MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) , active(U101(tt(), N, XS)) -> mark(fst(splitAt(N, XS))) , active(fst(X)) -> fst(active(X)) , active(fst(pair(X, Y))) -> mark(U21(and(isLNat(X), isLNat(Y)), X)) , active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) , active(splitAt(X1, X2)) -> splitAt(active(X1), X2) , active(splitAt(s(N), cons(X, XS))) -> mark(U81(and(isNatural(N), and(isNatural(X), isLNat(XS))), N, X, XS)) , active(splitAt(0(), XS)) -> mark(U71(isLNat(XS), XS)) , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) , active(U11(tt(), N, XS)) -> mark(snd(splitAt(N, XS))) , active(snd(X)) -> snd(active(X)) , active(snd(pair(X, Y))) -> mark(U61(and(isLNat(X), isLNat(Y)), Y)) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), X)) -> mark(X) , active(U31(X1, X2)) -> U31(active(X1), X2) , active(U31(tt(), N)) -> mark(N) , active(U41(X1, X2)) -> U41(active(X1), X2) , active(U41(tt(), N)) -> mark(cons(N, natsFrom(s(N)))) , active(cons(X1, X2)) -> cons(active(X1), X2) , active(natsFrom(N)) -> mark(U41(isNatural(N), N)) , active(natsFrom(X)) -> natsFrom(active(X)) , active(s(X)) -> s(active(X)) , active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) , active(U51(tt(), N, XS)) -> mark(head(afterNth(N, XS))) , active(head(X)) -> head(active(X)) , active(head(cons(N, XS))) -> mark(U31(and(isNatural(N), isLNat(XS)), N)) , active(afterNth(N, XS)) -> mark(U11(and(isNatural(N), isLNat(XS)), N, XS)) , active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) , active(afterNth(X1, X2)) -> afterNth(active(X1), X2) , active(U61(X1, X2)) -> U61(active(X1), X2) , active(U61(tt(), Y)) -> mark(Y) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), XS)) -> mark(pair(nil(), XS)) , active(pair(X1, X2)) -> pair(X1, active(X2)) , active(pair(X1, X2)) -> pair(active(X1), X2) , active(U81(X1, X2, X3, X4)) -> U81(active(X1), X2, X3, X4) , active(U81(tt(), N, X, XS)) -> mark(U82(splitAt(N, XS), X)) , active(U82(X1, X2)) -> U82(active(X1), X2) , active(U82(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) , active(U91(X1, X2)) -> U91(active(X1), X2) , active(U91(tt(), XS)) -> mark(XS) , active(and(X1, X2)) -> and(active(X1), X2) , active(and(tt(), X)) -> mark(X) , active(isNatural(s(V1))) -> mark(isNatural(V1)) , active(isNatural(head(V1))) -> mark(isLNat(V1)) , active(isNatural(0())) -> mark(tt()) , active(isNatural(sel(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) , active(isLNat(fst(V1))) -> mark(isPLNat(V1)) , active(isLNat(snd(V1))) -> mark(isPLNat(V1)) , active(isLNat(cons(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) , active(isLNat(natsFrom(V1))) -> mark(isNatural(V1)) , active(isLNat(afterNth(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) , active(isLNat(nil())) -> mark(tt()) , active(isLNat(tail(V1))) -> mark(isLNat(V1)) , active(isLNat(take(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) , active(isPLNat(splitAt(V1, V2))) -> mark(and(isNatural(V1), isLNat(V2))) , active(isPLNat(pair(V1, V2))) -> mark(and(isLNat(V1), isLNat(V2))) , active(tail(X)) -> tail(active(X)) , active(tail(cons(N, XS))) -> mark(U91(and(isNatural(N), isLNat(XS)), XS)) , active(take(N, XS)) -> mark(U101(and(isNatural(N), isLNat(XS)), N, XS)) , active(take(X1, X2)) -> take(X1, active(X2)) , active(take(X1, X2)) -> take(active(X1), X2) , active(sel(N, XS)) -> mark(U51(and(isNatural(N), isLNat(XS)), N, XS)) , active(sel(X1, X2)) -> sel(X1, active(X2)) , active(sel(X1, X2)) -> sel(active(X1), X2) , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) , fst(mark(X)) -> mark(fst(X)) , fst(ok(X)) -> ok(fst(X)) , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) , snd(mark(X)) -> mark(snd(X)) , snd(ok(X)) -> ok(snd(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U31(mark(X1), X2) -> mark(U31(X1, X2)) , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) , U41(mark(X1), X2) -> mark(U41(X1, X2)) , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)) , cons(mark(X1), X2) -> mark(cons(X1, X2)) , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) , natsFrom(mark(X)) -> mark(natsFrom(X)) , natsFrom(ok(X)) -> ok(natsFrom(X)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) , U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) , head(mark(X)) -> mark(head(X)) , head(ok(X)) -> ok(head(X)) , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) , U61(mark(X1), X2) -> mark(U61(X1, X2)) , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , pair(X1, mark(X2)) -> mark(pair(X1, X2)) , pair(mark(X1), X2) -> mark(pair(X1, X2)) , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) , U81(mark(X1), X2, X3, X4) -> mark(U81(X1, X2, X3, X4)) , U81(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U81(X1, X2, X3, X4)) , U82(mark(X1), X2) -> mark(U82(X1, X2)) , U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) , U91(mark(X1), X2) -> mark(U91(X1, X2)) , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) , and(mark(X1), X2) -> mark(and(X1, X2)) , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) , isNatural(ok(X)) -> ok(isNatural(X)) , isLNat(ok(X)) -> ok(isLNat(X)) , isPLNat(ok(X)) -> ok(isPLNat(X)) , tail(mark(X)) -> mark(tail(X)) , tail(ok(X)) -> ok(tail(X)) , take(X1, mark(X2)) -> mark(take(X1, X2)) , take(mark(X1), X2) -> mark(take(X1, X2)) , take(ok(X1), ok(X2)) -> ok(take(X1, X2)) , sel(X1, mark(X2)) -> mark(sel(X1, X2)) , sel(mark(X1), X2) -> mark(sel(X1, X2)) , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) , proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) , proper(tt()) -> ok(tt()) , proper(fst(X)) -> fst(proper(X)) , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) , proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) , proper(snd(X)) -> snd(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) , proper(natsFrom(X)) -> natsFrom(proper(X)) , proper(s(X)) -> s(proper(X)) , proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) , proper(head(X)) -> head(proper(X)) , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) , proper(nil()) -> ok(nil()) , proper(U81(X1, X2, X3, X4)) -> U81(proper(X1), proper(X2), proper(X3), proper(X4)) , proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) , proper(isNatural(X)) -> isNatural(proper(X)) , proper(isLNat(X)) -> isLNat(proper(X)) , proper(isPLNat(X)) -> isPLNat(proper(X)) , proper(tail(X)) -> tail(proper(X)) , proper(take(X1, X2)) -> take(proper(X1), proper(X2)) , proper(0()) -> ok(0()) , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) , top(mark(X)) -> top(proper(X)) , top(ok(X)) -> top(active(X)) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: 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 input cannot be shown compatible 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 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 minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..