MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(tt(), x) -> f(isDouble(x), s(s(x))) , isDouble(s(s(x))) -> isDouble(x) , isDouble(0()) -> tt() } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { f^#(tt(), x) -> c_1(f^#(isDouble(x), s(s(x))), isDouble^#(x)) , isDouble^#(s(s(x))) -> c_2(isDouble^#(x)) , isDouble^#(0()) -> 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^#(tt(), x) -> c_1(f^#(isDouble(x), s(s(x))), isDouble^#(x)) , isDouble^#(s(s(x))) -> c_2(isDouble^#(x)) , isDouble^#(0()) -> c_3() } Weak Trs: { f(tt(), x) -> f(isDouble(x), s(s(x))) , isDouble(s(s(x))) -> isDouble(x) , isDouble(0()) -> tt() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {1,2}. Here rules are labeled as follows: DPs: { 1: f^#(tt(), x) -> c_1(f^#(isDouble(x), s(s(x))), isDouble^#(x)) , 2: isDouble^#(s(s(x))) -> c_2(isDouble^#(x)) , 3: isDouble^#(0()) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(tt(), x) -> c_1(f^#(isDouble(x), s(s(x))), isDouble^#(x)) , isDouble^#(s(s(x))) -> c_2(isDouble^#(x)) } Weak DPs: { isDouble^#(0()) -> c_3() } Weak Trs: { f(tt(), x) -> f(isDouble(x), s(s(x))) , isDouble(s(s(x))) -> isDouble(x) , isDouble(0()) -> tt() } 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. { isDouble^#(0()) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(tt(), x) -> c_1(f^#(isDouble(x), s(s(x))), isDouble^#(x)) , isDouble^#(s(s(x))) -> c_2(isDouble^#(x)) } Weak Trs: { f(tt(), x) -> f(isDouble(x), s(s(x))) , isDouble(s(s(x))) -> isDouble(x) , isDouble(0()) -> tt() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Weak Usable Rules: { isDouble(s(s(x))) -> isDouble(x) , isDouble(0()) -> tt() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(tt(), x) -> c_1(f^#(isDouble(x), s(s(x))), isDouble^#(x)) , isDouble^#(s(s(x))) -> c_2(isDouble^#(x)) } Weak Trs: { isDouble(s(s(x))) -> isDouble(x) , isDouble(0()) -> tt() } 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..