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