MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { zeros() -> cons(0(), zeros()) , and(tt(), X) -> X , length(cons(N, L)) -> s(length(L)) , length(nil()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { zeros^#() -> c_1(zeros^#()) , and^#(tt(), X) -> c_2() , length^#(cons(N, L)) -> c_3(length^#(L)) , length^#(nil()) -> c_4() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { zeros^#() -> c_1(zeros^#()) , and^#(tt(), X) -> c_2() , length^#(cons(N, L)) -> c_3(length^#(L)) , length^#(nil()) -> c_4() } Strict Trs: { zeros() -> cons(0(), zeros()) , and(tt(), X) -> X , length(cons(N, L)) -> s(length(L)) , length(nil()) -> 0() } 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: { zeros^#() -> c_1(zeros^#()) , and^#(tt(), X) -> c_2() , length^#(cons(N, L)) -> c_3(length^#(L)) , length^#(nil()) -> c_4() } 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_3) = {1} TcT has computed following constructor-restricted matrix interpretation. [cons](x1, x2) = [1] x2 + [1] [tt] = [1] [nil] = [2] [zeros^#] = [2] [c_1](x1) = [1] x1 + [1] [and^#](x1, x2) = [1] x1 + [2] [c_2] = [2] [length^#](x1) = [2] x1 + [2] [c_3](x1) = [1] x1 + [1] [c_4] = [1] This order satisfies following ordering constraints: 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: { zeros^#() -> c_1(zeros^#()) } Weak DPs: { and^#(tt(), X) -> c_2() , length^#(cons(N, L)) -> c_3(length^#(L)) , length^#(nil()) -> c_4() } 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. { and^#(tt(), X) -> c_2() , length^#(cons(N, L)) -> c_3(length^#(L)) , length^#(nil()) -> c_4() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { zeros^#() -> c_1(zeros^#()) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..