MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { +(1(), x) -> +(+(0(), 1()), x) , +(0(), x) -> x } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { +^#(1(), x) -> c_1(+^#(+(0(), 1()), x), +^#(0(), 1())) , +^#(0(), x) -> c_2() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { +^#(1(), x) -> c_1(+^#(+(0(), 1()), x), +^#(0(), 1())) , +^#(0(), x) -> c_2() } Weak Trs: { +(1(), x) -> +(+(0(), 1()), x) , +(0(), x) -> x } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2} by applications of Pre({2}) = {1}. Here rules are labeled as follows: DPs: { 1: +^#(1(), x) -> c_1(+^#(+(0(), 1()), x), +^#(0(), 1())) , 2: +^#(0(), x) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { +^#(1(), x) -> c_1(+^#(+(0(), 1()), x), +^#(0(), 1())) } Weak DPs: { +^#(0(), x) -> c_2() } Weak Trs: { +(1(), x) -> +(+(0(), 1()), x) , +(0(), x) -> x } 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. { +^#(0(), x) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { +^#(1(), x) -> c_1(+^#(+(0(), 1()), x), +^#(0(), 1())) } Weak Trs: { +(1(), x) -> +(+(0(), 1()), x) , +(0(), x) -> x } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { +^#(1(), x) -> c_1(+^#(+(0(), 1()), x), +^#(0(), 1())) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { +^#(1(), x) -> c_1(+^#(+(0(), 1()), x)) } Weak Trs: { +(1(), x) -> +(+(0(), 1()), x) , +(0(), x) -> x } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..