MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { equal0(Nil()) -> number42(Nil()) , equal0(Cons(x, xs)) -> equal0(Cons(x, xs)) , number42(x) -> Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Nil())))))))))))))))))))))))))))))))))))))))))) , goal(x) -> equal0(x) } Obligation: innermost runtime complexity Answer: MAYBE 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) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: We add the following innermost weak dependency pairs: Strict DPs: { equal0^#(Nil()) -> c_1(number42^#(Nil())) , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) , number42^#(x) -> c_3() , goal^#(x) -> c_4(equal0^#(x)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1(number42^#(Nil())) , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) , number42^#(x) -> c_3() , goal^#(x) -> c_4(equal0^#(x)) } Strict Trs: { equal0(Nil()) -> number42(Nil()) , equal0(Cons(x, xs)) -> equal0(Cons(x, xs)) , number42(x) -> Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Cons(Nil(), Nil())))))))))))))))))))))))))))))))))))))))))) , goal(x) -> equal0(x) } Obligation: innermost runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1(number42^#(Nil())) , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) , number42^#(x) -> c_3() , goal^#(x) -> c_4(equal0^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_4) = {1} TcT has computed the following constructor-restricted matrix interpretation. [Nil] = [0] [0] [Cons](x1, x2) = [1 0] x1 + [1 0] x2 + [0] [0 0] [0 0] [0] [equal0^#](x1) = [0] [0] [c_1](x1) = [1 0] x1 + [1] [0 1] [0] [number42^#](x1) = [1 2] x1 + [0] [2 1] [0] [c_2](x1) = [1 0] x1 + [1] [0 1] [1] [c_3] = [1] [0] [goal^#](x1) = [1 2] x1 + [2] [2 1] [2] [c_4](x1) = [1 0] x1 + [1] [0 1] [2] The following symbols are considered usable {equal0^#, number42^#, goal^#} The order satisfies the following ordering constraints: [equal0^#(Nil())] = [0] [0] ? [1] [0] = [c_1(number42^#(Nil()))] [equal0^#(Cons(x, xs))] = [0] [0] ? [1] [1] = [c_2(equal0^#(Cons(x, xs)))] [number42^#(x)] = [1 2] x + [0] [2 1] [0] ? [1] [0] = [c_3()] [goal^#(x)] = [1 2] x + [2] [2 1] [2] > [1] [2] = [c_4(equal0^#(x))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1(number42^#(Nil())) , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) , number42^#(x) -> c_3() } Weak DPs: { goal^#(x) -> c_4(equal0^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {1}. Here rules are labeled as follows: DPs: { 1: equal0^#(Nil()) -> c_1(number42^#(Nil())) , 2: equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) , 3: number42^#(x) -> c_3() , 4: goal^#(x) -> c_4(equal0^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1(number42^#(Nil())) , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) } Weak DPs: { number42^#(x) -> c_3() , goal^#(x) -> c_4(equal0^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { number42^#(x) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1(number42^#(Nil())) , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) } Weak DPs: { goal^#(x) -> c_4(equal0^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { equal0^#(Nil()) -> c_1(number42^#(Nil())) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1() , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) } Weak DPs: { goal^#(x) -> c_3(equal0^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE Consider the dependency graph 1: equal0^#(Nil()) -> c_1() 2: equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) -->_1 equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) :2 3: goal^#(x) -> c_3(equal0^#(x)) -->_1 equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) :2 -->_1 equal0^#(Nil()) -> c_1() :1 Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts). { goal^#(x) -> c_3(equal0^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Nil()) -> c_1() , equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) } Obligation: innermost runtime complexity Answer: MAYBE Consider the dependency graph 1: equal0^#(Nil()) -> c_1() 2: equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) -->_1 equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) :2 Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts). { equal0^#(Nil()) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) } Obligation: innermost runtime complexity Answer: MAYBE 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) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 2) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 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) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) '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 input cannot be shown compatible 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible Arrrr..