MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond(true(), x, y) -> cond(gr(x, y), p(x), s(y)) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y), p^#(x)) , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) , gr^#(s(x), 0()) -> c_3() , gr^#(0(), x) -> c_4() , p^#(s(x)) -> c_5() , p^#(0()) -> c_6() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y), p^#(x)) , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) , gr^#(s(x), 0()) -> c_3() , gr^#(0(), x) -> c_4() , p^#(s(x)) -> c_5() , p^#(0()) -> c_6() } Weak Trs: { cond(true(), x, y) -> cond(gr(x, y), p(x), s(y)) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3,4,5,6} by applications of Pre({3,4,5,6}) = {1,2}. Here rules are labeled as follows: DPs: { 1: cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y), p^#(x)) , 2: gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) , 3: gr^#(s(x), 0()) -> c_3() , 4: gr^#(0(), x) -> c_4() , 5: p^#(s(x)) -> c_5() , 6: p^#(0()) -> c_6() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y), p^#(x)) , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) } Weak DPs: { gr^#(s(x), 0()) -> c_3() , gr^#(0(), x) -> c_4() , p^#(s(x)) -> c_5() , p^#(0()) -> c_6() } Weak Trs: { cond(true(), x, y) -> cond(gr(x, y), p(x), s(y)) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } 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. { gr^#(s(x), 0()) -> c_3() , gr^#(0(), x) -> c_4() , p^#(s(x)) -> c_5() , p^#(0()) -> c_6() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y), p^#(x)) , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) } Weak Trs: { cond(true(), x, y) -> cond(gr(x, y), p(x), s(y)) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y), p^#(x)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y)) , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) } Weak Trs: { cond(true(), x, y) -> cond(gr(x, y), p(x), s(y)) , gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Weak Usable Rules: { gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), p(x), s(y)), gr^#(x, y)) , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) } Weak Trs: { gr(s(x), s(y)) -> gr(x, y) , gr(s(x), 0()) -> true() , gr(0(), x) -> false() , p(s(x)) -> x , p(0()) -> 0() } 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..