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 when applying the reduction pair processor with usable rules to remove from the DP problem pairs: top#(mark(X)) -> top#(proper(X)) rules: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) active(f(X1, X2)) -> f(active(X1), X2) active(g(X)) -> g(active(X)) f(mark(X1), X2) -> mark(f(X1, X2)) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) the pairs top#(mark(X)) -> top#(proper(X)) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(top#) = [(epsilon,0),(1,1)] Argument Filter: pi(top#/1) = [] pi(mark/1) = [1] pi(proper/1) = 1 pi(f/2) = 1 pi(g/1) = 1 pi(ok/1) = [] RPO with the following precedence precedence(mark[1]) = 0 precedence(top#[1]) = 1 precedence(ok[1]) = 2 precedence(_) = 0 and the following status status(mark[1]) = lex status(top#[1]) = lex status(ok[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair top#(mark(X)) -> top#(proper(X)) strictly: [(top#(mark(X)),0),(mark(X),1)] >mu [(top#(proper(X)),0),(proper(X),1)] could not be ensured