MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a(x1) -> x1 , a(x1) -> b(c(x1)) , c(b(b(b(x1)))) -> b(a(b(a(x1)))) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { a^#(x1) -> c_1() , a^#(x1) -> c_2(c^#(x1)) , c^#(b(b(b(x1)))) -> c_3(a^#(b(a(x1))), a^#(x1)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a^#(x1) -> c_1() , a^#(x1) -> c_2(c^#(x1)) , c^#(b(b(b(x1)))) -> c_3(a^#(b(a(x1))), a^#(x1)) } Weak Trs: { a(x1) -> x1 , a(x1) -> b(c(x1)) , c(b(b(b(x1)))) -> b(a(b(a(x1)))) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1} by applications of Pre({1}) = {3}. Here rules are labeled as follows: DPs: { 1: a^#(x1) -> c_1() , 2: a^#(x1) -> c_2(c^#(x1)) , 3: c^#(b(b(b(x1)))) -> c_3(a^#(b(a(x1))), a^#(x1)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a^#(x1) -> c_2(c^#(x1)) , c^#(b(b(b(x1)))) -> c_3(a^#(b(a(x1))), a^#(x1)) } Weak DPs: { a^#(x1) -> c_1() } Weak Trs: { a(x1) -> x1 , a(x1) -> b(c(x1)) , c(b(b(b(x1)))) -> b(a(b(a(x1)))) } 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. { a^#(x1) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a^#(x1) -> c_2(c^#(x1)) , c^#(b(b(b(x1)))) -> c_3(a^#(b(a(x1))), a^#(x1)) } Weak Trs: { a(x1) -> x1 , a(x1) -> b(c(x1)) , c(b(b(b(x1)))) -> b(a(b(a(x1)))) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..