MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) , a__sel(0(), cons(X, Y)) -> mark(X) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { a__from^#(X) -> c_1(mark^#(X)) , a__from^#(X) -> c_2() , mark^#(cons(X1, X2)) -> c_3(mark^#(X1)) , mark^#(from(X)) -> c_4(a__from^#(mark(X)), mark^#(X)) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(0()) -> c_6() , mark^#(sel(X1, X2)) -> c_7(a__sel^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , a__sel^#(X1, X2) -> c_8() , a__sel^#(s(X), cons(Y, Z)) -> c_9(a__sel^#(mark(X), mark(Z)), mark^#(X), mark^#(Z)) , a__sel^#(0(), cons(X, Y)) -> c_10(mark^#(X)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__from^#(X) -> c_1(mark^#(X)) , a__from^#(X) -> c_2() , mark^#(cons(X1, X2)) -> c_3(mark^#(X1)) , mark^#(from(X)) -> c_4(a__from^#(mark(X)), mark^#(X)) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(0()) -> c_6() , mark^#(sel(X1, X2)) -> c_7(a__sel^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , a__sel^#(X1, X2) -> c_8() , a__sel^#(s(X), cons(Y, Z)) -> c_9(a__sel^#(mark(X), mark(Z)), mark^#(X), mark^#(Z)) , a__sel^#(0(), cons(X, Y)) -> c_10(mark^#(X)) } Weak Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) , a__sel(0(), cons(X, Y)) -> mark(X) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2,6,8} by applications of Pre({2,6,8}) = {1,3,4,5,7,9,10}. Here rules are labeled as follows: DPs: { 1: a__from^#(X) -> c_1(mark^#(X)) , 2: a__from^#(X) -> c_2() , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1)) , 4: mark^#(from(X)) -> c_4(a__from^#(mark(X)), mark^#(X)) , 5: mark^#(s(X)) -> c_5(mark^#(X)) , 6: mark^#(0()) -> c_6() , 7: mark^#(sel(X1, X2)) -> c_7(a__sel^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , 8: a__sel^#(X1, X2) -> c_8() , 9: a__sel^#(s(X), cons(Y, Z)) -> c_9(a__sel^#(mark(X), mark(Z)), mark^#(X), mark^#(Z)) , 10: a__sel^#(0(), cons(X, Y)) -> c_10(mark^#(X)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__from^#(X) -> c_1(mark^#(X)) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1)) , mark^#(from(X)) -> c_4(a__from^#(mark(X)), mark^#(X)) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(sel(X1, X2)) -> c_7(a__sel^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , a__sel^#(s(X), cons(Y, Z)) -> c_9(a__sel^#(mark(X), mark(Z)), mark^#(X), mark^#(Z)) , a__sel^#(0(), cons(X, Y)) -> c_10(mark^#(X)) } Weak DPs: { a__from^#(X) -> c_2() , mark^#(0()) -> c_6() , a__sel^#(X1, X2) -> c_8() } Weak Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) , a__sel(0(), cons(X, Y)) -> mark(X) } 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. { a__from^#(X) -> c_2() , mark^#(0()) -> c_6() , a__sel^#(X1, X2) -> c_8() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__from^#(X) -> c_1(mark^#(X)) , mark^#(cons(X1, X2)) -> c_3(mark^#(X1)) , mark^#(from(X)) -> c_4(a__from^#(mark(X)), mark^#(X)) , mark^#(s(X)) -> c_5(mark^#(X)) , mark^#(sel(X1, X2)) -> c_7(a__sel^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , a__sel^#(s(X), cons(Y, Z)) -> c_9(a__sel^#(mark(X), mark(Z)), mark^#(X), mark^#(Z)) , a__sel^#(0(), cons(X, Y)) -> c_10(mark^#(X)) } Weak Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) , a__sel(0(), cons(X, Y)) -> mark(X) } 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..