MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(h(x)) -> f(i(x)) , f(i(x)) -> a() , i(x) -> h(x) } Obligation: runtime complexity Answer: MAYBE 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(f) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [7] [h](x1) = [1] x1 + [7] [i](x1) = [1] x1 + [7] [a] = [5] The following symbols are considered usable {f, i} The order satisfies the following ordering constraints: [f(h(x))] = [1] x + [14] >= [1] x + [14] = [f(i(x))] [f(i(x))] = [1] x + [14] > [5] = [a()] [i(x)] = [1] x + [7] >= [1] x + [7] = [h(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: { f(h(x)) -> f(i(x)) , i(x) -> h(x) } Weak Trs: { f(i(x)) -> a() } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [7] [h](x1) = [1] x1 + [7] [i](x1) = [1] x1 + [3] [a] = [1] The following symbols are considered usable {f, i} The order satisfies the following ordering constraints: [f(h(x))] = [1] x + [14] > [1] x + [10] = [f(i(x))] [f(i(x))] = [1] x + [10] > [1] = [a()] [i(x)] = [1] x + [3] ? [1] x + [7] = [h(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: { i(x) -> h(x) } Weak Trs: { f(h(x)) -> f(i(x)) , f(i(x)) -> a() } Obligation: 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) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { f^#(h(x)) -> c_1(f^#(i(x))) , f^#(i(x)) -> c_2() , i^#(x) -> c_3(x) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(h(x)) -> c_1(f^#(i(x))) , f^#(i(x)) -> c_2() , i^#(x) -> c_3(x) } Strict Trs: { f(h(x)) -> f(i(x)) , f(i(x)) -> a() , i(x) -> h(x) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2} by applications of Pre({2}) = {1,3}. Here rules are labeled as follows: DPs: { 1: f^#(h(x)) -> c_1(f^#(i(x))) , 2: f^#(i(x)) -> c_2() , 3: i^#(x) -> c_3(x) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(h(x)) -> c_1(f^#(i(x))) , i^#(x) -> c_3(x) } Strict Trs: { f(h(x)) -> f(i(x)) , f(i(x)) -> a() , i(x) -> h(x) } Weak DPs: { f^#(i(x)) -> c_2() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..