MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(X) -> c_1(f^#(g(X)), g^#(X)) , g^#(0()) -> c_2() , g^#(s(X)) -> c_3(g^#(X)) , sel^#(0(), cons(X, Y)) -> c_4() , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(g(X)), g^#(X)) , g^#(0()) -> c_2() , g^#(s(X)) -> c_3(g^#(X)) , sel^#(0(), cons(X, Y)) -> c_4() , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) } Weak Trs: { f(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2,4} by applications of Pre({2,4}) = {1,3,5}. Here rules are labeled as follows: DPs: { 1: f^#(X) -> c_1(f^#(g(X)), g^#(X)) , 2: g^#(0()) -> c_2() , 3: g^#(s(X)) -> c_3(g^#(X)) , 4: sel^#(0(), cons(X, Y)) -> c_4() , 5: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(g(X)), g^#(X)) , g^#(s(X)) -> c_3(g^#(X)) , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) } Weak DPs: { g^#(0()) -> c_2() , sel^#(0(), cons(X, Y)) -> c_4() } Weak Trs: { f(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } 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. { g^#(0()) -> c_2() , sel^#(0(), cons(X, Y)) -> c_4() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(g(X)), g^#(X)) , g^#(s(X)) -> c_3(g^#(X)) , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) } Weak Trs: { f(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Weak Usable Rules: { g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(g(X)), g^#(X)) , g^#(s(X)) -> c_3(g^#(X)) , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) } Weak Trs: { g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrices' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrix interpretation of dimension 4' failed due to the following reason: The input cannot be shown compatible 2) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 3) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 4) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 5) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 6) 'matrix interpretation of dimension 1' failed due to the following reason: The input cannot be shown compatible 2) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. Arrrr..