MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> cons(X, n__f(n__g(X))) , f(X) -> n__f(X) , g(X) -> n__g(X) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) , activate(X) -> X , activate(n__f(X)) -> f(activate(X)) , activate(n__g(X)) -> g(activate(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: 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: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 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^#(X) -> c_1(X, X) , f^#(X) -> c_2(X) , g^#(X) -> c_3(X) , g^#(0()) -> c_4() , g^#(s(X)) -> c_5(g^#(X)) , sel^#(0(), cons(X, Y)) -> c_6(X) , sel^#(s(X), cons(Y, Z)) -> c_7(sel^#(X, activate(Z))) , activate^#(X) -> c_8(X) , activate^#(n__f(X)) -> c_9(f^#(activate(X))) , activate^#(n__g(X)) -> c_10(g^#(activate(X))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(X, X) , f^#(X) -> c_2(X) , g^#(X) -> c_3(X) , g^#(0()) -> c_4() , g^#(s(X)) -> c_5(g^#(X)) , sel^#(0(), cons(X, Y)) -> c_6(X) , sel^#(s(X), cons(Y, Z)) -> c_7(sel^#(X, activate(Z))) , activate^#(X) -> c_8(X) , activate^#(n__f(X)) -> c_9(f^#(activate(X))) , activate^#(n__g(X)) -> c_10(g^#(activate(X))) } Strict Trs: { f(X) -> cons(X, n__f(n__g(X))) , f(X) -> n__f(X) , g(X) -> n__g(X) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) , activate(X) -> X , activate(n__f(X)) -> f(activate(X)) , activate(n__g(X)) -> g(activate(X)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4} by applications of Pre({4}) = {1,2,3,5,6,8,10}. Here rules are labeled as follows: DPs: { 1: f^#(X) -> c_1(X, X) , 2: f^#(X) -> c_2(X) , 3: g^#(X) -> c_3(X) , 4: g^#(0()) -> c_4() , 5: g^#(s(X)) -> c_5(g^#(X)) , 6: sel^#(0(), cons(X, Y)) -> c_6(X) , 7: sel^#(s(X), cons(Y, Z)) -> c_7(sel^#(X, activate(Z))) , 8: activate^#(X) -> c_8(X) , 9: activate^#(n__f(X)) -> c_9(f^#(activate(X))) , 10: activate^#(n__g(X)) -> c_10(g^#(activate(X))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(X, X) , f^#(X) -> c_2(X) , g^#(X) -> c_3(X) , g^#(s(X)) -> c_5(g^#(X)) , sel^#(0(), cons(X, Y)) -> c_6(X) , sel^#(s(X), cons(Y, Z)) -> c_7(sel^#(X, activate(Z))) , activate^#(X) -> c_8(X) , activate^#(n__f(X)) -> c_9(f^#(activate(X))) , activate^#(n__g(X)) -> c_10(g^#(activate(X))) } Strict Trs: { f(X) -> cons(X, n__f(n__g(X))) , f(X) -> n__f(X) , g(X) -> n__g(X) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) , activate(X) -> X , activate(n__f(X)) -> f(activate(X)) , activate(n__g(X)) -> g(activate(X)) } Weak DPs: { g^#(0()) -> c_4() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..