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