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 below the reduction pair processor 1.1.2.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: active#(U11(X)) -> active#(X) active#(U12(X)) -> active#(X) active#(isNePal(X)) -> active#(X) rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(mark(X1), X2) -> mark(__(X1, X2)) __(X1, mark(X2)) -> mark(__(X1, X2)) __(ok(X1), ok(X2)) -> ok(__(X1, X2)) active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) active(__(X, nil)) -> mark(X) active(__(nil, X)) -> mark(X) active(U11(tt)) -> mark(U12(tt)) active(U12(tt)) -> mark(tt) active(isNePal(__(I, __(P, I)))) -> mark(U11(tt)) active(__(X1, X2)) -> __(active(X1), X2) active(__(X1, X2)) -> __(X1, active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(__(X1, X2)) -> __(proper(X1), proper(X2)) proper(nil) -> ok(nil) proper(U11(X)) -> U11(proper(X)) proper(tt) -> ok(tt) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) the pairs active#(U12(X)) -> active#(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(active#) = [(epsilon,0),(1,0)] Argument Filter: pi(active#/1) = [] pi(U11/1) = 1 pi(U12/1) = [1] pi(isNePal/1) = 1 RPO with the following precedence precedence(active#[1]) = 0 precedence(U12[1]) = 1 precedence(_) = 0 and the following status status(active#[1]) = lex status(U12[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair active#(U11(X)) -> active#(X) weakly: [(active#(U11(X)),0),(U11(X),0)] >=mu [(active#(X),0),(X,0)] could not be ensured