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