YES LCTRS Theories Core, Ints Signature g2: (Int, Int) -> Int triangle2: Int -> Int u_16: Int -> Int u_23: Int -> Int Rules u_23(!w_8) -> !w_8 g2(!n, !s) -> u_23(g2(-(!n, 1), +(!n, !s))) [>(!n, 0)] g2(!n, !s) -> !s [<=(!n, 0)] u_16(!w_6) -> !w_6 triangle2(!n) -> u_16(g2(!n, 0)) DPGraph with indexed dependency pairs {1: g2#(!n, !s) -> u_23#(g2(-(!n, 1), +(!n, !s))) [>(!n, 0)] , 2: g2#(!n, !s) -> g2#(-(!n, 1), +(!n, !s)) [>(!n, 0)] , 3: triangle2#(!n) -> u_16#(g2(!n, 0)) , 4: triangle2#(!n) -> g2#(!n, 0)} and edges 1 -> {} 2 -> {1, 2} 3 -> {} 4 -> {1, 2} with 1 SCC(s) SCC: {g2#(!n, !s) -> g2#(-(!n, 1), +(!n, !s)) [>(!n, 0)]} Reduction Pair with dependency pairs: dependency pairs: {g2#(!n, !s) -> g2#(-(!n, 1), +(!n, !s)) [>(!n, 0)]} rules: {u_23(!w_8) -> !w_8 , g2(!n, !s) -> u_23(g2(-(!n, 1), +(!n, !s))) [>(!n, 0)] , g2(!n, !s) -> !s [<=(!n, 0)] , u_16(!w_6) -> !w_6 , triangle2(!n) -> u_16(g2(!n, 0))} Value criterion after 1 iteration(s) with the projections: Iteration 1: projection(s): v(g2#) = 1 removing the rule(s): {g2#(!n, !s) -> g2#(-(!n, 1), +(!n, !s)) [>(!n, 0)]} Elapsed Time: 34.10 ms