MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond1(true(), x) -> cond2(even(x), x) , cond2(true(), x) -> cond1(neq(x, 0()), div2(x)) , cond2(false(), x) -> cond1(neq(x, 0()), p(x)) , even(0()) -> true() , even(s(0())) -> false() , even(s(s(x))) -> even(x) , neq(0(), 0()) -> false() , neq(0(), s(x)) -> true() , neq(s(x), 0()) -> true() , neq(s(x), s(y())) -> neq(x, y()) , div2(0()) -> 0() , div2(s(0())) -> 0() , div2(s(s(x))) -> s(div2(x)) , p(0()) -> 0() , p(s(x)) -> x } 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: 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: 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: 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) '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 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. 2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { cond1^#(true(), x) -> c_1(cond2^#(even(x), x)) , cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x))) , cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x))) , even^#(0()) -> c_4() , even^#(s(0())) -> c_5() , even^#(s(s(x))) -> c_6(even^#(x)) , neq^#(0(), 0()) -> c_7() , neq^#(0(), s(x)) -> c_8() , neq^#(s(x), 0()) -> c_9() , neq^#(s(x), s(y())) -> c_10(neq^#(x, y())) , div2^#(0()) -> c_11() , div2^#(s(0())) -> c_12() , div2^#(s(s(x))) -> c_13(div2^#(x)) , p^#(0()) -> c_14() , p^#(s(x)) -> c_15(x) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(true(), x) -> c_1(cond2^#(even(x), x)) , cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x))) , cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x))) , even^#(0()) -> c_4() , even^#(s(0())) -> c_5() , even^#(s(s(x))) -> c_6(even^#(x)) , neq^#(0(), 0()) -> c_7() , neq^#(0(), s(x)) -> c_8() , neq^#(s(x), 0()) -> c_9() , neq^#(s(x), s(y())) -> c_10(neq^#(x, y())) , div2^#(0()) -> c_11() , div2^#(s(0())) -> c_12() , div2^#(s(s(x))) -> c_13(div2^#(x)) , p^#(0()) -> c_14() , p^#(s(x)) -> c_15(x) } Strict Trs: { cond1(true(), x) -> cond2(even(x), x) , cond2(true(), x) -> cond1(neq(x, 0()), div2(x)) , cond2(false(), x) -> cond1(neq(x, 0()), p(x)) , even(0()) -> true() , even(s(0())) -> false() , even(s(s(x))) -> even(x) , neq(0(), 0()) -> false() , neq(0(), s(x)) -> true() , neq(s(x), 0()) -> true() , neq(s(x), s(y())) -> neq(x, y()) , div2(0()) -> 0() , div2(s(0())) -> 0() , div2(s(s(x))) -> s(div2(x)) , p(0()) -> 0() , p(s(x)) -> x } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4,5,7,8,9,10,11,12,14} by applications of Pre({4,5,7,8,9,10,11,12,14}) = {6,13,15}. Here rules are labeled as follows: DPs: { 1: cond1^#(true(), x) -> c_1(cond2^#(even(x), x)) , 2: cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x))) , 3: cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x))) , 4: even^#(0()) -> c_4() , 5: even^#(s(0())) -> c_5() , 6: even^#(s(s(x))) -> c_6(even^#(x)) , 7: neq^#(0(), 0()) -> c_7() , 8: neq^#(0(), s(x)) -> c_8() , 9: neq^#(s(x), 0()) -> c_9() , 10: neq^#(s(x), s(y())) -> c_10(neq^#(x, y())) , 11: div2^#(0()) -> c_11() , 12: div2^#(s(0())) -> c_12() , 13: div2^#(s(s(x))) -> c_13(div2^#(x)) , 14: p^#(0()) -> c_14() , 15: p^#(s(x)) -> c_15(x) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(true(), x) -> c_1(cond2^#(even(x), x)) , cond2^#(true(), x) -> c_2(cond1^#(neq(x, 0()), div2(x))) , cond2^#(false(), x) -> c_3(cond1^#(neq(x, 0()), p(x))) , even^#(s(s(x))) -> c_6(even^#(x)) , div2^#(s(s(x))) -> c_13(div2^#(x)) , p^#(s(x)) -> c_15(x) } Strict Trs: { cond1(true(), x) -> cond2(even(x), x) , cond2(true(), x) -> cond1(neq(x, 0()), div2(x)) , cond2(false(), x) -> cond1(neq(x, 0()), p(x)) , even(0()) -> true() , even(s(0())) -> false() , even(s(s(x))) -> even(x) , neq(0(), 0()) -> false() , neq(0(), s(x)) -> true() , neq(s(x), 0()) -> true() , neq(s(x), s(y())) -> neq(x, y()) , div2(0()) -> 0() , div2(s(0())) -> 0() , div2(s(s(x))) -> s(div2(x)) , p(0()) -> 0() , p(s(x)) -> x } Weak DPs: { even^#(0()) -> c_4() , even^#(s(0())) -> c_5() , neq^#(0(), 0()) -> c_7() , neq^#(0(), s(x)) -> c_8() , neq^#(s(x), 0()) -> c_9() , neq^#(s(x), s(y())) -> c_10(neq^#(x, y())) , div2^#(0()) -> c_11() , div2^#(s(0())) -> c_12() , p^#(0()) -> c_14() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..