2.24/1.09 YES 2.24/1.09 2.24/1.09 Proof: 2.24/1.09 This system is confluent. 2.24/1.09 By \cite{ALS94}, Theorem 4.1. 2.24/1.09 This system is of type 3 or smaller. 2.24/1.09 This system is strongly deterministic. 2.24/1.09 This system is quasi-decreasing. 2.24/1.09 By \cite{A14}, Theorem 11.5.9. 2.24/1.09 This system is of type 3 or smaller. 2.24/1.09 This system is deterministic. 2.24/1.09 System R transformed to V(R) + Emb. 2.24/1.09 This system is terminating. 2.24/1.09 Call external tool: 2.24/1.09 ./ttt2.sh 2.24/1.09 Input: 2.24/1.09 f(x) -> g(x) 2.24/1.09 f(x) -> x 2.24/1.09 a -> c 2.24/1.09 b -> c 2.24/1.09 g(x) -> x 2.24/1.09 f(x) -> x 2.24/1.09 2.24/1.09 Polynomial Interpretation Processor: 2.24/1.09 dimension: 1 2.24/1.10 interpretation: 2.24/1.10 [b] = 1, 2.24/1.10 2.24/1.10 [c] = 0, 2.24/1.10 2.24/1.10 [a] = 1, 2.24/1.10 2.24/1.10 [g](x0) = x0 + 7x0x0 + 4, 2.24/1.10 2.24/1.10 [f](x0) = x0 + 7x0x0 + 5 2.24/1.10 orientation: 2.24/1.10 f(x) = x + 7x*x + 5 >= x + 7x*x + 4 = g(x) 2.24/1.10 2.24/1.10 f(x) = x + 7x*x + 5 >= x = x 2.24/1.10 2.24/1.10 a() = 1 >= 0 = c() 2.24/1.10 2.24/1.10 b() = 1 >= 0 = c() 2.24/1.10 2.24/1.10 g(x) = x + 7x*x + 4 >= x = x 2.24/1.10 problem: 2.24/1.10 2.24/1.10 Qed 2.24/1.10 All 0 critical pairs are joinable. 2.24/1.10 2.27/1.12 EOF