ceta_eq: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.1: error below the reduction pair processor 1.1.1.1: error below the reduction pair processor 1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1: error below the dependency graph processor 1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: mark#(fst(X1, X2)) -> mark#(X1) mark#(fst(X1, X2)) -> mark#(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 mark#(fst(X1, X2)) -> mark#(X1) mark#(fst(X1, X2)) -> mark#(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(mark#) = [(epsilon,0),(1,0)] polynomial interpretration over naturals with negative constants Pol(mark#(x_1)) = 1 Pol(fst(x_1, x_2)) = 1 + x_2 + x_1 problem when orienting DPs cannot orient pair mark#(fst(X1, X2)) -> mark#(X1) strictly: [(mark#(fst(X1, X2)),0),(fst(X1, X2),0)] >mu [(mark#(X1),0),(X1,0)] could not be ensured