MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)) , active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3) , active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3) , active(filter(cons(X, Y), 0(), M)) -> mark(cons(0(), filter(Y, M, M))) , active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))) , active(cons(X1, X2)) -> cons(active(X1), X2) , active(s(X)) -> s(active(X)) , active(sieve(X)) -> sieve(active(X)) , active(sieve(cons(0(), Y))) -> mark(cons(0(), sieve(Y))) , active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))) , active(nats(N)) -> mark(cons(N, nats(s(N)))) , active(nats(X)) -> nats(active(X)) , active(zprimes()) -> mark(sieve(nats(s(s(0()))))) , filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3)) , filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3)) , filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3)) , filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3)) , cons(mark(X1), X2) -> mark(cons(X1, X2)) , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , sieve(mark(X)) -> mark(sieve(X)) , sieve(ok(X)) -> ok(sieve(X)) , nats(mark(X)) -> mark(nats(X)) , nats(ok(X)) -> ok(nats(X)) , proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3)) , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) , proper(0()) -> ok(0()) , proper(s(X)) -> s(proper(X)) , proper(sieve(X)) -> sieve(proper(X)) , proper(nats(X)) -> nats(proper(X)) , proper(zprimes()) -> ok(zprimes()) , 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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'bsearch-popstar (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..