.04 [minus](x1, x2) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [s](x1) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [gt](x1, x2) = [0] 821.30/297.04 821.30/297.04 [true] = [4] 821.30/297.04 821.30/297.04 [false] = [4] 821.30/297.04 821.30/297.04 [0] = [4] 821.30/297.04 821.30/297.04 [gcd](x1, x2) = [1] x1 + [1] x2 + [1] 821.30/297.04 821.30/297.04 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 [ge](x1, x2) = [0] 821.30/297.04 821.30/297.04 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 The order satisfies the following ordering constraints: 821.30/297.04 821.30/297.04 [minus(s(x), y)] = [1] x + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [if(gt(s(x), y), x, y)] 821.30/297.04 821.30/297.04 [if(true(), x, y)] = [1] x + [4] 821.30/297.04 > [1] x + [0] 821.30/297.04 = [s(minus(x, y))] 821.30/297.04 821.30/297.04 [if(false(), x, y)] = [1] x + [4] 821.30/297.04 >= [4] 821.30/297.04 = [0()] 821.30/297.04 821.30/297.04 [gt(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [gt(x, y)] 821.30/297.04 821.30/297.04 [gt(s(x), 0())] = [0] 821.30/297.04 ? [4] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [gt(0(), y)] = [0] 821.30/297.04 ? [4] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [gcd(x, y)] = [1] x + [1] y + [1] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [if1(ge(x, y), x, y)] 821.30/297.04 821.30/297.04 [if1(true(), x, y)] = [1] x + [1] y + [4] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [if2(gt(y, 0()), x, y)] 821.30/297.04 821.30/297.04 [if1(false(), x, y)] = [1] x + [1] y + [4] 821.30/297.04 > [1] x + [1] y + [1] 821.30/297.04 = [gcd(y, x)] 821.30/297.04 821.30/297.04 [ge(x, 0())] = [0] 821.30/297.04 ? [4] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [ge(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [ge(x, y)] 821.30/297.04 821.30/297.04 [ge(0(), s(x))] = [0] 821.30/297.04 ? [4] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [if2(true(), x, y)] = [1] x + [1] y + [4] 821.30/297.04 > [1] x + [1] y + [1] 821.30/297.04 = [gcd(minus(x, y), y)] 821.30/297.04 821.30/297.04 [if2(false(), x, y)] = [1] x + [1] y + [4] 821.30/297.04 > [1] x + [0] 821.30/297.04 = [x] 821.30/297.04 821.30/297.04 821.30/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 821.30/297.04 821.30/297.04 We are left with following problem, upon which TcT provides the 821.30/297.04 certificate MAYBE. 821.30/297.04 821.30/297.04 Strict Trs: 821.30/297.04 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.04 , gt(s(x), s(y)) -> gt(x, y) 821.30/297.04 , gt(s(x), 0()) -> true() 821.30/297.04 , gt(0(), y) -> false() 821.30/297.04 , ge(x, 0()) -> true() 821.30/297.04 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.04 , ge(0(), s(x)) -> false() } 821.30/297.04 Weak Trs: 821.30/297.04 { if(true(), x, y) -> s(minus(x, y)) 821.30/297.04 , if(false(), x, y) -> 0() 821.30/297.04 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.04 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.04 , if1(false(), x, y) -> gcd(y, x) 821.30/297.04 , if2(true(), x, y) -> gcd(minus(x, y), y) 821.30/297.04 , if2(false(), x, y) -> x } 821.30/297.04 Obligation: 821.30/297.04 innermost runtime complexity 821.30/297.04 Answer: 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 The weightgap principle applies (using the following nonconstant 821.30/297.04 growth matrix-interpretation) 821.30/297.04 821.30/297.04 The following argument positions are usable: 821.30/297.04 Uargs(s) = {1}, Uargs(if) = {1}, Uargs(gcd) = {1}, 821.30/297.04 Uargs(if1) = {1}, Uargs(if2) = {1} 821.30/297.04 821.30/297.04 TcT has computed the following matrix interpretation satisfying 821.30/297.04 not(EDA) and not(IDA(1)). 821.30/297.04 821.30/297.04 [minus](x1, x2) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [s](x1) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [gt](x1, x2) = [1] 821.30/297.04 821.30/297.04 [true] = [1] 821.30/297.04 821.30/297.04 [false] = [0] 821.30/297.04 821.30/297.04 [0] = [0] 821.30/297.04 821.30/297.04 [gcd](x1, x2) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 [ge](x1, x2) = [0] 821.30/297.04 821.30/297.04 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 The order satisfies the following ordering constraints: 821.30/297.04 821.30/297.04 [minus(s(x), y)] = [1] x + [0] 821.30/297.04 ? [1] x + [1] 821.30/297.04 = [if(gt(s(x), y), x, y)] 821.30/297.04 821.30/297.04 [if(true(), x, y)] = [1] x + [1] 821.30/297.04 > [1] x + [0] 821.30/297.04 = [s(minus(x, y))] 821.30/297.04 821.30/297.04 [if(false(), x, y)] = [1] x + [0] 821.30/297.04 >= [0] 821.30/297.04 = [0()] 821.30/297.04 821.30/297.04 [gt(s(x), s(y))] = [1] 821.30/297.04 >= [1] 821.30/297.04 = [gt(x, y)] 821.30/297.04 821.30/297.04 [gt(s(x), 0())] = [1] 821.30/297.04 >= [1] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [gt(0(), y)] = [1] 821.30/297.04 > [0] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [gcd(x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [if1(ge(x, y), x, y)] 821.30/297.04 821.30/297.04 [if1(true(), x, y)] = [1] x + [1] y + [1] 821.30/297.04 >= [1] x + [1] y + [1] 821.30/297.04 = [if2(gt(y, 0()), x, y)] 821.30/297.04 821.30/297.04 [if1(false(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [gcd(y, x)] 821.30/297.04 821.30/297.04 [ge(x, 0())] = [0] 821.30/297.04 ? [1] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [ge(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [ge(x, y)] 821.30/297.04 821.30/297.04 [ge(0(), s(x))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [if2(true(), x, y)] = [1] x + [1] y + [1] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [gcd(minus(x, y), y)] 821.30/297.04 821.30/297.04 [if2(false(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [x] 821.30/297.04 821.30/297.04 821.30/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 821.30/297.04 821.30/297.04 We are left with following problem, upon which TcT provides the 821.30/297.04 certificate MAYBE. 821.30/297.04 821.30/297.04 Strict Trs: 821.30/297.04 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.04 , gt(s(x), s(y)) -> gt(x, y) 821.30/297.04 , gt(s(x), 0()) -> true() 821.30/297.04 , ge(x, 0()) -> true() 821.30/297.04 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.04 , ge(0(), s(x)) -> false() } 821.30/297.04 Weak Trs: 821.30/297.04 { if(true(), x, y) -> s(minus(x, y)) 821.30/297.04 , if(false(), x, y) -> 0() 821.30/297.04 , gt(0(), y) -> false() 821.30/297.04 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.04 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.04 , if1(false(), x, y) -> gcd(y, x) 821.30/297.04 , if2(true(), x, y) -> gcd(minus(x, y), y) 821.30/297.04 , if2(false(), x, y) -> x } 821.30/297.04 Obligation: 821.30/297.04 innermost runtime complexity 821.30/297.04 Answer: 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 The weightgap principle applies (using the following nonconstant 821.30/297.04 growth matrix-interpretation) 821.30/297.04 821.30/297.04 The following argument positions are usable: 821.30/297.04 Uargs(s) = {1}, Uargs(if) = {1}, Uargs(gcd) = {1}, 821.30/297.04 Uargs(if1) = {1}, Uargs(if2) = {1} 821.30/297.04 821.30/297.04 TcT has computed the following matrix interpretation satisfying 821.30/297.04 not(EDA) and not(IDA(1)). 821.30/297.04 821.30/297.04 [minus](x1, x2) = [1] x1 + [1] 821.30/297.04 821.30/297.04 [s](x1) = [1] x1 + [0] 821.30/297.04 821.30/297.04 [if](x1, x2, x3) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [gt](x1, x2) = [0] 821.30/297.04 821.30/297.04 [true] = [1] 821.30/297.04 821.30/297.04 [false] = [0] 821.30/297.04 821.30/297.04 [0] = [0] 821.30/297.04 821.30/297.04 [gcd](x1, x2) = [1] x1 + [1] x2 + [0] 821.30/297.04 821.30/297.04 [if1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 [ge](x1, x2) = [0] 821.30/297.04 821.30/297.04 [if2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 821.30/297.04 821.30/297.04 The order satisfies the following ordering constraints: 821.30/297.04 821.30/297.04 [minus(s(x), y)] = [1] x + [1] 821.30/297.04 > [1] x + [0] 821.30/297.04 = [if(gt(s(x), y), x, y)] 821.30/297.04 821.30/297.04 [if(true(), x, y)] = [1] x + [1] 821.30/297.04 >= [1] x + [1] 821.30/297.04 = [s(minus(x, y))] 821.30/297.04 821.30/297.04 [if(false(), x, y)] = [1] x + [0] 821.30/297.04 >= [0] 821.30/297.04 = [0()] 821.30/297.04 821.30/297.04 [gt(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [gt(x, y)] 821.30/297.04 821.30/297.04 [gt(s(x), 0())] = [0] 821.30/297.04 ? [1] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [gt(0(), y)] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [gcd(x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [if1(ge(x, y), x, y)] 821.30/297.04 821.30/297.04 [if1(true(), x, y)] = [1] x + [1] y + [1] 821.30/297.04 > [1] x + [1] y + [0] 821.30/297.04 = [if2(gt(y, 0()), x, y)] 821.30/297.04 821.30/297.04 [if1(false(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [1] y + [0] 821.30/297.04 = [gcd(y, x)] 821.30/297.04 821.30/297.04 [ge(x, 0())] = [0] 821.30/297.04 ? [1] 821.30/297.04 = [true()] 821.30/297.04 821.30/297.04 [ge(s(x), s(y))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [ge(x, y)] 821.30/297.04 821.30/297.04 [ge(0(), s(x))] = [0] 821.30/297.04 >= [0] 821.30/297.04 = [false()] 821.30/297.04 821.30/297.04 [if2(true(), x, y)] = [1] x + [1] y + [1] 821.30/297.04 >= [1] x + [1] y + [1] 821.30/297.04 = [gcd(minus(x, y), y)] 821.30/297.04 821.30/297.04 [if2(false(), x, y)] = [1] x + [1] y + [0] 821.30/297.04 >= [1] x + [0] 821.30/297.04 = [x] 821.30/297.04 821.30/297.04 821.30/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 821.30/297.04 821.30/297.04 We are left with following problem, upon which TcT provides the 821.30/297.04 certificate MAYBE. 821.30/297.04 821.30/297.04 Strict Trs: 821.30/297.04 { gt(s(x), s(y)) -> gt(x, y) 821.30/297.04 , gt(s(x), 0()) -> true() 821.30/297.04 , ge(x, 0()) -> true() 821.30/297.04 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.04 , ge(0(), s(x)) -> false() } 821.30/297.04 Weak Trs: 821.30/297.04 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.04 , if(true(), x, y) -> s(minus(x, y)) 821.30/297.04 , if(false(), x, y) -> 0() 821.30/297.04 , gt(0(), y) -> false() 821.30/297.04 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.04 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.04 , if1(false(), x, y) -> gcd(y, x) 821.30/297.04 , if2(true(), x, y) -> gcd(minus(x, y), y) 821.30/297.04 , if2(false(), x, y) -> x } 821.30/297.04 Obligation: 821.30/297.04 innermost runtime complexity 821.30/297.04 Answer: 821.30/297.04 MAYBE 821.30/297.04 821.30/297.04 None of the processors succeeded. 821.30/297.04 821.30/297.04 Details of failed attempt(s): 821.30/297.04 ----------------------------- 821.30/297.04 1) 'empty' failed due to the following reason: 821.30/297.04 821.30/297.04 Empty strict component of the problem is NOT empty. 821.30/297.04 821.30/297.04 2) 'With Problem ...' failed due to the following reason: 821.30/297.04 821.30/297.04 None of the processors succeeded. 821.30/297.04 821.30/297.04 Details of failed attempt(s): 821.30/297.04 ----------------------------- 821.30/297.05 1) 'empty' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 2) 'Fastest' failed due to the following reason: 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'With Problem ...' failed due to the following reason: 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'empty' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 2) 'With Problem ...' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 821.30/297.05 2) 'With Problem ...' failed due to the following reason: 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'empty' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 2) 'With Problem ...' failed due to the following reason: 821.30/297.05 821.30/297.05 The weightgap principle applies (using the following nonconstant 821.30/297.05 growth matrix-interpretation) 821.30/297.05 821.30/297.05 The following argument positions are usable: 821.30/297.05 Uargs(s) = {1}, Uargs(if) = {1}, Uargs(gcd) = {1}, 821.30/297.05 Uargs(if1) = {1}, Uargs(if2) = {1} 821.30/297.05 821.30/297.05 TcT has computed the following matrix interpretation satisfying 821.30/297.05 not(EDA) and not(IDA(1)). 821.30/297.05 821.30/297.05 [minus](x1, x2) = [1 0] x1 + [0] 821.30/297.05 [0 0] [0] 821.30/297.05 821.30/297.05 [s](x1) = [1 0] x1 + [4] 821.30/297.05 [0 0] [0] 821.30/297.05 821.30/297.05 [if](x1, x2, x3) = [1 0] x1 + [1 0] x2 + [3] 821.30/297.05 [0 1] [0 0] [0] 821.30/297.05 821.30/297.05 [gt](x1, x2) = [0 0] x1 + [0] 821.30/297.05 [0 1] [0] 821.30/297.05 821.30/297.05 [true] = [1] 821.30/297.05 [0] 821.30/297.05 821.30/297.05 [false] = [0] 821.30/297.05 [1] 821.30/297.05 821.30/297.05 [0] = [0] 821.30/297.05 [1] 821.30/297.05 821.30/297.05 [gcd](x1, x2) = [1 0] x1 + [1 0] x2 + [2] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 821.30/297.05 [if1](x1, x2, x3) = [1 4] x1 + [1 0] x2 + [1 0] x3 + [0] 821.30/297.05 [0 0] [0 1] [0 1] [0] 821.30/297.05 821.30/297.05 [ge](x1, x2) = [2] 821.30/297.05 [0] 821.30/297.05 821.30/297.05 [if2](x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [1] 821.30/297.05 [0 0] [0 1] [0 1] [0] 821.30/297.05 821.30/297.05 The order satisfies the following ordering constraints: 821.30/297.05 821.30/297.05 [minus(s(x), y)] = [1 0] x + [4] 821.30/297.05 [0 0] [0] 821.30/297.05 > [1 0] x + [3] 821.30/297.05 [0 0] [0] 821.30/297.05 = [if(gt(s(x), y), x, y)] 821.30/297.05 821.30/297.05 [if(true(), x, y)] = [1 0] x + [4] 821.30/297.05 [0 0] [0] 821.30/297.05 >= [1 0] x + [4] 821.30/297.05 [0 0] [0] 821.30/297.05 = [s(minus(x, y))] 821.30/297.05 821.30/297.05 [if(false(), x, y)] = [1 0] x + [3] 821.30/297.05 [0 0] [1] 821.30/297.05 > [0] 821.30/297.05 [1] 821.30/297.05 = [0()] 821.30/297.05 821.30/297.05 [gt(s(x), s(y))] = [0] 821.30/297.05 [0] 821.30/297.05 ? [0 0] x + [0] 821.30/297.05 [0 1] [0] 821.30/297.05 = [gt(x, y)] 821.30/297.05 821.30/297.05 [gt(s(x), 0())] = [0] 821.30/297.05 [0] 821.30/297.05 ? [1] 821.30/297.05 [0] 821.30/297.05 = [true()] 821.30/297.05 821.30/297.05 [gt(0(), y)] = [0] 821.30/297.05 [1] 821.30/297.05 >= [0] 821.30/297.05 [1] 821.30/297.05 = [false()] 821.30/297.05 821.30/297.05 [gcd(x, y)] = [1 0] x + [1 0] y + [2] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 >= [1 0] x + [1 0] y + [2] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 = [if1(ge(x, y), x, y)] 821.30/297.05 821.30/297.05 [if1(true(), x, y)] = [1 0] x + [1 0] y + [1] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 >= [1 0] x + [1 0] y + [1] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 = [if2(gt(y, 0()), x, y)] 821.30/297.05 821.30/297.05 [if1(false(), x, y)] = [1 0] x + [1 0] y + [4] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 > [1 0] x + [1 0] y + [2] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 = [gcd(y, x)] 821.30/297.05 821.30/297.05 [ge(x, 0())] = [2] 821.30/297.05 [0] 821.30/297.05 > [1] 821.30/297.05 [0] 821.30/297.05 = [true()] 821.30/297.05 821.30/297.05 [ge(s(x), s(y))] = [2] 821.30/297.05 [0] 821.30/297.05 >= [2] 821.30/297.05 [0] 821.30/297.05 = [ge(x, y)] 821.30/297.05 821.30/297.05 [ge(0(), s(x))] = [2] 821.30/297.05 [0] 821.30/297.05 ? [0] 821.30/297.05 [1] 821.30/297.05 = [false()] 821.30/297.05 821.30/297.05 [if2(true(), x, y)] = [1 0] x + [1 0] y + [2] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 >= [1 0] x + [1 0] y + [2] 821.30/297.05 [0 0] [0 1] [0] 821.30/297.05 = [gcd(minus(x, y), y)] 821.30/297.05 821.30/297.05 [if2(false(), x, y)] = [1 0] x + [1 0] y + [1] 821.30/297.05 [0 1] [0 1] [0] 821.30/297.05 > [1 0] x + [0] 821.30/297.05 [0 1] [0] 821.30/297.05 = [x] 821.30/297.05 821.30/297.05 821.30/297.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 821.30/297.05 821.30/297.05 We are left with following problem, upon which TcT provides the 821.30/297.05 certificate MAYBE. 821.30/297.05 821.30/297.05 Strict Trs: 821.30/297.05 { gt(s(x), s(y)) -> gt(x, y) 821.30/297.05 , gt(s(x), 0()) -> true() 821.30/297.05 , ge(s(x), s(y)) -> ge(x, y) 821.30/297.05 , ge(0(), s(x)) -> false() } 821.30/297.05 Weak Trs: 821.30/297.05 { minus(s(x), y) -> if(gt(s(x), y), x, y) 821.30/297.05 , if(true(), x, y) -> s(minus(x, y)) 821.30/297.05 , if(false(), x, y) -> 0() 821.30/297.05 , gt(0(), y) -> false() 821.30/297.05 , gcd(x, y) -> if1(ge(x, y), x, y) 821.30/297.05 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 821.30/297.05 , if1(false(), x, y) -> gcd(y, x) 821.30/297.05 , ge(x, 0()) -> true() 821.30/297.05 , if2(true(), x, y) -> gcd(minus(x, y), y) 821.30/297.05 , if2(false(), x, y) -> x } 821.30/297.05 Obligation: 821.30/297.05 innermost runtime complexity 821.30/297.05 Answer: 821.30/297.05 MAYBE 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'empty' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 2) 'With Problem ...' failed due to the following reason: 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'empty' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 2) 'With Problem ...' failed due to the following reason: 821.30/297.05 821.30/297.05 Empty strict component of the problem is NOT empty. 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 2) 'Best' failed due to the following reason: 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 821.30/297.05 following reason: 821.30/297.05 821.30/297.05 The input cannot be shown compatible 821.30/297.05 821.30/297.05 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 821.30/297.05 to the following reason: 821.30/297.05 821.30/297.05 The input cannot be shown compatible 821.30/297.05 821.30/297.05 821.30/297.05 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 821.30/297.05 failed due to the following reason: 821.30/297.05 821.30/297.05 None of the processors succeeded. 821.30/297.05 821.30/297.05 Details of failed attempt(s): 821.30/297.05 ----------------------------- 821.30/297.05 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 821.30/297.05 failed due to the following reason: 821.30/297.05 821.30/297.05 match-boundness of the problem could not be verified. 821.30/297.05 821.30/297.05 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 821.30/297.05 failed due to the following reason: 821.30/297.05 821.30/297.05 match-boundness of the problem could not be verified. 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 821.30/297.05 Arrrr.. 821.45/297.17 EOF