MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } 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: 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 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: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x)))) , round^#(s(s(x))) -> c_2(round^#(x)) , round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x)))) , round^#(s(s(x))) -> c_2(round^#(x)) , round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } Strict Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,4,5} by applications of Pre({3,4,5}) = {2}. Here rules are labeled as follows: DPs: { 1: f^#(s(x), x) -> c_1(f^#(s(x), round(s(x)))) , 2: round^#(s(s(x))) -> c_2(round^#(x)) , 3: round^#(s(0())) -> c_3() , 4: round^#(0()) -> c_4() , 5: round^#(0()) -> c_5() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x)))) , round^#(s(s(x))) -> c_2(round^#(x)) } Strict Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } Weak DPs: { round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..