MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { from(X) -> cons(X, from(s(X))) , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X , 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(XS, nil()) -> nil() , zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, 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: 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) 'WithProblem' failed due to the following reason: 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) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: 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) 'WithProblem' failed due to the following reason: 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) 'WithProblem' failed due to the following reason: 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) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: 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) 'WithProblem' 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) '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, from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_3(X) , minus^#(X, 0()) -> c_4() , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , zWquot^#(nil(), XS) -> c_10() } 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, from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_3(X) , minus^#(X, 0()) -> c_4() , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , zWquot^#(nil(), XS) -> c_10() } Strict Trs: { from(X) -> cons(X, from(s(X))) , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X , 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(XS, nil()) -> nil() , zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS)) , zWquot(nil(), XS) -> nil() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4,7,8,10} by applications of Pre({4,7,8,10}) = {1,3,5,6,9}. Here rules are labeled as follows: DPs: { 1: from^#(X) -> c_1(X, from^#(s(X))) , 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , 3: sel^#(0(), cons(X, XS)) -> c_3(X) , 4: minus^#(X, 0()) -> c_4() , 5: minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , 6: quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , 7: quot^#(0(), s(Y)) -> c_7() , 8: zWquot^#(XS, nil()) -> c_8() , 9: zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) , 10: zWquot^#(nil(), XS) -> c_10() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_1(X, from^#(s(X))) , sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) , sel^#(0(), cons(X, XS)) -> c_3(X) , minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y)) , quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y))) , zWquot^#(cons(X, XS), cons(Y, YS)) -> c_9(quot^#(X, Y), zWquot^#(XS, YS)) } Strict Trs: { from(X) -> cons(X, from(s(X))) , sel(s(N), cons(X, XS)) -> sel(N, XS) , sel(0(), cons(X, XS)) -> X , 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(XS, nil()) -> nil() , zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS)) , zWquot(nil(), XS) -> nil() } Weak DPs: { minus^#(X, 0()) -> c_4() , quot^#(0(), s(Y)) -> c_7() , zWquot^#(XS, nil()) -> c_8() , zWquot^#(nil(), XS) -> c_10() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..