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 with usable rules to remove from the DP problem pairs: log#(s(s(x))) -> log#(s(quot(x, s(s(0))))) rules: if_minus(true, s(x), y) -> 0 if_minus(false, s(x), y) -> s(minus(x, y)) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) log(s(0)) -> 0 log(s(s(x))) -> s(log(s(quot(x, s(s(0)))))) minus(0, y) -> 0 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) the pairs log#(s(s(x))) -> log#(s(quot(x, s(s(0))))) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(log#) = [(epsilon,0),(1,0)] Argument Filter: pi(log#/1) = [] pi(s/1) = [1] pi(quot/2) = 1 pi(0/0) = [] pi(minus/2) = 1 pi(if_minus/3) = 2 pi(le/2) = [] pi(false/0) = [] pi(true/0) = [] RPO with the following precedence precedence(log#[1]) = 2 precedence(s[1]) = 1 precedence(0[0]) = 0 precedence(le[2]) = 0 precedence(false[0]) = 3 precedence(true[0]) = 0 precedence(_) = 0 and the following status status(log#[1]) = lex status(s[1]) = lex status(0[0]) = lex status(le[2]) = lex status(false[0]) = lex status(true[0]) = lex status(_) = lex problem when orienting DPs cannot orient pair log#(s(s(x))) -> log#(s(quot(x, s(s(0))))) strictly: [(log#(s(s(x))),0),(s(s(x)),0)] >mu [(log#(s(quot(x, s(s(0))))),0),(s(quot(x, s(s(0)))),0)] could not be ensured