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 when applying the reduction pair processor with usable rules to remove from the DP problem pairs: minus#(+(x, y)) -> minus#(y) minus#(+(x, y)) -> minus#(x) rules: *(x, 1) -> x *(x, 0) -> 0 *(x, +(y, z)) -> +(*(x, y), *(x, z)) *(x, minus(y)) -> minus(*(x, y)) +(x, 0) -> x +(minus(x), x) -> 0 minus(0) -> 0 minus(minus(x)) -> x minus(+(x, y)) -> +(minus(y), minus(x)) the pairs minus#(+(x, y)) -> minus#(y) minus#(+(x, y)) -> minus#(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(minus#) = [(epsilon,0),(1,0)] polynomial interpretration over naturals with negative constants Pol(minus#(x_1)) = 1 Pol(+(x_1, x_2)) = 1 + x_2 + x_1 problem when orienting DPs cannot orient pair minus#(+(x, y)) -> minus#(y) strictly: [(minus#(+(x, y)),0),(+(x, y),0)] >mu [(minus#(y),0),(y,0)] could not be ensured