MAYBE 889.13/297.03 MAYBE 889.13/297.03 889.13/297.03 We are left with following problem, upon which TcT provides the 889.13/297.03 certificate MAYBE. 889.13/297.03 889.13/297.03 Strict Trs: 889.13/297.03 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.03 , cond1(true(), x, y) -> 0() 889.13/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.03 , equal(0(), 0()) -> true() 889.13/297.03 , equal(0(), s(y)) -> false() 889.13/297.03 , equal(s(x), 0()) -> false() 889.13/297.03 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.03 , gt(0(), v) -> false() 889.13/297.03 , gt(s(u), 0()) -> true() 889.13/297.03 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.03 Obligation: 889.13/297.03 runtime complexity 889.13/297.03 Answer: 889.13/297.03 MAYBE 889.13/297.03 889.13/297.03 None of the processors succeeded. 889.13/297.03 889.13/297.03 Details of failed attempt(s): 889.13/297.03 ----------------------------- 889.13/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 889.13/297.03 following reason: 889.13/297.03 889.13/297.03 Computation stopped due to timeout after 297.0 seconds. 889.13/297.03 889.13/297.03 2) 'Best' failed due to the following reason: 889.13/297.03 889.13/297.03 None of the processors succeeded. 889.13/297.03 889.13/297.03 Details of failed attempt(s): 889.13/297.03 ----------------------------- 889.13/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 889.13/297.03 seconds)' failed due to the following reason: 889.13/297.03 889.13/297.03 The weightgap principle applies (using the following nonconstant 889.13/297.03 growth matrix-interpretation) 889.13/297.03 889.13/297.03 The following argument positions are usable: 889.13/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 889.13/297.03 889.13/297.03 TcT has computed the following matrix interpretation satisfying 889.13/297.03 not(EDA) and not(IDA(1)). 889.13/297.03 889.13/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [1] 889.13/297.03 889.13/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.03 889.13/297.03 [equal](x1, x2) = [0] 889.13/297.03 889.13/297.03 [true] = [0] 889.13/297.03 889.13/297.03 [0] = [7] 889.13/297.03 889.13/297.03 [false] = [0] 889.13/297.03 889.13/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.03 889.13/297.03 [gt](x1, x2) = [0] 889.13/297.03 889.13/297.03 [s](x1) = [1] x1 + [0] 889.13/297.03 889.13/297.03 The order satisfies the following ordering constraints: 889.13/297.03 889.13/297.03 [diff(x, y)] = [1] x + [1] y + [1] 889.13/297.03 > [1] x + [1] y + [0] 889.13/297.03 = [cond1(equal(x, y), x, y)] 889.13/297.03 889.13/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.03 ? [7] 889.13/297.03 = [0()] 889.13/297.03 889.13/297.03 [cond1(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.03 >= [1] x + [1] y + [0] 889.13/297.03 = [cond2(gt(x, y), x, y)] 889.13/297.03 889.13/297.03 [equal(0(), 0())] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [true()] 889.13/297.03 889.13/297.03 [equal(0(), s(y))] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [false()] 889.13/297.03 889.13/297.03 [equal(s(x), 0())] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [false()] 889.13/297.03 889.13/297.03 [equal(s(x), s(y))] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [equal(x, y)] 889.13/297.03 889.13/297.03 [cond2(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.03 ? [1] x + [1] y + [1] 889.13/297.03 = [s(diff(x, s(y)))] 889.13/297.03 889.13/297.03 [cond2(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.03 ? [1] x + [1] y + [1] 889.13/297.03 = [s(diff(s(x), y))] 889.13/297.03 889.13/297.03 [gt(0(), v)] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [false()] 889.13/297.03 889.13/297.03 [gt(s(u), 0())] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [true()] 889.13/297.03 889.13/297.03 [gt(s(u), s(v))] = [0] 889.13/297.03 >= [0] 889.13/297.03 = [gt(u, v)] 889.13/297.03 889.13/297.03 889.13/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 889.13/297.03 889.13/297.03 We are left with following problem, upon which TcT provides the 889.13/297.03 certificate MAYBE. 889.13/297.03 889.13/297.03 Strict Trs: 889.13/297.03 { cond1(true(), x, y) -> 0() 889.13/297.03 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.03 , equal(0(), 0()) -> true() 889.13/297.03 , equal(0(), s(y)) -> false() 889.13/297.03 , equal(s(x), 0()) -> false() 889.13/297.03 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.03 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.03 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.03 , gt(0(), v) -> false() 889.13/297.03 , gt(s(u), 0()) -> true() 889.13/297.03 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.03 Weak Trs: { diff(x, y) -> cond1(equal(x, y), x, y) } 889.13/297.03 Obligation: 889.13/297.03 runtime complexity 889.13/297.03 Answer: 889.13/297.03 MAYBE 889.13/297.03 889.13/297.03 The weightgap principle applies (using the following nonconstant 889.13/297.03 growth matrix-interpretation) 889.13/297.03 889.13/297.03 The following argument positions are usable: 889.13/297.03 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 889.13/297.03 889.13/297.03 TcT has computed the following matrix interpretation satisfying 889.13/297.03 not(EDA) and not(IDA(1)). 889.13/297.03 889.13/297.03 [diff](x1, x2) = [1] x1 + [1] x2 + [1] 889.13/297.03 889.13/297.03 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.03 889.13/297.03 [equal](x1, x2) = [1] 889.13/297.03 889.13/297.03 [true] = [0] 889.13/297.03 889.13/297.03 [0] = [7] 889.13/297.03 889.13/297.03 [false] = [0] 889.13/297.03 889.13/297.03 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.03 889.13/297.03 [gt](x1, x2) = [0] 889.13/297.03 889.13/297.03 [s](x1) = [1] x1 + [0] 889.13/297.03 889.13/297.03 The order satisfies the following ordering constraints: 889.13/297.03 889.13/297.03 [diff(x, y)] = [1] x + [1] y + [1] 889.13/297.03 >= [1] x + [1] y + [1] 889.13/297.03 = [cond1(equal(x, y), x, y)] 889.13/297.03 889.13/297.03 [cond1(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.03 ? [7] 889.13/297.04 = [0()] 889.13/297.04 889.13/297.04 [cond1(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 >= [1] x + [1] y + [0] 889.13/297.04 = [cond2(gt(x, y), x, y)] 889.13/297.04 889.13/297.04 [equal(0(), 0())] = [1] 889.13/297.04 > [0] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [equal(0(), s(y))] = [1] 889.13/297.04 > [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), 0())] = [1] 889.13/297.04 > [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), s(y))] = [1] 889.13/297.04 >= [1] 889.13/297.04 = [equal(x, y)] 889.13/297.04 889.13/297.04 [cond2(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [1] 889.13/297.04 = [s(diff(x, s(y)))] 889.13/297.04 889.13/297.04 [cond2(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [1] 889.13/297.04 = [s(diff(s(x), y))] 889.13/297.04 889.13/297.04 [gt(0(), v)] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [gt(s(u), 0())] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [gt(s(u), s(v))] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [gt(u, v)] 889.13/297.04 889.13/297.04 889.13/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 889.13/297.04 889.13/297.04 We are left with following problem, upon which TcT provides the 889.13/297.04 certificate MAYBE. 889.13/297.04 889.13/297.04 Strict Trs: 889.13/297.04 { cond1(true(), x, y) -> 0() 889.13/297.04 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.04 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.04 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.04 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.04 , gt(0(), v) -> false() 889.13/297.04 , gt(s(u), 0()) -> true() 889.13/297.04 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.04 Weak Trs: 889.13/297.04 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.04 , equal(0(), 0()) -> true() 889.13/297.04 , equal(0(), s(y)) -> false() 889.13/297.04 , equal(s(x), 0()) -> false() } 889.13/297.04 Obligation: 889.13/297.04 runtime complexity 889.13/297.04 Answer: 889.13/297.04 MAYBE 889.13/297.04 889.13/297.04 The weightgap principle applies (using the following nonconstant 889.13/297.04 growth matrix-interpretation) 889.13/297.04 889.13/297.04 The following argument positions are usable: 889.13/297.04 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 889.13/297.04 889.13/297.04 TcT has computed the following matrix interpretation satisfying 889.13/297.04 not(EDA) and not(IDA(1)). 889.13/297.04 889.13/297.04 [diff](x1, x2) = [1] x1 + [1] x2 + [0] 889.13/297.04 889.13/297.04 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.04 889.13/297.04 [equal](x1, x2) = [0] 889.13/297.04 889.13/297.04 [true] = [0] 889.13/297.04 889.13/297.04 [0] = [7] 889.13/297.04 889.13/297.04 [false] = [0] 889.13/297.04 889.13/297.04 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.04 889.13/297.04 [gt](x1, x2) = [1] 889.13/297.04 889.13/297.04 [s](x1) = [1] x1 + [0] 889.13/297.04 889.13/297.04 The order satisfies the following ordering constraints: 889.13/297.04 889.13/297.04 [diff(x, y)] = [1] x + [1] y + [0] 889.13/297.04 >= [1] x + [1] y + [0] 889.13/297.04 = [cond1(equal(x, y), x, y)] 889.13/297.04 889.13/297.04 [cond1(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [7] 889.13/297.04 = [0()] 889.13/297.04 889.13/297.04 [cond1(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [1] 889.13/297.04 = [cond2(gt(x, y), x, y)] 889.13/297.04 889.13/297.04 [equal(0(), 0())] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [equal(0(), s(y))] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), 0())] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), s(y))] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [equal(x, y)] 889.13/297.04 889.13/297.04 [cond2(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 >= [1] x + [1] y + [0] 889.13/297.04 = [s(diff(x, s(y)))] 889.13/297.04 889.13/297.04 [cond2(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 >= [1] x + [1] y + [0] 889.13/297.04 = [s(diff(s(x), y))] 889.13/297.04 889.13/297.04 [gt(0(), v)] = [1] 889.13/297.04 > [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [gt(s(u), 0())] = [1] 889.13/297.04 > [0] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [gt(s(u), s(v))] = [1] 889.13/297.04 >= [1] 889.13/297.04 = [gt(u, v)] 889.13/297.04 889.13/297.04 889.13/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 889.13/297.04 889.13/297.04 We are left with following problem, upon which TcT provides the 889.13/297.04 certificate MAYBE. 889.13/297.04 889.13/297.04 Strict Trs: 889.13/297.04 { cond1(true(), x, y) -> 0() 889.13/297.04 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.04 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.04 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.04 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.04 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.04 Weak Trs: 889.13/297.04 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.04 , equal(0(), 0()) -> true() 889.13/297.04 , equal(0(), s(y)) -> false() 889.13/297.04 , equal(s(x), 0()) -> false() 889.13/297.04 , gt(0(), v) -> false() 889.13/297.04 , gt(s(u), 0()) -> true() } 889.13/297.04 Obligation: 889.13/297.04 runtime complexity 889.13/297.04 Answer: 889.13/297.04 MAYBE 889.13/297.04 889.13/297.04 The weightgap principle applies (using the following nonconstant 889.13/297.04 growth matrix-interpretation) 889.13/297.04 889.13/297.04 The following argument positions are usable: 889.13/297.04 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 889.13/297.04 889.13/297.04 TcT has computed the following matrix interpretation satisfying 889.13/297.04 not(EDA) and not(IDA(1)). 889.13/297.04 889.13/297.04 [diff](x1, x2) = [1] x1 + [1] x2 + [4] 889.13/297.04 889.13/297.04 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.04 889.13/297.04 [equal](x1, x2) = [4] 889.13/297.04 889.13/297.04 [true] = [1] 889.13/297.04 889.13/297.04 [0] = [0] 889.13/297.04 889.13/297.04 [false] = [0] 889.13/297.04 889.13/297.04 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.04 889.13/297.04 [gt](x1, x2) = [1] 889.13/297.04 889.13/297.04 [s](x1) = [1] x1 + [0] 889.13/297.04 889.13/297.04 The order satisfies the following ordering constraints: 889.13/297.04 889.13/297.04 [diff(x, y)] = [1] x + [1] y + [4] 889.13/297.04 >= [1] x + [1] y + [4] 889.13/297.04 = [cond1(equal(x, y), x, y)] 889.13/297.04 889.13/297.04 [cond1(true(), x, y)] = [1] x + [1] y + [1] 889.13/297.04 > [0] 889.13/297.04 = [0()] 889.13/297.04 889.13/297.04 [cond1(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [1] 889.13/297.04 = [cond2(gt(x, y), x, y)] 889.13/297.04 889.13/297.04 [equal(0(), 0())] = [4] 889.13/297.04 > [1] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [equal(0(), s(y))] = [4] 889.13/297.04 > [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), 0())] = [4] 889.13/297.04 > [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), s(y))] = [4] 889.13/297.04 >= [4] 889.13/297.04 = [equal(x, y)] 889.13/297.04 889.13/297.04 [cond2(true(), x, y)] = [1] x + [1] y + [1] 889.13/297.04 ? [1] x + [1] y + [4] 889.13/297.04 = [s(diff(x, s(y)))] 889.13/297.04 889.13/297.04 [cond2(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [4] 889.13/297.04 = [s(diff(s(x), y))] 889.13/297.04 889.13/297.04 [gt(0(), v)] = [1] 889.13/297.04 > [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [gt(s(u), 0())] = [1] 889.13/297.04 >= [1] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [gt(s(u), s(v))] = [1] 889.13/297.04 >= [1] 889.13/297.04 = [gt(u, v)] 889.13/297.04 889.13/297.04 889.13/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 889.13/297.04 889.13/297.04 We are left with following problem, upon which TcT provides the 889.13/297.04 certificate MAYBE. 889.13/297.04 889.13/297.04 Strict Trs: 889.13/297.04 { cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.04 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.04 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.04 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.04 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.04 Weak Trs: 889.13/297.04 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.04 , cond1(true(), x, y) -> 0() 889.13/297.04 , equal(0(), 0()) -> true() 889.13/297.04 , equal(0(), s(y)) -> false() 889.13/297.04 , equal(s(x), 0()) -> false() 889.13/297.04 , gt(0(), v) -> false() 889.13/297.04 , gt(s(u), 0()) -> true() } 889.13/297.04 Obligation: 889.13/297.04 runtime complexity 889.13/297.04 Answer: 889.13/297.04 MAYBE 889.13/297.04 889.13/297.04 The weightgap principle applies (using the following nonconstant 889.13/297.04 growth matrix-interpretation) 889.13/297.04 889.13/297.04 The following argument positions are usable: 889.13/297.04 Uargs(cond1) = {1}, Uargs(cond2) = {1}, Uargs(s) = {1} 889.13/297.04 889.13/297.04 TcT has computed the following matrix interpretation satisfying 889.13/297.04 not(EDA) and not(IDA(1)). 889.13/297.04 889.13/297.04 [diff](x1, x2) = [1] x1 + [1] x2 + [1] 889.13/297.04 889.13/297.04 [cond1](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] 889.13/297.04 889.13/297.04 [equal](x1, x2) = [0] 889.13/297.04 889.13/297.04 [true] = [0] 889.13/297.04 889.13/297.04 [0] = [1] 889.13/297.04 889.13/297.04 [false] = [0] 889.13/297.04 889.13/297.04 [cond2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 889.13/297.04 889.13/297.04 [gt](x1, x2) = [0] 889.13/297.04 889.13/297.04 [s](x1) = [1] x1 + [0] 889.13/297.04 889.13/297.04 The order satisfies the following ordering constraints: 889.13/297.04 889.13/297.04 [diff(x, y)] = [1] x + [1] y + [1] 889.13/297.04 >= [1] x + [1] y + [1] 889.13/297.04 = [cond1(equal(x, y), x, y)] 889.13/297.04 889.13/297.04 [cond1(true(), x, y)] = [1] x + [1] y + [1] 889.13/297.04 >= [1] 889.13/297.04 = [0()] 889.13/297.04 889.13/297.04 [cond1(false(), x, y)] = [1] x + [1] y + [1] 889.13/297.04 > [1] x + [1] y + [0] 889.13/297.04 = [cond2(gt(x, y), x, y)] 889.13/297.04 889.13/297.04 [equal(0(), 0())] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [equal(0(), s(y))] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), 0())] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [equal(s(x), s(y))] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [equal(x, y)] 889.13/297.04 889.13/297.04 [cond2(true(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [1] 889.13/297.04 = [s(diff(x, s(y)))] 889.13/297.04 889.13/297.04 [cond2(false(), x, y)] = [1] x + [1] y + [0] 889.13/297.04 ? [1] x + [1] y + [1] 889.13/297.04 = [s(diff(s(x), y))] 889.13/297.04 889.13/297.04 [gt(0(), v)] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [false()] 889.13/297.04 889.13/297.04 [gt(s(u), 0())] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [true()] 889.13/297.04 889.13/297.04 [gt(s(u), s(v))] = [0] 889.13/297.04 >= [0] 889.13/297.04 = [gt(u, v)] 889.13/297.04 889.13/297.04 889.13/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 889.13/297.04 889.13/297.04 We are left with following problem, upon which TcT provides the 889.13/297.04 certificate MAYBE. 889.13/297.04 889.13/297.04 Strict Trs: 889.13/297.04 { equal(s(x), s(y)) -> equal(x, y) 889.13/297.04 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.04 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.04 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.04 Weak Trs: 889.13/297.04 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.04 , cond1(true(), x, y) -> 0() 889.13/297.04 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.04 , equal(0(), 0()) -> true() 889.13/297.04 , equal(0(), s(y)) -> false() 889.13/297.04 , equal(s(x), 0()) -> false() 889.13/297.04 , gt(0(), v) -> false() 889.13/297.04 , gt(s(u), 0()) -> true() } 889.13/297.04 Obligation: 889.13/297.04 runtime complexity 889.13/297.04 Answer: 889.13/297.04 MAYBE 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'empty' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 2) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'empty' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 2) 'Fastest' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'empty' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 2) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'empty' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 2) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'empty' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 2) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 889.13/297.04 889.13/297.04 889.13/297.04 2) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'empty' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 2) 'With Problem ...' failed due to the following reason: 889.13/297.04 889.13/297.04 Empty strict component of the problem is NOT empty. 889.13/297.04 889.13/297.04 889.13/297.04 889.13/297.04 889.13/297.04 889.13/297.04 2) 'Best' failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 889.13/297.04 following reason: 889.13/297.04 889.13/297.04 The processor is inapplicable, reason: 889.13/297.04 Processor only applicable for innermost runtime complexity analysis 889.13/297.04 889.13/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 889.13/297.04 to the following reason: 889.13/297.04 889.13/297.04 The processor is inapplicable, reason: 889.13/297.04 Processor only applicable for innermost runtime complexity analysis 889.13/297.04 889.13/297.04 889.13/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 889.13/297.04 failed due to the following reason: 889.13/297.04 889.13/297.04 None of the processors succeeded. 889.13/297.04 889.13/297.04 Details of failed attempt(s): 889.13/297.04 ----------------------------- 889.13/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 889.13/297.04 failed due to the following reason: 889.13/297.04 889.13/297.04 match-boundness of the problem could not be verified. 889.13/297.04 889.13/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 889.13/297.04 failed due to the following reason: 889.13/297.04 889.13/297.04 match-boundness of the problem could not be verified. 889.13/297.04 889.13/297.04 889.13/297.04 889.13/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 889.13/297.04 the following reason: 889.13/297.04 889.13/297.04 We add the following weak dependency pairs: 889.13/297.04 889.13/297.04 Strict DPs: 889.13/297.04 { diff^#(x, y) -> c_1(cond1^#(equal(x, y), x, y)) 889.13/297.04 , cond1^#(true(), x, y) -> c_2() 889.13/297.04 , cond1^#(false(), x, y) -> c_3(cond2^#(gt(x, y), x, y)) 889.13/297.04 , cond2^#(true(), x, y) -> c_8(diff^#(x, s(y))) 889.13/297.04 , cond2^#(false(), x, y) -> c_9(diff^#(s(x), y)) 889.13/297.04 , equal^#(0(), 0()) -> c_4() 889.13/297.04 , equal^#(0(), s(y)) -> c_5() 889.13/297.04 , equal^#(s(x), 0()) -> c_6() 889.13/297.04 , equal^#(s(x), s(y)) -> c_7(equal^#(x, y)) 889.13/297.04 , gt^#(0(), v) -> c_10() 889.13/297.04 , gt^#(s(u), 0()) -> c_11() 889.13/297.04 , gt^#(s(u), s(v)) -> c_12(gt^#(u, v)) } 889.13/297.04 889.13/297.04 and mark the set of starting terms. 889.13/297.04 889.13/297.04 We are left with following problem, upon which TcT provides the 889.13/297.04 certificate MAYBE. 889.13/297.04 889.13/297.04 Strict DPs: 889.13/297.04 { diff^#(x, y) -> c_1(cond1^#(equal(x, y), x, y)) 889.13/297.05 , cond1^#(true(), x, y) -> c_2() 889.13/297.05 , cond1^#(false(), x, y) -> c_3(cond2^#(gt(x, y), x, y)) 889.13/297.05 , cond2^#(true(), x, y) -> c_8(diff^#(x, s(y))) 889.13/297.05 , cond2^#(false(), x, y) -> c_9(diff^#(s(x), y)) 889.13/297.05 , equal^#(0(), 0()) -> c_4() 889.13/297.05 , equal^#(0(), s(y)) -> c_5() 889.13/297.05 , equal^#(s(x), 0()) -> c_6() 889.13/297.05 , equal^#(s(x), s(y)) -> c_7(equal^#(x, y)) 889.13/297.05 , gt^#(0(), v) -> c_10() 889.13/297.05 , gt^#(s(u), 0()) -> c_11() 889.13/297.05 , gt^#(s(u), s(v)) -> c_12(gt^#(u, v)) } 889.13/297.05 Strict Trs: 889.13/297.05 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.05 , cond1(true(), x, y) -> 0() 889.13/297.05 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.05 , equal(0(), 0()) -> true() 889.13/297.05 , equal(0(), s(y)) -> false() 889.13/297.05 , equal(s(x), 0()) -> false() 889.13/297.05 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.05 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.05 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.05 , gt(0(), v) -> false() 889.13/297.05 , gt(s(u), 0()) -> true() 889.13/297.05 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.05 Obligation: 889.13/297.05 runtime complexity 889.13/297.05 Answer: 889.13/297.05 MAYBE 889.13/297.05 889.13/297.05 We estimate the number of application of {2,6,7,8,10,11} by 889.13/297.05 applications of Pre({2,6,7,8,10,11}) = {1,9,12}. Here rules are 889.13/297.05 labeled as follows: 889.13/297.05 889.13/297.05 DPs: 889.13/297.05 { 1: diff^#(x, y) -> c_1(cond1^#(equal(x, y), x, y)) 889.13/297.05 , 2: cond1^#(true(), x, y) -> c_2() 889.13/297.05 , 3: cond1^#(false(), x, y) -> c_3(cond2^#(gt(x, y), x, y)) 889.13/297.05 , 4: cond2^#(true(), x, y) -> c_8(diff^#(x, s(y))) 889.13/297.05 , 5: cond2^#(false(), x, y) -> c_9(diff^#(s(x), y)) 889.13/297.05 , 6: equal^#(0(), 0()) -> c_4() 889.13/297.05 , 7: equal^#(0(), s(y)) -> c_5() 889.13/297.05 , 8: equal^#(s(x), 0()) -> c_6() 889.13/297.05 , 9: equal^#(s(x), s(y)) -> c_7(equal^#(x, y)) 889.13/297.05 , 10: gt^#(0(), v) -> c_10() 889.13/297.05 , 11: gt^#(s(u), 0()) -> c_11() 889.13/297.05 , 12: gt^#(s(u), s(v)) -> c_12(gt^#(u, v)) } 889.13/297.05 889.13/297.05 We are left with following problem, upon which TcT provides the 889.13/297.05 certificate MAYBE. 889.13/297.05 889.13/297.05 Strict DPs: 889.13/297.05 { diff^#(x, y) -> c_1(cond1^#(equal(x, y), x, y)) 889.13/297.05 , cond1^#(false(), x, y) -> c_3(cond2^#(gt(x, y), x, y)) 889.13/297.05 , cond2^#(true(), x, y) -> c_8(diff^#(x, s(y))) 889.13/297.05 , cond2^#(false(), x, y) -> c_9(diff^#(s(x), y)) 889.13/297.05 , equal^#(s(x), s(y)) -> c_7(equal^#(x, y)) 889.13/297.05 , gt^#(s(u), s(v)) -> c_12(gt^#(u, v)) } 889.13/297.05 Strict Trs: 889.13/297.05 { diff(x, y) -> cond1(equal(x, y), x, y) 889.13/297.05 , cond1(true(), x, y) -> 0() 889.13/297.05 , cond1(false(), x, y) -> cond2(gt(x, y), x, y) 889.13/297.05 , equal(0(), 0()) -> true() 889.13/297.05 , equal(0(), s(y)) -> false() 889.13/297.05 , equal(s(x), 0()) -> false() 889.13/297.05 , equal(s(x), s(y)) -> equal(x, y) 889.13/297.05 , cond2(true(), x, y) -> s(diff(x, s(y))) 889.13/297.05 , cond2(false(), x, y) -> s(diff(s(x), y)) 889.13/297.05 , gt(0(), v) -> false() 889.13/297.05 , gt(s(u), 0()) -> true() 889.13/297.05 , gt(s(u), s(v)) -> gt(u, v) } 889.13/297.05 Weak DPs: 889.13/297.05 { cond1^#(true(), x, y) -> c_2() 889.13/297.05 , equal^#(0(), 0()) -> c_4() 889.13/297.05 , equal^#(0(), s(y)) -> c_5() 889.13/297.05 , equal^#(s(x), 0()) -> c_6() 889.13/297.05 , gt^#(0(), v) -> c_10() 889.13/297.05 , gt^#(s(u), 0()) -> c_11() } 889.13/297.05 Obligation: 889.13/297.05 runtime complexity 889.13/297.05 Answer: 889.13/297.05 MAYBE 889.13/297.05 889.13/297.05 Empty strict component of the problem is NOT empty. 889.13/297.05 889.13/297.05 889.13/297.05 Arrrr.. 889.40/297.21 EOF