MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(x, x) -> f(0(), 1()) , f(x, 2()) -> 2() , f(2(), x) -> 2() , 0() -> 2() , 1() -> 2() } Obligation: innermost runtime complexity Answer: MAYBE We add following weak dependency pairs: Strict DPs: { f^#(x, x) -> c_1(f^#(0(), 1())) , f^#(x, 2()) -> c_2() , f^#(2(), x) -> c_3() , 0^#() -> c_4() , 1^#() -> 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^#(x, x) -> c_1(f^#(0(), 1())) , f^#(x, 2()) -> c_2() , f^#(2(), x) -> c_3() , 0^#() -> c_4() , 1^#() -> c_5() } Strict Trs: { f(x, x) -> f(0(), 1()) , f(x, 2()) -> 2() , f(2(), x) -> 2() , 0() -> 2() , 1() -> 2() } Obligation: innermost runtime complexity Answer: MAYBE We replace rewrite rules by usable rules: Strict Usable Rules: { 0() -> 2() , 1() -> 2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x, x) -> c_1(f^#(0(), 1())) , f^#(x, 2()) -> c_2() , f^#(2(), x) -> c_3() , 0^#() -> c_4() , 1^#() -> c_5() } Strict Trs: { 0() -> 2() , 1() -> 2() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(f^#) = {1, 2}, Uargs(c_1) = {1} TcT has computed following constructor-restricted matrix interpretation. [0] = [2] [1] = [2] [2] = [1] [f^#](x1, x2) = [1] x1 + [2] x2 + [1] [c_1](x1) = [1] x1 + [0] [c_2] = [1] [c_3] = [1] [0^#] = [1] [c_4] = [0] [1^#] = [1] [c_5] = [0] This order satisfies following ordering constraints: [0()] = [2] > [1] = [2()] [1()] = [2] > [1] = [2()] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x, x) -> c_1(f^#(0(), 1())) } Weak DPs: { f^#(x, 2()) -> c_2() , f^#(2(), x) -> c_3() , 0^#() -> c_4() , 1^#() -> c_5() } Weak Trs: { 0() -> 2() , 1() -> 2() } 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. { f^#(x, 2()) -> c_2() , f^#(2(), x) -> c_3() , 0^#() -> c_4() , 1^#() -> c_5() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(x, x) -> c_1(f^#(0(), 1())) } Weak Trs: { 0() -> 2() , 1() -> 2() } 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..