YES LCTRS Theories Core, Ints Signature f: Int -> Int g: Int -> Int h: Int -> Int Rules f(!x) -> 2 [and(<=(1, !x), <=(!x, 3))] f(!x) -> g(!x) [and(<=(2, !x), <=(!x, 4))] g(!x) -> h(!x) h(!x) -> !y [and(!x = 2, !y = !x)] h(!x) -> !y [and(!x = 3, !y = 2)] * DPGraph approximation on the DP problem dependency pairs: {f#(!x) -> g#(!x) [and(<=(2, !x), <=(!x, 4))], g#(!x) -> h#(!x)} rules: {f(!x) -> 2 [and(<=(1, !x), <=(!x, 3))] , f(!x) -> g(!x) [and(<=(2, !x), <=(!x, 4))] , g(!x) -> h(!x) , h(!x) -> !y [and(=(!x, 2), =(!y, !x))] , h(!x) -> !y [and(=(!x, 3), =(!y, 2))]} resulting in the DP graph DPGraph with indexed dependency pairs {1: f#(!x) -> g#(!x) [and(<=(2, !x), <=(!x, 4))], 2: g#(!x) -> h#(!x)} and edges 1 -> {2} 2 -> {} with 0 SCC(s) Elapsed Time: 18.72 ms