MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { badd(x', Cons(x, xs)) -> badd(Cons(Nil(), Nil()), badd(x', xs)) , badd(x, Nil()) -> x , goal(x, y) -> badd(x, y) } 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: Uargs(badd) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [badd](x1, x2) = [1] x1 + [1] x2 + [0] [Cons](x1, x2) = [1] x1 + [1] x2 + [7] [Nil] = [0] [goal](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {badd, goal} The order satisfies the following ordering constraints: [badd(x', Cons(x, xs))] = [1] x' + [1] x + [1] xs + [7] >= [1] x' + [1] xs + [7] = [badd(Cons(Nil(), Nil()), badd(x', xs))] [badd(x, Nil())] = [1] x + [0] >= [1] x + [0] = [x] [goal(x, y)] = [1] x + [1] y + [7] > [1] x + [1] y + [0] = [badd(x, y)] 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: { badd(x', Cons(x, xs)) -> badd(Cons(Nil(), Nil()), badd(x', xs)) , badd(x, Nil()) -> x } Weak Trs: { goal(x, y) -> badd(x, y) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(badd) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [badd](x1, x2) = [1] x1 + [1] x2 + [0] [Cons](x1, x2) = [1] x2 + [0] [Nil] = [1] [goal](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {badd, goal} The order satisfies the following ordering constraints: [badd(x', Cons(x, xs))] = [1] x' + [1] xs + [0] ? [1] x' + [1] xs + [1] = [badd(Cons(Nil(), Nil()), badd(x', xs))] [badd(x, Nil())] = [1] x + [1] > [1] x + [0] = [x] [goal(x, y)] = [1] x + [1] y + [7] > [1] x + [1] y + [0] = [badd(x, y)] 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: { badd(x', Cons(x, xs)) -> badd(Cons(Nil(), Nil()), badd(x', xs)) } Weak Trs: { badd(x, Nil()) -> x , goal(x, y) -> badd(x, y) } 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..