YES Proof: This system is confluent. By \cite{ALS94}, Theorem 4.1. This system is of type 3 or smaller. This system is strongly deterministic. There are no critical pairs. By \cite{A14}, Theorem 11.5.9. This system is of type 3 or smaller. This system is deterministic. System R transformed to V(R) + Emb. Call external tool: ttt2 - trs 30 Input: f(x, x) -> a f(x, x) -> g(x) g(x) -> x f(x, y) -> x f(x, y) -> y DP Processor: DPs: f#(x,x) -> g#(x) TRS: f(x,x) -> a() f(x,x) -> g(x) g(x) -> x f(x,y) -> x f(x,y) -> y TDG Processor: DPs: f#(x,x) -> g#(x) TRS: f(x,x) -> a() f(x,x) -> g(x) g(x) -> x f(x,y) -> x f(x,y) -> y graph: Qed