MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { pred(s(x)) -> x , minus(x, s(y)) -> pred(minus(x, y)) , minus(x, 0()) -> x , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) , quot(0(), s(y)) -> 0() , log(s(s(x))) -> s(log(s(quot(x, s(s(0())))))) , log(s(0())) -> 0() } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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) '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) '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 processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { pred^#(s(x)) -> c_1(x) , minus^#(x, s(y)) -> c_2(pred^#(minus(x, y))) , minus^#(x, 0()) -> c_3(x) , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) , quot^#(0(), s(y)) -> c_5() , log^#(s(s(x))) -> c_6(log^#(s(quot(x, s(s(0())))))) , log^#(s(0())) -> c_7() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { pred^#(s(x)) -> c_1(x) , minus^#(x, s(y)) -> c_2(pred^#(minus(x, y))) , minus^#(x, 0()) -> c_3(x) , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) , quot^#(0(), s(y)) -> c_5() , log^#(s(s(x))) -> c_6(log^#(s(quot(x, s(s(0())))))) , log^#(s(0())) -> c_7() } Strict Trs: { pred(s(x)) -> x , minus(x, s(y)) -> pred(minus(x, y)) , minus(x, 0()) -> x , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) , quot(0(), s(y)) -> 0() , log(s(s(x))) -> s(log(s(quot(x, s(s(0())))))) , log(s(0())) -> 0() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {5,7} by applications of Pre({5,7}) = {1,3,4,6}. Here rules are labeled as follows: DPs: { 1: pred^#(s(x)) -> c_1(x) , 2: minus^#(x, s(y)) -> c_2(pred^#(minus(x, y))) , 3: minus^#(x, 0()) -> c_3(x) , 4: quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) , 5: quot^#(0(), s(y)) -> c_5() , 6: log^#(s(s(x))) -> c_6(log^#(s(quot(x, s(s(0())))))) , 7: log^#(s(0())) -> c_7() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { pred^#(s(x)) -> c_1(x) , minus^#(x, s(y)) -> c_2(pred^#(minus(x, y))) , minus^#(x, 0()) -> c_3(x) , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) , log^#(s(s(x))) -> c_6(log^#(s(quot(x, s(s(0())))))) } Strict Trs: { pred(s(x)) -> x , minus(x, s(y)) -> pred(minus(x, y)) , minus(x, 0()) -> x , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) , quot(0(), s(y)) -> 0() , log(s(s(x))) -> s(log(s(quot(x, s(s(0())))))) , log(s(0())) -> 0() } Weak DPs: { quot^#(0(), s(y)) -> c_5() , log^#(s(0())) -> c_7() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..