MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) , +(x, 0()) -> x , +(x, s(y)) -> s(+(x, y)) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , fib^#(s(s(x))) -> c_3(+^#(fib(s(x)), fib(x)), fib^#(s(x)), fib^#(x)) , +^#(x, 0()) -> c_4() , +^#(x, s(y)) -> c_5(+^#(x, y)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , fib^#(s(s(x))) -> c_3(+^#(fib(s(x)), fib(x)), fib^#(s(x)), fib^#(x)) , +^#(x, 0()) -> c_4() , +^#(x, s(y)) -> c_5(+^#(x, y)) } Weak Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) , +(x, 0()) -> x , +(x, s(y)) -> s(+(x, y)) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1,2,4} by applications of Pre({1,2,4}) = {3,5}. Here rules are labeled as follows: DPs: { 1: fib^#(0()) -> c_1() , 2: fib^#(s(0())) -> c_2() , 3: fib^#(s(s(x))) -> c_3(+^#(fib(s(x)), fib(x)), fib^#(s(x)), fib^#(x)) , 4: +^#(x, 0()) -> c_4() , 5: +^#(x, s(y)) -> c_5(+^#(x, y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fib^#(s(s(x))) -> c_3(+^#(fib(s(x)), fib(x)), fib^#(s(x)), fib^#(x)) , +^#(x, s(y)) -> c_5(+^#(x, y)) } Weak DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , +^#(x, 0()) -> c_4() } Weak Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) , +(x, 0()) -> x , +(x, s(y)) -> s(+(x, 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. { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , +^#(x, 0()) -> c_4() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fib^#(s(s(x))) -> c_3(+^#(fib(s(x)), fib(x)), fib^#(s(x)), fib^#(x)) , +^#(x, s(y)) -> c_5(+^#(x, y)) } Weak Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) , +(x, 0()) -> x , +(x, s(y)) -> s(+(x, y)) } 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..