MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(U11(X1, X2, X3, X4)) -> U11(active(X1), X2, X3, X4) , active(U11(tt(), N, X, XS)) -> mark(U12(splitAt(N, XS), X)) , active(U12(X1, X2)) -> U12(active(X1), X2) , active(U12(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) , active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) , active(splitAt(X1, X2)) -> splitAt(active(X1), X2) , active(splitAt(s(N), cons(X, XS))) -> mark(U11(tt(), N, X, XS)) , active(splitAt(0(), XS)) -> mark(pair(nil(), XS)) , active(pair(X1, X2)) -> pair(X1, active(X2)) , active(pair(X1, X2)) -> pair(active(X1), X2) , active(cons(X1, X2)) -> cons(active(X1), X2) , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS))) , active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) , active(afterNth(X1, X2)) -> afterNth(active(X1), X2) , active(snd(X)) -> snd(active(X)) , active(snd(pair(X, Y))) -> mark(Y) , active(and(X1, X2)) -> and(active(X1), X2) , active(and(tt(), X)) -> mark(X) , active(fst(X)) -> fst(active(X)) , active(fst(pair(X, Y))) -> mark(X) , active(head(X)) -> head(active(X)) , active(head(cons(N, XS))) -> mark(N) , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N)))) , active(natsFrom(X)) -> natsFrom(active(X)) , active(s(X)) -> s(active(X)) , active(sel(N, XS)) -> mark(head(afterNth(N, XS))) , active(sel(X1, X2)) -> sel(X1, active(X2)) , active(sel(X1, X2)) -> sel(active(X1), X2) , active(tail(X)) -> tail(active(X)) , active(tail(cons(N, XS))) -> mark(XS) , active(take(N, XS)) -> mark(fst(splitAt(N, XS))) , active(take(X1, X2)) -> take(X1, active(X2)) , active(take(X1, X2)) -> take(active(X1), X2) , U11(mark(X1), X2, X3, X4) -> mark(U11(X1, X2, X3, X4)) , U11(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U11(X1, X2, X3, X4)) , U12(mark(X1), X2) -> mark(U12(X1, X2)) , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) , 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)) , 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)) , cons(mark(X1), X2) -> mark(cons(X1, X2)) , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) , 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)) , snd(mark(X)) -> mark(snd(X)) , snd(ok(X)) -> ok(snd(X)) , and(mark(X1), X2) -> mark(and(X1, X2)) , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) , fst(mark(X)) -> mark(fst(X)) , fst(ok(X)) -> ok(fst(X)) , head(mark(X)) -> mark(head(X)) , head(ok(X)) -> ok(head(X)) , natsFrom(mark(X)) -> mark(natsFrom(X)) , natsFrom(ok(X)) -> ok(natsFrom(X)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , 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)) , 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)) , proper(U11(X1, X2, X3, X4)) -> U11(proper(X1), proper(X2), proper(X3), proper(X4)) , proper(tt()) -> ok(tt()) , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) , proper(snd(X)) -> snd(proper(X)) , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) , proper(fst(X)) -> fst(proper(X)) , proper(head(X)) -> head(proper(X)) , proper(natsFrom(X)) -> natsFrom(proper(X)) , proper(s(X)) -> s(proper(X)) , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) , proper(0()) -> ok(0()) , proper(nil()) -> ok(nil()) , proper(tail(X)) -> tail(proper(X)) , proper(take(X1, X2)) -> take(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 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. Arrrr..