MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { pairNs() -> cons(0(), n__incr(n__oddNs())) , cons(X1, X2) -> n__cons(X1, X2) , oddNs() -> n__oddNs() , oddNs() -> incr(pairNs()) , incr(X) -> n__incr(X) , incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) , activate(X) -> X , activate(n__incr(X)) -> incr(activate(X)) , activate(n__oddNs()) -> oddNs() , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) , activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2)) , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) , activate(n__repItems(X)) -> repItems(activate(X)) , take(X1, X2) -> n__take(X1, X2) , take(0(), XS) -> nil() , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) , zip(X1, X2) -> n__zip(X1, X2) , zip(X, nil()) -> nil() , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS))) , zip(nil(), XS) -> nil() , tail(cons(X, XS)) -> activate(XS) , repItems(X) -> n__repItems(X) , repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS)))) , repItems(nil()) -> nil() } 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: { pairNs^#() -> c_1(cons^#(0(), n__incr(n__oddNs()))) , cons^#(X1, X2) -> c_2(X1, X2) , oddNs^#() -> c_3() , oddNs^#() -> c_4(incr^#(pairNs())) , incr^#(X) -> c_5(X) , incr^#(cons(X, XS)) -> c_6(cons^#(s(X), n__incr(activate(XS)))) , activate^#(X) -> c_7(X) , activate^#(n__incr(X)) -> c_8(incr^#(activate(X))) , activate^#(n__oddNs()) -> c_9(oddNs^#()) , activate^#(n__take(X1, X2)) -> c_10(take^#(activate(X1), activate(X2))) , activate^#(n__zip(X1, X2)) -> c_11(zip^#(activate(X1), activate(X2))) , activate^#(n__cons(X1, X2)) -> c_12(cons^#(activate(X1), X2)) , activate^#(n__repItems(X)) -> c_13(repItems^#(activate(X))) , take^#(X1, X2) -> c_14(X1, X2) , take^#(0(), XS) -> c_15() , take^#(s(N), cons(X, XS)) -> c_16(cons^#(X, n__take(N, activate(XS)))) , zip^#(X1, X2) -> c_17(X1, X2) , zip^#(X, nil()) -> c_18() , zip^#(cons(X, XS), cons(Y, YS)) -> c_19(cons^#(pair(X, Y), n__zip(activate(XS), activate(YS)))) , zip^#(nil(), XS) -> c_20() , repItems^#(X) -> c_22(X) , repItems^#(cons(X, XS)) -> c_23(cons^#(X, n__cons(X, n__repItems(activate(XS))))) , repItems^#(nil()) -> c_24() , tail^#(cons(X, XS)) -> c_21(activate^#(XS)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { pairNs^#() -> c_1(cons^#(0(), n__incr(n__oddNs()))) , cons^#(X1, X2) -> c_2(X1, X2) , oddNs^#() -> c_3() , oddNs^#() -> c_4(incr^#(pairNs())) , incr^#(X) -> c_5(X) , incr^#(cons(X, XS)) -> c_6(cons^#(s(X), n__incr(activate(XS)))) , activate^#(X) -> c_7(X) , activate^#(n__incr(X)) -> c_8(incr^#(activate(X))) , activate^#(n__oddNs()) -> c_9(oddNs^#()) , activate^#(n__take(X1, X2)) -> c_10(take^#(activate(X1), activate(X2))) , activate^#(n__zip(X1, X2)) -> c_11(zip^#(activate(X1), activate(X2))) , activate^#(n__cons(X1, X2)) -> c_12(cons^#(activate(X1), X2)) , activate^#(n__repItems(X)) -> c_13(repItems^#(activate(X))) , take^#(X1, X2) -> c_14(X1, X2) , take^#(0(), XS) -> c_15() , take^#(s(N), cons(X, XS)) -> c_16(cons^#(X, n__take(N, activate(XS)))) , zip^#(X1, X2) -> c_17(X1, X2) , zip^#(X, nil()) -> c_18() , zip^#(cons(X, XS), cons(Y, YS)) -> c_19(cons^#(pair(X, Y), n__zip(activate(XS), activate(YS)))) , zip^#(nil(), XS) -> c_20() , repItems^#(X) -> c_22(X) , repItems^#(cons(X, XS)) -> c_23(cons^#(X, n__cons(X, n__repItems(activate(XS))))) , repItems^#(nil()) -> c_24() , tail^#(cons(X, XS)) -> c_21(activate^#(XS)) } Strict Trs: { pairNs() -> cons(0(), n__incr(n__oddNs())) , cons(X1, X2) -> n__cons(X1, X2) , oddNs() -> n__oddNs() , oddNs() -> incr(pairNs()) , incr(X) -> n__incr(X) , incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) , activate(X) -> X , activate(n__incr(X)) -> incr(activate(X)) , activate(n__oddNs()) -> oddNs() , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) , activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2)) , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) , activate(n__repItems(X)) -> repItems(activate(X)) , take(X1, X2) -> n__take(X1, X2) , take(0(), XS) -> nil() , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) , zip(X1, X2) -> n__zip(X1, X2) , zip(X, nil()) -> nil() , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS))) , zip(nil(), XS) -> nil() , tail(cons(X, XS)) -> activate(XS) , repItems(X) -> n__repItems(X) , repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS)))) , repItems(nil()) -> nil() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,15,18,20,23} by applications of Pre({3,15,18,20,23}) = {2,5,7,9,10,11,13,14,17,21}. Here rules are labeled as follows: DPs: { 1: pairNs^#() -> c_1(cons^#(0(), n__incr(n__oddNs()))) , 2: cons^#(X1, X2) -> c_2(X1, X2) , 3: oddNs^#() -> c_3() , 4: oddNs^#() -> c_4(incr^#(pairNs())) , 5: incr^#(X) -> c_5(X) , 6: incr^#(cons(X, XS)) -> c_6(cons^#(s(X), n__incr(activate(XS)))) , 7: activate^#(X) -> c_7(X) , 8: activate^#(n__incr(X)) -> c_8(incr^#(activate(X))) , 9: activate^#(n__oddNs()) -> c_9(oddNs^#()) , 10: activate^#(n__take(X1, X2)) -> c_10(take^#(activate(X1), activate(X2))) , 11: activate^#(n__zip(X1, X2)) -> c_11(zip^#(activate(X1), activate(X2))) , 12: activate^#(n__cons(X1, X2)) -> c_12(cons^#(activate(X1), X2)) , 13: activate^#(n__repItems(X)) -> c_13(repItems^#(activate(X))) , 14: take^#(X1, X2) -> c_14(X1, X2) , 15: take^#(0(), XS) -> c_15() , 16: take^#(s(N), cons(X, XS)) -> c_16(cons^#(X, n__take(N, activate(XS)))) , 17: zip^#(X1, X2) -> c_17(X1, X2) , 18: zip^#(X, nil()) -> c_18() , 19: zip^#(cons(X, XS), cons(Y, YS)) -> c_19(cons^#(pair(X, Y), n__zip(activate(XS), activate(YS)))) , 20: zip^#(nil(), XS) -> c_20() , 21: repItems^#(X) -> c_22(X) , 22: repItems^#(cons(X, XS)) -> c_23(cons^#(X, n__cons(X, n__repItems(activate(XS))))) , 23: repItems^#(nil()) -> c_24() , 24: tail^#(cons(X, XS)) -> c_21(activate^#(XS)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { pairNs^#() -> c_1(cons^#(0(), n__incr(n__oddNs()))) , cons^#(X1, X2) -> c_2(X1, X2) , oddNs^#() -> c_4(incr^#(pairNs())) , incr^#(X) -> c_5(X) , incr^#(cons(X, XS)) -> c_6(cons^#(s(X), n__incr(activate(XS)))) , activate^#(X) -> c_7(X) , activate^#(n__incr(X)) -> c_8(incr^#(activate(X))) , activate^#(n__oddNs()) -> c_9(oddNs^#()) , activate^#(n__take(X1, X2)) -> c_10(take^#(activate(X1), activate(X2))) , activate^#(n__zip(X1, X2)) -> c_11(zip^#(activate(X1), activate(X2))) , activate^#(n__cons(X1, X2)) -> c_12(cons^#(activate(X1), X2)) , activate^#(n__repItems(X)) -> c_13(repItems^#(activate(X))) , take^#(X1, X2) -> c_14(X1, X2) , take^#(s(N), cons(X, XS)) -> c_16(cons^#(X, n__take(N, activate(XS)))) , zip^#(X1, X2) -> c_17(X1, X2) , zip^#(cons(X, XS), cons(Y, YS)) -> c_19(cons^#(pair(X, Y), n__zip(activate(XS), activate(YS)))) , repItems^#(X) -> c_22(X) , repItems^#(cons(X, XS)) -> c_23(cons^#(X, n__cons(X, n__repItems(activate(XS))))) , tail^#(cons(X, XS)) -> c_21(activate^#(XS)) } Strict Trs: { pairNs() -> cons(0(), n__incr(n__oddNs())) , cons(X1, X2) -> n__cons(X1, X2) , oddNs() -> n__oddNs() , oddNs() -> incr(pairNs()) , incr(X) -> n__incr(X) , incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) , activate(X) -> X , activate(n__incr(X)) -> incr(activate(X)) , activate(n__oddNs()) -> oddNs() , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) , activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2)) , activate(n__cons(X1, X2)) -> cons(activate(X1), X2) , activate(n__repItems(X)) -> repItems(activate(X)) , take(X1, X2) -> n__take(X1, X2) , take(0(), XS) -> nil() , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) , zip(X1, X2) -> n__zip(X1, X2) , zip(X, nil()) -> nil() , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS))) , zip(nil(), XS) -> nil() , tail(cons(X, XS)) -> activate(XS) , repItems(X) -> n__repItems(X) , repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS)))) , repItems(nil()) -> nil() } Weak DPs: { oddNs^#() -> c_3() , take^#(0(), XS) -> c_15() , zip^#(X, nil()) -> c_18() , zip^#(nil(), XS) -> c_20() , repItems^#(nil()) -> c_24() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..