MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) , a__after(X1, X2) -> after(X1, X2) , a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) , a__after(0(), XS) -> mark(XS) } 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) '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) '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 perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { a__from^#(X) -> c_1(mark^#(X), X) , a__from^#(X) -> c_2(X) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , mark^#(from(X)) -> c_4(a__from^#(mark(X))) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(0()) -> c_6() , mark^#(after(X1, X2)) -> c_7(a__after^#(mark(X1), mark(X2))) , a__after^#(X1, X2) -> c_8(X1, X2) , a__after^#(s(N), cons(X, XS)) -> c_9(a__after^#(mark(N), mark(XS))) , a__after^#(0(), XS) -> c_10(mark^#(XS)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__from^#(X) -> c_1(mark^#(X), X) , a__from^#(X) -> c_2(X) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , mark^#(from(X)) -> c_4(a__from^#(mark(X))) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(0()) -> c_6() , mark^#(after(X1, X2)) -> c_7(a__after^#(mark(X1), mark(X2))) , a__after^#(X1, X2) -> c_8(X1, X2) , a__after^#(s(N), cons(X, XS)) -> c_9(a__after^#(mark(N), mark(XS))) , a__after^#(0(), XS) -> c_10(mark^#(XS)) } Strict Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) , a__after(X1, X2) -> after(X1, X2) , a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) , a__after(0(), XS) -> mark(XS) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {6} by applications of Pre({6}) = {1,2,3,5,8,10}. Here rules are labeled as follows: DPs: { 1: a__from^#(X) -> c_1(mark^#(X), X) , 2: a__from^#(X) -> c_2(X) , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , 4: mark^#(from(X)) -> c_4(a__from^#(mark(X))) , 5: mark^#(s(X)) -> c_5(mark^#(X)) , 6: mark^#(0()) -> c_6() , 7: mark^#(after(X1, X2)) -> c_7(a__after^#(mark(X1), mark(X2))) , 8: a__after^#(X1, X2) -> c_8(X1, X2) , 9: a__after^#(s(N), cons(X, XS)) -> c_9(a__after^#(mark(N), mark(XS))) , 10: a__after^#(0(), XS) -> c_10(mark^#(XS)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__from^#(X) -> c_1(mark^#(X), X) , a__from^#(X) -> c_2(X) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , mark^#(from(X)) -> c_4(a__from^#(mark(X))) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(after(X1, X2)) -> c_7(a__after^#(mark(X1), mark(X2))) , a__after^#(X1, X2) -> c_8(X1, X2) , a__after^#(s(N), cons(X, XS)) -> c_9(a__after^#(mark(N), mark(XS))) , a__after^#(0(), XS) -> c_10(mark^#(XS)) } Strict Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) , a__after(X1, X2) -> after(X1, X2) , a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) , a__after(0(), XS) -> mark(XS) } Weak DPs: { mark^#(0()) -> c_6() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..