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: *#(x, +(y, z)) -> *#(x, y) *#(x, +(y, z)) -> *#(x, z) *#(x, minus(y)) -> *#(x, y) 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 *#(x, +(y, z)) -> *#(x, y) *#(x, +(y, z)) -> *#(x, z) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(*#) = [(epsilon,0),(2,1)] Argument Filter: pi(*#/2) = [] pi(+/2) = [1,2] pi(minus/1) = 1 RPO with the following precedence precedence(*#[2]) = 0 precedence(+[2]) = 1 precedence(_) = 0 and the following status status(*#[2]) = lex status(+[2]) = lex status(_) = lex problem when orienting DPs cannot orient pair *#(x, minus(y)) -> *#(x, y) weakly: [(*#(x, minus(y)),0),(minus(y),1)] >=mu [(*#(x, y),0),(y,1)] could not be ensured