MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) , if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) , if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2,3} by applications of Pre({2,3}) = {1}. Here rules are labeled as follows: DPs: { 1: f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) , 2: if^#(true(), X, Y) -> c_2() , 3: if^#(false(), X, Y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) } Weak DPs: { if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } 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. { if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(true())) } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } 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: { f^#(X) -> c_1(f^#(true())) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..