MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x))) , round^#(s(s(x))) -> c_2(round^#(x)) , round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x))) , round^#(s(s(x))) -> c_2(round^#(x)) , round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } Weak Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3,4,5} by applications of Pre({3,4,5}) = {1,2}. Here rules are labeled as follows: DPs: { 1: f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x))) , 2: round^#(s(s(x))) -> c_2(round^#(x)) , 3: round^#(s(0())) -> c_3() , 4: round^#(0()) -> c_4() , 5: round^#(0()) -> c_5() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x))) , round^#(s(s(x))) -> c_2(round^#(x)) } Weak DPs: { round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } Weak Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } 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. { round^#(s(0())) -> c_3() , round^#(0()) -> c_4() , round^#(0()) -> c_5() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x))) , round^#(s(s(x))) -> c_2(round^#(x)) } Weak Trs: { f(s(x), x) -> f(s(x), round(s(x))) , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Weak Usable Rules: { round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x))) , round^#(s(s(x))) -> c_2(round^#(x)) } Weak Trs: { round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(0()) , round(0()) -> s(0()) , round(0()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrices' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrix interpretation of dimension 4' failed due to the following reason: The input cannot be shown compatible 2) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 3) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 4) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 5) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 6) 'matrix interpretation of dimension 1' failed due to the following reason: The input cannot be shown compatible 2) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. Arrrr..