MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(S(x)) -> x , f(0()) -> 0() , g(x) -> g(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: We add the following innermost weak dependency pairs: Strict DPs: { f^#(S(x)) -> c_1() , f^#(0()) -> c_2() , g^#(x) -> c_3(g^#(x)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(S(x)) -> c_1() , f^#(0()) -> c_2() , g^#(x) -> c_3(g^#(x)) } Strict Trs: { f(S(x)) -> x , f(0()) -> 0() , g(x) -> g(x) } Obligation: innermost runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(S(x)) -> c_1() , f^#(0()) -> c_2() , g^#(x) -> c_3(g^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_3) = {1} TcT has computed the following constructor-restricted matrix interpretation. [S](x1) = [1] [2] [0] = [1] [1] [f^#](x1) = [1 1] x1 + [2] [1 1] [1] [c_1] = [0] [0] [c_2] = [1] [1] [g^#](x1) = [2 1] x1 + [2] [1 1] [2] [c_3](x1) = [1 0] x1 + [1] [0 1] [2] The following symbols are considered usable {f^#, g^#} The order satisfies the following ordering constraints: [f^#(S(x))] = [5] [4] > [0] [0] = [c_1()] [f^#(0())] = [4] [3] > [1] [1] = [c_2()] [g^#(x)] = [2 1] x + [2] [1 1] [2] ? [2 1] x + [3] [1 1] [4] = [c_3(g^#(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 DPs: { g^#(x) -> c_3(g^#(x)) } Weak DPs: { f^#(S(x)) -> c_1() , f^#(0()) -> c_2() } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { f^#(S(x)) -> c_1() , f^#(0()) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x) -> c_3(g^#(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) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 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) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 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)). [f](x1) = [1] x1 + [7] [S](x1) = [1] x1 + [7] [0] = [7] [g](x1) = [1] x1 + [0] The following symbols are considered usable {f, g} The order satisfies the following ordering constraints: [f(S(x))] = [1] x + [14] > [1] x + [0] = [x] [f(0())] = [14] > [7] = [0()] [g(x)] = [1] x + [0] >= [1] x + [0] = [g(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(x) -> g(x) } Weak Trs: { f(S(x)) -> x , f(0()) -> 0() } 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..