MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { first(X1, X2) -> n__first(X1, X2) , first(0(), X) -> nil() , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) , s(X) -> n__s(X) , activate(X) -> X , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(activate(X)) , from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(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: { first^#(X1, X2) -> c_1(X1, X2) , first^#(0(), X) -> c_2() , first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z)) , activate^#(X) -> c_5(X) , activate^#(n__first(X1, X2)) -> c_6(first^#(activate(X1), activate(X2))) , activate^#(n__from(X)) -> c_7(from^#(activate(X))) , activate^#(n__s(X)) -> c_8(s^#(activate(X))) , s^#(X) -> c_4(X) , from^#(X) -> c_9(X, X) , from^#(X) -> c_10(X) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { first^#(X1, X2) -> c_1(X1, X2) , first^#(0(), X) -> c_2() , first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z)) , activate^#(X) -> c_5(X) , activate^#(n__first(X1, X2)) -> c_6(first^#(activate(X1), activate(X2))) , activate^#(n__from(X)) -> c_7(from^#(activate(X))) , activate^#(n__s(X)) -> c_8(s^#(activate(X))) , s^#(X) -> c_4(X) , from^#(X) -> c_9(X, X) , from^#(X) -> c_10(X) } Strict Trs: { first(X1, X2) -> n__first(X1, X2) , first(0(), X) -> nil() , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) , s(X) -> n__s(X) , activate(X) -> X , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(activate(X)) , from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2} by applications of Pre({2}) = {1,3,4,5,8,9,10}. Here rules are labeled as follows: DPs: { 1: first^#(X1, X2) -> c_1(X1, X2) , 2: first^#(0(), X) -> c_2() , 3: first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z)) , 4: activate^#(X) -> c_5(X) , 5: activate^#(n__first(X1, X2)) -> c_6(first^#(activate(X1), activate(X2))) , 6: activate^#(n__from(X)) -> c_7(from^#(activate(X))) , 7: activate^#(n__s(X)) -> c_8(s^#(activate(X))) , 8: s^#(X) -> c_4(X) , 9: from^#(X) -> c_9(X, X) , 10: from^#(X) -> c_10(X) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { first^#(X1, X2) -> c_1(X1, X2) , first^#(s(X), cons(Y, Z)) -> c_3(Y, X, activate^#(Z)) , activate^#(X) -> c_5(X) , activate^#(n__first(X1, X2)) -> c_6(first^#(activate(X1), activate(X2))) , activate^#(n__from(X)) -> c_7(from^#(activate(X))) , activate^#(n__s(X)) -> c_8(s^#(activate(X))) , s^#(X) -> c_4(X) , from^#(X) -> c_9(X, X) , from^#(X) -> c_10(X) } Strict Trs: { first(X1, X2) -> n__first(X1, X2) , first(0(), X) -> nil() , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) , s(X) -> n__s(X) , activate(X) -> X , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(activate(X)) , from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) } Weak DPs: { first^#(0(), X) -> c_2() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..