MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { fst(X1, X2) -> n__fst(X1, X2) , fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) , s(X) -> n__s(X) , activate(X) -> X , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2)) , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(X) , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) , activate(n__len(X)) -> len(activate(X)) , from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) , add(X1, X2) -> n__add(X1, X2) , add(0(), X) -> X , add(s(X), Y) -> s(n__add(activate(X), Y)) , len(X) -> n__len(X) , len(nil()) -> 0() , len(cons(X, Z)) -> s(n__len(activate(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: { fst^#(X1, X2) -> c_1(X1, X2) , fst^#(0(), Z) -> c_2() , fst^#(s(X), cons(Y, Z)) -> c_3(Y, activate^#(X), activate^#(Z)) , activate^#(X) -> c_5(X) , activate^#(n__fst(X1, X2)) -> c_6(fst^#(activate(X1), activate(X2))) , activate^#(n__from(X)) -> c_7(from^#(activate(X))) , activate^#(n__s(X)) -> c_8(s^#(X)) , activate^#(n__add(X1, X2)) -> c_9(add^#(activate(X1), activate(X2))) , activate^#(n__len(X)) -> c_10(len^#(activate(X))) , s^#(X) -> c_4(X) , from^#(X) -> c_11(X, X) , from^#(X) -> c_12(X) , add^#(X1, X2) -> c_13(X1, X2) , add^#(0(), X) -> c_14(X) , add^#(s(X), Y) -> c_15(s^#(n__add(activate(X), Y))) , len^#(X) -> c_16(X) , len^#(nil()) -> c_17() , len^#(cons(X, Z)) -> c_18(s^#(n__len(activate(Z)))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fst^#(X1, X2) -> c_1(X1, X2) , fst^#(0(), Z) -> c_2() , fst^#(s(X), cons(Y, Z)) -> c_3(Y, activate^#(X), activate^#(Z)) , activate^#(X) -> c_5(X) , activate^#(n__fst(X1, X2)) -> c_6(fst^#(activate(X1), activate(X2))) , activate^#(n__from(X)) -> c_7(from^#(activate(X))) , activate^#(n__s(X)) -> c_8(s^#(X)) , activate^#(n__add(X1, X2)) -> c_9(add^#(activate(X1), activate(X2))) , activate^#(n__len(X)) -> c_10(len^#(activate(X))) , s^#(X) -> c_4(X) , from^#(X) -> c_11(X, X) , from^#(X) -> c_12(X) , add^#(X1, X2) -> c_13(X1, X2) , add^#(0(), X) -> c_14(X) , add^#(s(X), Y) -> c_15(s^#(n__add(activate(X), Y))) , len^#(X) -> c_16(X) , len^#(nil()) -> c_17() , len^#(cons(X, Z)) -> c_18(s^#(n__len(activate(Z)))) } Strict Trs: { fst(X1, X2) -> n__fst(X1, X2) , fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) , s(X) -> n__s(X) , activate(X) -> X , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2)) , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(X) , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) , activate(n__len(X)) -> len(activate(X)) , from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) , add(X1, X2) -> n__add(X1, X2) , add(0(), X) -> X , add(s(X), Y) -> s(n__add(activate(X), Y)) , len(X) -> n__len(X) , len(nil()) -> 0() , len(cons(X, Z)) -> s(n__len(activate(Z))) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2,17} by applications of Pre({2,17}) = {1,3,4,5,9,10,11,12,13,14,16}. Here rules are labeled as follows: DPs: { 1: fst^#(X1, X2) -> c_1(X1, X2) , 2: fst^#(0(), Z) -> c_2() , 3: fst^#(s(X), cons(Y, Z)) -> c_3(Y, activate^#(X), activate^#(Z)) , 4: activate^#(X) -> c_5(X) , 5: activate^#(n__fst(X1, X2)) -> c_6(fst^#(activate(X1), activate(X2))) , 6: activate^#(n__from(X)) -> c_7(from^#(activate(X))) , 7: activate^#(n__s(X)) -> c_8(s^#(X)) , 8: activate^#(n__add(X1, X2)) -> c_9(add^#(activate(X1), activate(X2))) , 9: activate^#(n__len(X)) -> c_10(len^#(activate(X))) , 10: s^#(X) -> c_4(X) , 11: from^#(X) -> c_11(X, X) , 12: from^#(X) -> c_12(X) , 13: add^#(X1, X2) -> c_13(X1, X2) , 14: add^#(0(), X) -> c_14(X) , 15: add^#(s(X), Y) -> c_15(s^#(n__add(activate(X), Y))) , 16: len^#(X) -> c_16(X) , 17: len^#(nil()) -> c_17() , 18: len^#(cons(X, Z)) -> c_18(s^#(n__len(activate(Z)))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fst^#(X1, X2) -> c_1(X1, X2) , fst^#(s(X), cons(Y, Z)) -> c_3(Y, activate^#(X), activate^#(Z)) , activate^#(X) -> c_5(X) , activate^#(n__fst(X1, X2)) -> c_6(fst^#(activate(X1), activate(X2))) , activate^#(n__from(X)) -> c_7(from^#(activate(X))) , activate^#(n__s(X)) -> c_8(s^#(X)) , activate^#(n__add(X1, X2)) -> c_9(add^#(activate(X1), activate(X2))) , activate^#(n__len(X)) -> c_10(len^#(activate(X))) , s^#(X) -> c_4(X) , from^#(X) -> c_11(X, X) , from^#(X) -> c_12(X) , add^#(X1, X2) -> c_13(X1, X2) , add^#(0(), X) -> c_14(X) , add^#(s(X), Y) -> c_15(s^#(n__add(activate(X), Y))) , len^#(X) -> c_16(X) , len^#(cons(X, Z)) -> c_18(s^#(n__len(activate(Z)))) } Strict Trs: { fst(X1, X2) -> n__fst(X1, X2) , fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) , s(X) -> n__s(X) , activate(X) -> X , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2)) , activate(n__from(X)) -> from(activate(X)) , activate(n__s(X)) -> s(X) , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) , activate(n__len(X)) -> len(activate(X)) , from(X) -> cons(X, n__from(n__s(X))) , from(X) -> n__from(X) , add(X1, X2) -> n__add(X1, X2) , add(0(), X) -> X , add(s(X), Y) -> s(n__add(activate(X), Y)) , len(X) -> n__len(X) , len(nil()) -> 0() , len(cons(X, Z)) -> s(n__len(activate(Z))) } Weak DPs: { fst^#(0(), Z) -> c_2() , len^#(nil()) -> c_17() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..