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