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 when applying the reduction pair processor to remove from the DP problem pairs: f#(f(a, f(x, a)), a) -> f#(f(x, a), a) rules: f(f(a, f(x, a)), a) -> f(a, f(f(x, a), a)) the pairs f#(f(a, f(x, a)), a) -> f#(f(x, a), a) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MAX and the level mapping defined by pi(f#) = [(epsilon,0),(2,0)] Argument Filter: pi(f#/2) = 1 pi(f/2) = [1,2] pi(a/0) = [] RPO with the following precedence precedence(f[2]) = 0 precedence(a[0]) = 0 precedence(_) = 0 and the following status status(f[2]) = mul status(a[0]) = mul status(_) = lex problem when orienting (usable) rules could not orient f(f(a, f(x, a)), a) >= f(a, f(f(x, a), a)) pi( f(f(a, f(x, a)), a) ) = f(f(a, f(x, a)), a) pi( f(a, f(f(x, a), a)) ) = f(a, f(f(x, a), a)) could not orient f(f(a, f(x, a)), a) >=RPO f(a, f(f(x, a), a))