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: .#(.(x, y), z) -> .#(x, .(y, z)) .#(.(x, y), z) -> .#(y, z) rules: .(1, x) -> x .(x, 1) -> x .(i(x), x) -> 1 .(x, i(x)) -> 1 .(i(y), .(y, z)) -> z .(y, .(i(y), z)) -> z .(.(x, y), z) -> .(x, .(y, z)) i(1) -> 1 i(i(x)) -> x i(.(x, y)) -> .(i(y), i(x)) the pairs .#(.(x, y), z) -> .#(x, .(y, z)) .#(.(x, y), z) -> .#(y, 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),(1,2)] Argument Filter: pi(.#/2) = [] pi(./2) = [2,1] pi(1/0) = [] pi(i/1) = [1] RPO with the following precedence precedence(.#[2]) = 1 precedence(.[2]) = 0 precedence(1[0]) = 2 precedence(i[1]) = 3 precedence(_) = 0 and the following status status(.#[2]) = lex status(.[2]) = lex status(1[0]) = lex status(i[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair .#(.(x, y), z) -> .#(x, .(y, z)) strictly: [(.#(.(x, y), z),0),(.(x, y),2)] >mu [(.#(x, .(y, z)),0),(x,2)] could not be ensured