ceta_eq: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.3: error below the reduction pair processor 1.1.3.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: a#(x, s(y), h) -> a#(x, y, s(h)) a#(x, s(y), s(z)) -> a#(x, y, a(x, s(y), z)) a#(x, s(y), s(z)) -> a#(x, s(y), z) rules: a(h, h, x) -> s(x) a(x, s(y), h) -> a(x, y, s(h)) a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z)) a(s(x), h, z) -> a(x, z, z) app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h), l)) the pairs a#(x, s(y), h) -> a#(x, y, s(h)) a#(x, s(y), s(z)) -> a#(x, y, a(x, s(y), z)) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(a#) = [(epsilon,0),(2,3)] Argument Filter: pi(a#/3) = [] pi(s/1) = [1] pi(a/3) = 3 pi(h/0) = [] RPO with the following precedence precedence(a#[3]) = 1 precedence(s[1]) = 0 precedence(h[0]) = 0 precedence(_) = 0 and the following status status(a#[3]) = lex status(s[1]) = lex status(h[0]) = lex status(_) = lex problem when orienting DPs cannot orient pair a#(x, s(y), s(z)) -> a#(x, s(y), z) weakly: [(a#(x, s(y), s(z)),0),(s(y),3)] >=mu [(a#(x, s(y), z),0),(s(y),3)] could not be ensured