MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__f(X) -> cons(mark(X), f(g(X))) , a__f(X) -> f(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(f(X)) -> a__f(mark(X)) , mark(g(X)) -> a__g(mark(X)) , mark(0()) -> 0() , mark(s(X)) -> s(mark(X)) , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__g(X) -> g(X) , a__g(0()) -> s(0()) , a__g(s(X)) -> s(s(a__g(mark(X)))) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(0(), cons(X, Y)) -> mark(X) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 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: Computation stopped due to timeout after 30.0 seconds. 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__f^#(X) -> c_1(mark^#(X), X) , a__f^#(X) -> c_2(X) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , mark^#(f(X)) -> c_4(a__f^#(mark(X))) , mark^#(g(X)) -> c_5(a__g^#(mark(X))) , mark^#(0()) -> c_6() , mark^#(s(X)) -> c_7(mark^#(X)) , mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) , a__g^#(X) -> c_9(X) , a__g^#(0()) -> c_10() , a__g^#(s(X)) -> c_11(a__g^#(mark(X))) , a__sel^#(X1, X2) -> c_12(X1, X2) , a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) , a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__f^#(X) -> c_1(mark^#(X), X) , a__f^#(X) -> c_2(X) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , mark^#(f(X)) -> c_4(a__f^#(mark(X))) , mark^#(g(X)) -> c_5(a__g^#(mark(X))) , mark^#(0()) -> c_6() , mark^#(s(X)) -> c_7(mark^#(X)) , mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) , a__g^#(X) -> c_9(X) , a__g^#(0()) -> c_10() , a__g^#(s(X)) -> c_11(a__g^#(mark(X))) , a__sel^#(X1, X2) -> c_12(X1, X2) , a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) , a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } Strict Trs: { a__f(X) -> cons(mark(X), f(g(X))) , a__f(X) -> f(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(f(X)) -> a__f(mark(X)) , mark(g(X)) -> a__g(mark(X)) , mark(0()) -> 0() , mark(s(X)) -> s(mark(X)) , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__g(X) -> g(X) , a__g(0()) -> s(0()) , a__g(s(X)) -> s(s(a__g(mark(X)))) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(0(), cons(X, Y)) -> mark(X) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {6,10} by applications of Pre({6,10}) = {1,2,3,5,7,9,11,12,13}. Here rules are labeled as follows: DPs: { 1: a__f^#(X) -> c_1(mark^#(X), X) , 2: a__f^#(X) -> c_2(X) , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , 4: mark^#(f(X)) -> c_4(a__f^#(mark(X))) , 5: mark^#(g(X)) -> c_5(a__g^#(mark(X))) , 6: mark^#(0()) -> c_6() , 7: mark^#(s(X)) -> c_7(mark^#(X)) , 8: mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) , 9: a__g^#(X) -> c_9(X) , 10: a__g^#(0()) -> c_10() , 11: a__g^#(s(X)) -> c_11(a__g^#(mark(X))) , 12: a__sel^#(X1, X2) -> c_12(X1, X2) , 13: a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) , 14: a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__f^#(X) -> c_1(mark^#(X), X) , a__f^#(X) -> c_2(X) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) , mark^#(f(X)) -> c_4(a__f^#(mark(X))) , mark^#(g(X)) -> c_5(a__g^#(mark(X))) , mark^#(s(X)) -> c_7(mark^#(X)) , mark^#(sel(X1, X2)) -> c_8(a__sel^#(mark(X1), mark(X2))) , a__g^#(X) -> c_9(X) , a__g^#(s(X)) -> c_11(a__g^#(mark(X))) , a__sel^#(X1, X2) -> c_12(X1, X2) , a__sel^#(0(), cons(X, Y)) -> c_13(mark^#(X)) , a__sel^#(s(X), cons(Y, Z)) -> c_14(a__sel^#(mark(X), mark(Z))) } Strict Trs: { a__f(X) -> cons(mark(X), f(g(X))) , a__f(X) -> f(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(f(X)) -> a__f(mark(X)) , mark(g(X)) -> a__g(mark(X)) , mark(0()) -> 0() , mark(s(X)) -> s(mark(X)) , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__g(X) -> g(X) , a__g(0()) -> s(0()) , a__g(s(X)) -> s(s(a__g(mark(X)))) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(0(), cons(X, Y)) -> mark(X) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } Weak DPs: { mark^#(0()) -> c_6() , a__g^#(0()) -> c_10() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..