MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(Cons(x, xs), y) -> Cons(x, xs) , g(Nil(), y) -> h(Nil(), y) , h(Cons(x, xs), y) -> f(Cons(x, xs), y) , h(Nil(), y) -> h(Nil(), y) , f(Cons(x, xs), y) -> h(Cons(x, xs), y) , f(Nil(), y) -> g(Nil(), y) , sp1(x, y) -> f(x, y) , r(x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1, x2) = [1] x1 + [1] x2 + [7] [Cons](x1, x2) = [1] x1 + [1] x2 + [7] [h](x1, x2) = [1] x1 + [1] x2 + [7] [Nil] = [7] [f](x1, x2) = [1] x1 + [1] x2 + [7] [sp1](x1, x2) = [1] x1 + [1] x2 + [7] [r](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {g, h, f, sp1, r} The order satisfies the following ordering constraints: [g(Cons(x, xs), y)] = [1] x + [1] xs + [1] y + [14] > [1] x + [1] xs + [7] = [Cons(x, xs)] [g(Nil(), y)] = [1] y + [14] >= [1] y + [14] = [h(Nil(), y)] [h(Cons(x, xs), y)] = [1] x + [1] xs + [1] y + [14] >= [1] x + [1] xs + [1] y + [14] = [f(Cons(x, xs), y)] [h(Nil(), y)] = [1] y + [14] >= [1] y + [14] = [h(Nil(), y)] [f(Cons(x, xs), y)] = [1] x + [1] xs + [1] y + [14] >= [1] x + [1] xs + [1] y + [14] = [h(Cons(x, xs), y)] [f(Nil(), y)] = [1] y + [14] >= [1] y + [14] = [g(Nil(), y)] [sp1(x, y)] = [1] x + [1] y + [7] >= [1] x + [1] y + [7] = [f(x, y)] [r(x, y)] = [1] x + [1] y + [7] > [1] x + [0] = [x] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(Nil(), y) -> h(Nil(), y) , h(Cons(x, xs), y) -> f(Cons(x, xs), y) , h(Nil(), y) -> h(Nil(), y) , f(Cons(x, xs), y) -> h(Cons(x, xs), y) , f(Nil(), y) -> g(Nil(), y) , sp1(x, y) -> f(x, y) } Weak Trs: { g(Cons(x, xs), y) -> Cons(x, xs) , r(x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1, x2) = [1] x2 + [0] [Cons](x1, x2) = [0] [h](x1, x2) = [1] x2 + [0] [Nil] = [7] [f](x1, x2) = [1] x2 + [0] [sp1](x1, x2) = [1] x1 + [1] x2 + [7] [r](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {g, h, f, sp1, r} The order satisfies the following ordering constraints: [g(Cons(x, xs), y)] = [1] y + [0] >= [0] = [Cons(x, xs)] [g(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [h(Cons(x, xs), y)] = [1] y + [0] >= [1] y + [0] = [f(Cons(x, xs), y)] [h(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [f(Cons(x, xs), y)] = [1] y + [0] >= [1] y + [0] = [h(Cons(x, xs), y)] [f(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [g(Nil(), y)] [sp1(x, y)] = [1] x + [1] y + [7] > [1] y + [0] = [f(x, y)] [r(x, y)] = [1] x + [1] y + [0] >= [1] x + [0] = [x] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(Nil(), y) -> h(Nil(), y) , h(Cons(x, xs), y) -> f(Cons(x, xs), y) , h(Nil(), y) -> h(Nil(), y) , f(Cons(x, xs), y) -> h(Cons(x, xs), y) , f(Nil(), y) -> g(Nil(), y) } Weak Trs: { g(Cons(x, xs), y) -> Cons(x, xs) , sp1(x, y) -> f(x, y) , r(x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1, x2) = [1] x2 + [0] [Cons](x1, x2) = [0] [h](x1, x2) = [1] x2 + [0] [Nil] = [4] [f](x1, x2) = [1] x1 + [1] x2 + [0] [sp1](x1, x2) = [1] x1 + [1] x2 + [7] [r](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {g, h, f, sp1, r} The order satisfies the following ordering constraints: [g(Cons(x, xs), y)] = [1] y + [0] >= [0] = [Cons(x, xs)] [g(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [h(Cons(x, xs), y)] = [1] y + [0] >= [1] y + [0] = [f(Cons(x, xs), y)] [h(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [f(Cons(x, xs), y)] = [1] y + [0] >= [1] y + [0] = [h(Cons(x, xs), y)] [f(Nil(), y)] = [1] y + [4] > [1] y + [0] = [g(Nil(), y)] [sp1(x, y)] = [1] x + [1] y + [7] > [1] x + [1] y + [0] = [f(x, y)] [r(x, y)] = [1] x + [1] y + [0] >= [1] x + [0] = [x] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(Nil(), y) -> h(Nil(), y) , h(Cons(x, xs), y) -> f(Cons(x, xs), y) , h(Nil(), y) -> h(Nil(), y) , f(Cons(x, xs), y) -> h(Cons(x, xs), y) } Weak Trs: { g(Cons(x, xs), y) -> Cons(x, xs) , f(Nil(), y) -> g(Nil(), y) , sp1(x, y) -> f(x, y) , r(x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1, x2) = [1] x1 + [1] x2 + [0] [Cons](x1, x2) = [0] [h](x1, x2) = [1] x2 + [0] [Nil] = [4] [f](x1, x2) = [1] x1 + [1] x2 + [0] [sp1](x1, x2) = [1] x1 + [1] x2 + [7] [r](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {g, h, f, sp1, r} The order satisfies the following ordering constraints: [g(Cons(x, xs), y)] = [1] y + [0] >= [0] = [Cons(x, xs)] [g(Nil(), y)] = [1] y + [4] > [1] y + [0] = [h(Nil(), y)] [h(Cons(x, xs), y)] = [1] y + [0] >= [1] y + [0] = [f(Cons(x, xs), y)] [h(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [f(Cons(x, xs), y)] = [1] y + [0] >= [1] y + [0] = [h(Cons(x, xs), y)] [f(Nil(), y)] = [1] y + [4] >= [1] y + [4] = [g(Nil(), y)] [sp1(x, y)] = [1] x + [1] y + [7] > [1] x + [1] y + [0] = [f(x, y)] [r(x, y)] = [1] x + [1] y + [0] >= [1] x + [0] = [x] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { h(Cons(x, xs), y) -> f(Cons(x, xs), y) , h(Nil(), y) -> h(Nil(), y) , f(Cons(x, xs), y) -> h(Cons(x, xs), y) } Weak Trs: { g(Cons(x, xs), y) -> Cons(x, xs) , g(Nil(), y) -> h(Nil(), y) , f(Nil(), y) -> g(Nil(), y) , sp1(x, y) -> f(x, y) , r(x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: none TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [g](x1, x2) = [1] x1 + [1] x2 + [0] [Cons](x1, x2) = [4] [h](x1, x2) = [1] x1 + [1] x2 + [0] [Nil] = [0] [f](x1, x2) = [1] x2 + [0] [sp1](x1, x2) = [1] x1 + [1] x2 + [7] [r](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {g, h, f, sp1, r} The order satisfies the following ordering constraints: [g(Cons(x, xs), y)] = [1] y + [4] >= [4] = [Cons(x, xs)] [g(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [h(Cons(x, xs), y)] = [1] y + [4] > [1] y + [0] = [f(Cons(x, xs), y)] [h(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [h(Nil(), y)] [f(Cons(x, xs), y)] = [1] y + [0] ? [1] y + [4] = [h(Cons(x, xs), y)] [f(Nil(), y)] = [1] y + [0] >= [1] y + [0] = [g(Nil(), y)] [sp1(x, y)] = [1] x + [1] y + [7] > [1] y + [0] = [f(x, y)] [r(x, y)] = [1] x + [1] y + [0] >= [1] x + [0] = [x] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { h(Nil(), y) -> h(Nil(), y) , f(Cons(x, xs), y) -> h(Cons(x, xs), y) } Weak Trs: { g(Cons(x, xs), y) -> Cons(x, xs) , g(Nil(), y) -> h(Nil(), y) , h(Cons(x, xs), y) -> f(Cons(x, xs), y) , f(Nil(), y) -> g(Nil(), y) , sp1(x, y) -> f(x, y) , r(x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible Arrrr..