ceta_eq: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.2: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: fst#(mark(X1), X2) -> fst#(X1, X2) fst#(X1, mark(X2)) -> fst#(X1, X2) fst#(active(X1), X2) -> fst#(X1, X2) fst#(X1, active(X2)) -> fst#(X1, X2) rules: active(fst(0, Z)) -> mark(nil) active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(len(nil)) -> mark(0) active(len(cons(X, Z))) -> mark(s(len(Z))) add(mark(X1), X2) -> add(X1, X2) add(X1, mark(X2)) -> add(X1, X2) add(active(X1), X2) -> add(X1, X2) add(X1, active(X2)) -> add(X1, X2) cons(mark(X1), X2) -> cons(X1, X2) cons(X1, mark(X2)) -> cons(X1, X2) cons(active(X1), X2) -> cons(X1, X2) cons(X1, active(X2)) -> cons(X1, X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) fst(mark(X1), X2) -> fst(X1, X2) fst(X1, mark(X2)) -> fst(X1, X2) fst(active(X1), X2) -> fst(X1, X2) fst(X1, active(X2)) -> fst(X1, X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) mark(fst(X1, X2)) -> active(fst(mark(X1), mark(X2))) mark(0) -> active(0) mark(nil) -> active(nil) mark(s(X)) -> active(s(X)) mark(cons(X1, X2)) -> active(cons(mark(X1), X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1, X2)) -> active(add(mark(X1), mark(X2))) mark(len(X)) -> active(len(mark(X))) s(mark(X)) -> s(X) s(active(X)) -> s(X) the pairs fst#(active(X1), X2) -> fst#(X1, X2) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(fst#) = [(epsilon,0),(1,1)] Argument Filter: pi(fst#/2) = [] pi(mark/1) = 1 pi(active/1) = [1] RPO with the following precedence precedence(fst#[2]) = 0 precedence(active[1]) = 1 precedence(_) = 0 and the following status status(fst#[2]) = lex status(active[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair fst#(mark(X1), X2) -> fst#(X1, X2) weakly: [(fst#(mark(X1), X2),0),(mark(X1),1)] >=mu [(fst#(X1, X2),0),(X1,1)] could not be ensured