MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { fact(X) -> if(zero(X), n__s(0()), n__prod(X, fact(p(X)))) , if(true(), X, Y) -> activate(X) , if(false(), X, Y) -> activate(Y) , zero(0()) -> true() , zero(s(X)) -> false() , p(s(X)) -> X , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , s(X) -> n__s(X) , prod(X1, X2) -> n__prod(X1, X2) , prod(0(), X) -> 0() , prod(s(X), Y) -> add(Y, prod(X, Y)) , activate(X) -> X , activate(n__s(X)) -> s(X) , activate(n__prod(X1, X2)) -> prod(X1, X2) } 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) '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. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { fact^#(X) -> c_1(if^#(zero(X), n__s(0()), n__prod(X, fact(p(X))))) , if^#(true(), X, Y) -> c_2(activate^#(X)) , if^#(false(), X, Y) -> c_3(activate^#(Y)) , activate^#(X) -> c_13(X) , activate^#(n__s(X)) -> c_14(s^#(X)) , activate^#(n__prod(X1, X2)) -> c_15(prod^#(X1, X2)) , zero^#(0()) -> c_4() , zero^#(s(X)) -> c_5() , p^#(s(X)) -> c_6(X) , add^#(0(), X) -> c_7(X) , add^#(s(X), Y) -> c_8(s^#(add(X, Y))) , s^#(X) -> c_9(X) , prod^#(X1, X2) -> c_10(X1, X2) , prod^#(0(), X) -> c_11() , prod^#(s(X), Y) -> c_12(add^#(Y, prod(X, Y))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fact^#(X) -> c_1(if^#(zero(X), n__s(0()), n__prod(X, fact(p(X))))) , if^#(true(), X, Y) -> c_2(activate^#(X)) , if^#(false(), X, Y) -> c_3(activate^#(Y)) , activate^#(X) -> c_13(X) , activate^#(n__s(X)) -> c_14(s^#(X)) , activate^#(n__prod(X1, X2)) -> c_15(prod^#(X1, X2)) , zero^#(0()) -> c_4() , zero^#(s(X)) -> c_5() , p^#(s(X)) -> c_6(X) , add^#(0(), X) -> c_7(X) , add^#(s(X), Y) -> c_8(s^#(add(X, Y))) , s^#(X) -> c_9(X) , prod^#(X1, X2) -> c_10(X1, X2) , prod^#(0(), X) -> c_11() , prod^#(s(X), Y) -> c_12(add^#(Y, prod(X, Y))) } Strict Trs: { fact(X) -> if(zero(X), n__s(0()), n__prod(X, fact(p(X)))) , if(true(), X, Y) -> activate(X) , if(false(), X, Y) -> activate(Y) , zero(0()) -> true() , zero(s(X)) -> false() , p(s(X)) -> X , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , s(X) -> n__s(X) , prod(X1, X2) -> n__prod(X1, X2) , prod(0(), X) -> 0() , prod(s(X), Y) -> add(Y, prod(X, Y)) , activate(X) -> X , activate(n__s(X)) -> s(X) , activate(n__prod(X1, X2)) -> prod(X1, X2) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {7,8,14} by applications of Pre({7,8,14}) = {4,6,9,10,12,13}. Here rules are labeled as follows: DPs: { 1: fact^#(X) -> c_1(if^#(zero(X), n__s(0()), n__prod(X, fact(p(X))))) , 2: if^#(true(), X, Y) -> c_2(activate^#(X)) , 3: if^#(false(), X, Y) -> c_3(activate^#(Y)) , 4: activate^#(X) -> c_13(X) , 5: activate^#(n__s(X)) -> c_14(s^#(X)) , 6: activate^#(n__prod(X1, X2)) -> c_15(prod^#(X1, X2)) , 7: zero^#(0()) -> c_4() , 8: zero^#(s(X)) -> c_5() , 9: p^#(s(X)) -> c_6(X) , 10: add^#(0(), X) -> c_7(X) , 11: add^#(s(X), Y) -> c_8(s^#(add(X, Y))) , 12: s^#(X) -> c_9(X) , 13: prod^#(X1, X2) -> c_10(X1, X2) , 14: prod^#(0(), X) -> c_11() , 15: prod^#(s(X), Y) -> c_12(add^#(Y, prod(X, Y))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fact^#(X) -> c_1(if^#(zero(X), n__s(0()), n__prod(X, fact(p(X))))) , if^#(true(), X, Y) -> c_2(activate^#(X)) , if^#(false(), X, Y) -> c_3(activate^#(Y)) , activate^#(X) -> c_13(X) , activate^#(n__s(X)) -> c_14(s^#(X)) , activate^#(n__prod(X1, X2)) -> c_15(prod^#(X1, X2)) , p^#(s(X)) -> c_6(X) , add^#(0(), X) -> c_7(X) , add^#(s(X), Y) -> c_8(s^#(add(X, Y))) , s^#(X) -> c_9(X) , prod^#(X1, X2) -> c_10(X1, X2) , prod^#(s(X), Y) -> c_12(add^#(Y, prod(X, Y))) } Strict Trs: { fact(X) -> if(zero(X), n__s(0()), n__prod(X, fact(p(X)))) , if(true(), X, Y) -> activate(X) , if(false(), X, Y) -> activate(Y) , zero(0()) -> true() , zero(s(X)) -> false() , p(s(X)) -> X , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , s(X) -> n__s(X) , prod(X1, X2) -> n__prod(X1, X2) , prod(0(), X) -> 0() , prod(s(X), Y) -> add(Y, prod(X, Y)) , activate(X) -> X , activate(n__s(X)) -> s(X) , activate(n__prod(X1, X2)) -> prod(X1, X2) } Weak DPs: { zero^#(0()) -> c_4() , zero^#(s(X)) -> c_5() , prod^#(0(), X) -> c_11() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..