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