ceta_eq: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.3: error below the reduction pair processor 1.1.3.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3) U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3) U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3) U21#(X1, active(X2), X3) -> U21#(X1, X2, X3) U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3) rules: U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) the pairs U21#(X1, active(X2), X3) -> U21#(X1, X2, X3) U21#(X1, X2, active(X3)) -> U21#(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(U21#) = [(2,2),(3,3)] polynomial interpretration over naturals with negative constants Pol(U21#(x_1, x_2, x_3)) = 0 Pol(mark(x_1)) = x_1 Pol(active(x_1)) = 1 + x_1 problem when orienting DPs cannot orient pair U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3) weakly: [(mark(X2),2),(X3,3)] >=mu [(X2,2),(X3,3)] could not be ensured