1.53/1.08 YES 1.53/1.08 1.53/1.08 Proof: 1.53/1.08 This system is confluent. 1.53/1.08 By \cite{ALS94}, Theorem 4.1. 1.53/1.08 This system is of type 3 or smaller. 1.53/1.08 This system is strongly deterministic. 1.53/1.08 This system is quasi-decreasing. 1.53/1.08 By \cite{A14}, Theorem 11.5.9. 1.53/1.08 This system is of type 3 or smaller. 1.53/1.08 This system is deterministic. 1.53/1.08 System R transformed to V(R) + Emb. 1.53/1.08 This system is terminating. 1.53/1.08 Call external tool: 1.53/1.08 ./ttt2.sh 1.53/1.08 Input: 1.53/1.08 f(x) -> a 1.53/1.08 f(x) -> x 1.53/1.08 f(x) -> x 1.53/1.08 1.53/1.08 Polynomial Interpretation Processor: 1.53/1.08 dimension: 1 1.53/1.08 interpretation: 1.53/1.08 [a] = 0, 1.53/1.08 1.53/1.08 [f](x0) = 2x0 + 5x0x0 + 1 1.53/1.08 orientation: 1.53/1.08 f(x) = 2x + 5x*x + 1 >= 0 = a() 1.53/1.08 1.53/1.08 f(x) = 2x + 5x*x + 1 >= x = x 1.53/1.08 problem: 1.53/1.08 1.53/1.08 Qed 1.53/1.08 All 0 critical pairs are joinable. 1.53/1.08 2.22/1.10 EOF