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 below the reduction pair processor 1.1.2.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: f#(mark(X1), X2, X3) -> f#(X1, X2, X3) f#(X1, X2, mark(X3)) -> f#(X1, X2, X3) f#(active(X1), X2, X3) -> f#(X1, X2, X3) f#(X1, active(X2), X3) -> f#(X1, X2, X3) f#(X1, X2, active(X3)) -> f#(X1, X2, X3) rules: active(f(a, X, X)) -> mark(f(X, b, b)) active(b) -> mark(a) f(mark(X1), X2, X3) -> f(X1, X2, X3) f(X1, mark(X2), X3) -> f(X1, X2, X3) f(X1, X2, mark(X3)) -> f(X1, X2, X3) f(active(X1), X2, X3) -> f(X1, X2, X3) f(X1, active(X2), X3) -> f(X1, X2, X3) f(X1, X2, active(X3)) -> f(X1, X2, X3) mark(f(X1, X2, X3)) -> active(f(X1, mark(X2), X3)) mark(a) -> active(a) mark(b) -> active(b) the pairs f#(mark(X1), X2, X3) -> f#(X1, X2, X3) f#(X1, X2, mark(X3)) -> f#(X1, X2, X3) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(f#) = [(epsilon,0),(1,3),(2,0),(3,0)] Argument Filter: pi(f#/3) = [3,1] pi(mark/1) = [1] pi(active/1) = 1 RPO with the following precedence precedence(f#[3]) = 0 precedence(mark[1]) = 1 precedence(_) = 0 and the following status status(f#[3]) = lex status(mark[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair f#(active(X1), X2, X3) -> f#(X1, X2, X3) weakly: [(f#(active(X1), X2, X3),0),(active(X1),3),(X2,0),(X3,0)] >=mu [(f#(X1, X2, X3),0),(X1,3),(X2,0),(X3,0)] could not be ensured