MAYBE 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 We are left with following problem, upon which TcT provides the 704.70/297.03 certificate MAYBE. 704.70/297.03 704.70/297.03 Strict Trs: 704.70/297.03 { diff(x, y) -> cond1(equal(x, y), x, y) 704.70/297.03 , cond1(true(), x, y) -> 0() 704.70/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 704.70/297.03 , equal(0(), 0()) -> true() 704.70/297.03 , equal(0(), s(y)) -> false() 704.70/297.03 , equal(s(x), 0()) -> false() 704.70/297.03 , equal(s(x), s(y)) -> equal(x, y) 704.70/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 704.70/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 704.70/297.03 , gt(0(), v) -> false() 704.70/297.03 , gt(s(u), 0()) -> true() 704.70/297.03 , gt(s(u), s(v)) -> gt(u, v) } 704.70/297.03 Obligation: 704.70/297.03 innermost runtime complexity 704.70/297.03 Answer: 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'Best' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 704.70/297.03 following reason: 704.70/297.03 704.70/297.03 Computation stopped due to timeout after 297.0 seconds. 704.70/297.03 704.70/297.03 2) 'Best' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 704.70/297.03 seconds)' failed due to the following reason: 704.70/297.03 704.70/297.03 The weightgap principle applies (using the following nonconstant 704.70/297.03 growth matrix-interpretation) 704.70/297.03 704.70/297.03 The following argument positions are usable: 704.70/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 704.70/297.03 704.70/297.03 TcT has computed the following matrix interpretation satisfying 704.70/297.03 not(EDA) and not(IDA(1)). 704.70/297.03 704.70/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [1] 704.70/297.03 704.70/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [equal](x1, x2) = [0] 704.70/297.03 704.70/297.03 [true] = [0] 704.70/297.03 704.70/297.03 [0] = [7] 704.70/297.03 704.70/297.03 [false] = [0] 704.70/297.03 704.70/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [gt](x1, x2) = [0] 704.70/297.03 704.70/297.03 [s](x1) = [1] x1 + [0] 704.70/297.03 704.70/297.03 The order satisfies the following ordering constraints: 704.70/297.03 704.70/297.03 [diff(x, y)] = [1] x + [1] y + [1] 704.70/297.03 > [1] x + [1] y + [0] 704.70/297.03 = [cond1(equal(x, y), x, y)] 704.70/297.03 704.70/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [7] 704.70/297.03 = [0()] 704.70/297.03 704.70/297.03 [cond1(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 >= [1] x + [1] y + [0] 704.70/297.03 = [cond2(gt(x, y), x, y)] 704.70/297.03 704.70/297.03 [equal(0(), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [equal(0(), s(y))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), s(y))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [equal(x, y)] 704.70/297.03 704.70/297.03 [cond2(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [s(diff(x, s(y)))] 704.70/297.03 704.70/297.03 [cond2(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [s(diff(s(x), y))] 704.70/297.03 704.70/297.03 [gt(0(), v)] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [gt(s(u), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [gt(s(u), s(v))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [gt(u, v)] 704.70/297.03 704.70/297.03 704.70/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 704.70/297.03 704.70/297.03 We are left with following problem, upon which TcT provides the 704.70/297.03 certificate MAYBE. 704.70/297.03 704.70/297.03 Strict Trs: 704.70/297.03 { cond1(true(), x, y) -> 0() 704.70/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 704.70/297.03 , equal(0(), 0()) -> true() 704.70/297.03 , equal(0(), s(y)) -> false() 704.70/297.03 , equal(s(x), 0()) -> false() 704.70/297.03 , equal(s(x), s(y)) -> equal(x, y) 704.70/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 704.70/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 704.70/297.03 , gt(0(), v) -> false() 704.70/297.03 , gt(s(u), 0()) -> true() 704.70/297.03 , gt(s(u), s(v)) -> gt(u, v) } 704.70/297.03 Weak Trs: { diff(x, y) -> cond1(equal(x, y), x, y) } 704.70/297.03 Obligation: 704.70/297.03 innermost runtime complexity 704.70/297.03 Answer: 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 The weightgap principle applies (using the following nonconstant 704.70/297.03 growth matrix-interpretation) 704.70/297.03 704.70/297.03 The following argument positions are usable: 704.70/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 704.70/297.03 704.70/297.03 TcT has computed the following matrix interpretation satisfying 704.70/297.03 not(EDA) and not(IDA(1)). 704.70/297.03 704.70/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [1] 704.70/297.03 704.70/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [equal](x1, x2) = [1] 704.70/297.03 704.70/297.03 [true] = [0] 704.70/297.03 704.70/297.03 [0] = [7] 704.70/297.03 704.70/297.03 [false] = [0] 704.70/297.03 704.70/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [gt](x1, x2) = [0] 704.70/297.03 704.70/297.03 [s](x1) = [1] x1 + [0] 704.70/297.03 704.70/297.03 The order satisfies the following ordering constraints: 704.70/297.03 704.70/297.03 [diff(x, y)] = [1] x + [1] y + [1] 704.70/297.03 >= [1] x + [1] y + [1] 704.70/297.03 = [cond1(equal(x, y), x, y)] 704.70/297.03 704.70/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [7] 704.70/297.03 = [0()] 704.70/297.03 704.70/297.03 [cond1(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 >= [1] x + [1] y + [0] 704.70/297.03 = [cond2(gt(x, y), x, y)] 704.70/297.03 704.70/297.03 [equal(0(), 0())] = [1] 704.70/297.03 > [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [equal(0(), s(y))] = [1] 704.70/297.03 > [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), 0())] = [1] 704.70/297.03 > [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), s(y))] = [1] 704.70/297.03 >= [1] 704.70/297.03 = [equal(x, y)] 704.70/297.03 704.70/297.03 [cond2(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [s(diff(x, s(y)))] 704.70/297.03 704.70/297.03 [cond2(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [s(diff(s(x), y))] 704.70/297.03 704.70/297.03 [gt(0(), v)] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [gt(s(u), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [gt(s(u), s(v))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [gt(u, v)] 704.70/297.03 704.70/297.03 704.70/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 704.70/297.03 704.70/297.03 We are left with following problem, upon which TcT provides the 704.70/297.03 certificate MAYBE. 704.70/297.03 704.70/297.03 Strict Trs: 704.70/297.03 { cond1(true(), x, y) -> 0() 704.70/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 704.70/297.03 , equal(s(x), s(y)) -> equal(x, y) 704.70/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 704.70/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 704.70/297.03 , gt(0(), v) -> false() 704.70/297.03 , gt(s(u), 0()) -> true() 704.70/297.03 , gt(s(u), s(v)) -> gt(u, v) } 704.70/297.03 Weak Trs: 704.70/297.03 { diff(x, y) -> cond1(equal(x, y), x, y) 704.70/297.03 , equal(0(), 0()) -> true() 704.70/297.03 , equal(0(), s(y)) -> false() 704.70/297.03 , equal(s(x), 0()) -> false() } 704.70/297.03 Obligation: 704.70/297.03 innermost runtime complexity 704.70/297.03 Answer: 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 The weightgap principle applies (using the following nonconstant 704.70/297.03 growth matrix-interpretation) 704.70/297.03 704.70/297.03 The following argument positions are usable: 704.70/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 704.70/297.03 704.70/297.03 TcT has computed the following matrix interpretation satisfying 704.70/297.03 not(EDA) and not(IDA(1)). 704.70/297.03 704.70/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [0] 704.70/297.03 704.70/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [equal](x1, x2) = [0] 704.70/297.03 704.70/297.03 [true] = [0] 704.70/297.03 704.70/297.03 [0] = [7] 704.70/297.03 704.70/297.03 [false] = [0] 704.70/297.03 704.70/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [gt](x1, x2) = [1] 704.70/297.03 704.70/297.03 [s](x1) = [1] x1 + [0] 704.70/297.03 704.70/297.03 The order satisfies the following ordering constraints: 704.70/297.03 704.70/297.03 [diff(x, y)] = [1] x + [1] y + [0] 704.70/297.03 >= [1] x + [1] y + [0] 704.70/297.03 = [cond1(equal(x, y), x, y)] 704.70/297.03 704.70/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [7] 704.70/297.03 = [0()] 704.70/297.03 704.70/297.03 [cond1(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [cond2(gt(x, y), x, y)] 704.70/297.03 704.70/297.03 [equal(0(), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [equal(0(), s(y))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), s(y))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [equal(x, y)] 704.70/297.03 704.70/297.03 [cond2(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 >= [1] x + [1] y + [0] 704.70/297.03 = [s(diff(x, s(y)))] 704.70/297.03 704.70/297.03 [cond2(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 >= [1] x + [1] y + [0] 704.70/297.03 = [s(diff(s(x), y))] 704.70/297.03 704.70/297.03 [gt(0(), v)] = [1] 704.70/297.03 > [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [gt(s(u), 0())] = [1] 704.70/297.03 > [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [gt(s(u), s(v))] = [1] 704.70/297.03 >= [1] 704.70/297.03 = [gt(u, v)] 704.70/297.03 704.70/297.03 704.70/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 704.70/297.03 704.70/297.03 We are left with following problem, upon which TcT provides the 704.70/297.03 certificate MAYBE. 704.70/297.03 704.70/297.03 Strict Trs: 704.70/297.03 { cond1(true(), x, y) -> 0() 704.70/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 704.70/297.03 , equal(s(x), s(y)) -> equal(x, y) 704.70/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 704.70/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 704.70/297.03 , gt(s(u), s(v)) -> gt(u, v) } 704.70/297.03 Weak Trs: 704.70/297.03 { diff(x, y) -> cond1(equal(x, y), x, y) 704.70/297.03 , equal(0(), 0()) -> true() 704.70/297.03 , equal(0(), s(y)) -> false() 704.70/297.03 , equal(s(x), 0()) -> false() 704.70/297.03 , gt(0(), v) -> false() 704.70/297.03 , gt(s(u), 0()) -> true() } 704.70/297.03 Obligation: 704.70/297.03 innermost runtime complexity 704.70/297.03 Answer: 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 The weightgap principle applies (using the following nonconstant 704.70/297.03 growth matrix-interpretation) 704.70/297.03 704.70/297.03 The following argument positions are usable: 704.70/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 704.70/297.03 704.70/297.03 TcT has computed the following matrix interpretation satisfying 704.70/297.03 not(EDA) and not(IDA(1)). 704.70/297.03 704.70/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [4] 704.70/297.03 704.70/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [equal](x1, x2) = [4] 704.70/297.03 704.70/297.03 [true] = [1] 704.70/297.03 704.70/297.03 [0] = [0] 704.70/297.03 704.70/297.03 [false] = [0] 704.70/297.03 704.70/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [gt](x1, x2) = [1] 704.70/297.03 704.70/297.03 [s](x1) = [1] x1 + [0] 704.70/297.03 704.70/297.03 The order satisfies the following ordering constraints: 704.70/297.03 704.70/297.03 [diff(x, y)] = [1] x + [1] y + [4] 704.70/297.03 >= [1] x + [1] y + [4] 704.70/297.03 = [cond1(equal(x, y), x, y)] 704.70/297.03 704.70/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [1] 704.70/297.03 > [0] 704.70/297.03 = [0()] 704.70/297.03 704.70/297.03 [cond1(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [cond2(gt(x, y), x, y)] 704.70/297.03 704.70/297.03 [equal(0(), 0())] = [4] 704.70/297.03 > [1] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [equal(0(), s(y))] = [4] 704.70/297.03 > [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), 0())] = [4] 704.70/297.03 > [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), s(y))] = [4] 704.70/297.03 >= [4] 704.70/297.03 = [equal(x, y)] 704.70/297.03 704.70/297.03 [cond2(true(), x, y)] = [1] x + [1] y + [1] 704.70/297.03 ? [1] x + [1] y + [4] 704.70/297.03 = [s(diff(x, s(y)))] 704.70/297.03 704.70/297.03 [cond2(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [4] 704.70/297.03 = [s(diff(s(x), y))] 704.70/297.03 704.70/297.03 [gt(0(), v)] = [1] 704.70/297.03 > [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [gt(s(u), 0())] = [1] 704.70/297.03 >= [1] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [gt(s(u), s(v))] = [1] 704.70/297.03 >= [1] 704.70/297.03 = [gt(u, v)] 704.70/297.03 704.70/297.03 704.70/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 704.70/297.03 704.70/297.03 We are left with following problem, upon which TcT provides the 704.70/297.03 certificate MAYBE. 704.70/297.03 704.70/297.03 Strict Trs: 704.70/297.03 { cond1(false(), x, y) -> cond2(gt(x, y), x, y) 704.70/297.03 , equal(s(x), s(y)) -> equal(x, y) 704.70/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 704.70/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 704.70/297.03 , gt(s(u), s(v)) -> gt(u, v) } 704.70/297.03 Weak Trs: 704.70/297.03 { diff(x, y) -> cond1(equal(x, y), x, y) 704.70/297.03 , cond1(true(), x, y) -> 0() 704.70/297.03 , equal(0(), 0()) -> true() 704.70/297.03 , equal(0(), s(y)) -> false() 704.70/297.03 , equal(s(x), 0()) -> false() 704.70/297.03 , gt(0(), v) -> false() 704.70/297.03 , gt(s(u), 0()) -> true() } 704.70/297.03 Obligation: 704.70/297.03 innermost runtime complexity 704.70/297.03 Answer: 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 The weightgap principle applies (using the following nonconstant 704.70/297.03 growth matrix-interpretation) 704.70/297.03 704.70/297.03 The following argument positions are usable: 704.70/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 704.70/297.03 704.70/297.03 TcT has computed the following matrix interpretation satisfying 704.70/297.03 not(EDA) and not(IDA(1)). 704.70/297.03 704.70/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [1] 704.70/297.03 704.70/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] 704.70/297.03 704.70/297.03 [equal](x1, x2) = [0] 704.70/297.03 704.70/297.03 [true] = [0] 704.70/297.03 704.70/297.03 [0] = [1] 704.70/297.03 704.70/297.03 [false] = [0] 704.70/297.03 704.70/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 704.70/297.03 704.70/297.03 [gt](x1, x2) = [0] 704.70/297.03 704.70/297.03 [s](x1) = [1] x1 + [0] 704.70/297.03 704.70/297.03 The order satisfies the following ordering constraints: 704.70/297.03 704.70/297.03 [diff(x, y)] = [1] x + [1] y + [1] 704.70/297.03 >= [1] x + [1] y + [1] 704.70/297.03 = [cond1(equal(x, y), x, y)] 704.70/297.03 704.70/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [1] 704.70/297.03 >= [1] 704.70/297.03 = [0()] 704.70/297.03 704.70/297.03 [cond1(false(), x, y)] = [1] x + [1] y + [1] 704.70/297.03 > [1] x + [1] y + [0] 704.70/297.03 = [cond2(gt(x, y), x, y)] 704.70/297.03 704.70/297.03 [equal(0(), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [equal(0(), s(y))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [equal(s(x), s(y))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [equal(x, y)] 704.70/297.03 704.70/297.03 [cond2(true(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [s(diff(x, s(y)))] 704.70/297.03 704.70/297.03 [cond2(false(), x, y)] = [1] x + [1] y + [0] 704.70/297.03 ? [1] x + [1] y + [1] 704.70/297.03 = [s(diff(s(x), y))] 704.70/297.03 704.70/297.03 [gt(0(), v)] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [false()] 704.70/297.03 704.70/297.03 [gt(s(u), 0())] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [true()] 704.70/297.03 704.70/297.03 [gt(s(u), s(v))] = [0] 704.70/297.03 >= [0] 704.70/297.03 = [gt(u, v)] 704.70/297.03 704.70/297.03 704.70/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 704.70/297.03 704.70/297.03 We are left with following problem, upon which TcT provides the 704.70/297.03 certificate MAYBE. 704.70/297.03 704.70/297.03 Strict Trs: 704.70/297.03 { equal(s(x), s(y)) -> equal(x, y) 704.70/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 704.70/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 704.70/297.03 , gt(s(u), s(v)) -> gt(u, v) } 704.70/297.03 Weak Trs: 704.70/297.03 { diff(x, y) -> cond1(equal(x, y), x, y) 704.70/297.03 , cond1(true(), x, y) -> 0() 704.70/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 704.70/297.03 , equal(0(), 0()) -> true() 704.70/297.03 , equal(0(), s(y)) -> false() 704.70/297.03 , equal(s(x), 0()) -> false() 704.70/297.03 , gt(0(), v) -> false() 704.70/297.03 , gt(s(u), 0()) -> true() } 704.70/297.03 Obligation: 704.70/297.03 innermost runtime complexity 704.70/297.03 Answer: 704.70/297.03 MAYBE 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'Fastest' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 2) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'empty' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 2) 'With Problem ...' failed due to the following reason: 704.70/297.03 704.70/297.03 Empty strict component of the problem is NOT empty. 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 2) 'Best' failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 704.70/297.03 following reason: 704.70/297.03 704.70/297.03 The input cannot be shown compatible 704.70/297.03 704.70/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 704.70/297.03 to the following reason: 704.70/297.03 704.70/297.03 The input cannot be shown compatible 704.70/297.03 704.70/297.03 704.70/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 704.70/297.03 failed due to the following reason: 704.70/297.03 704.70/297.03 None of the processors succeeded. 704.70/297.03 704.70/297.03 Details of failed attempt(s): 704.70/297.03 ----------------------------- 704.70/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 704.70/297.03 failed due to the following reason: 704.70/297.03 704.70/297.03 match-boundness of the problem could not be verified. 704.70/297.03 704.70/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 704.70/297.03 failed due to the following reason: 704.70/297.03 704.70/297.03 match-boundness of the problem could not be verified. 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 704.70/297.03 Arrrr.. 704.81/297.17 EOF