1.27/1.14 YES 1.27/1.14 1.27/1.14 Proof: 1.27/1.14 This system is confluent. 1.27/1.14 By \cite{ALS94}, Theorem 4.1. 1.27/1.14 This system is of type 3 or smaller. 1.27/1.14 This system is strongly deterministic. 1.27/1.14 This system is quasi-decreasing. 1.27/1.14 By \cite{A14}, Theorem 11.5.9. 1.27/1.14 This system is of type 3 or smaller. 1.27/1.14 This system is deterministic. 1.27/1.14 System R transformed to V(R) + Emb. 1.27/1.14 This system is terminating. 1.27/1.14 Call external tool: 1.27/1.14 ./ttt2.sh 1.27/1.14 Input: 1.27/1.14 f(x, x) -> a 1.27/1.14 f(x, x) -> g(x) 1.27/1.14 g(x) -> x 1.27/1.14 f(x, y) -> x 1.27/1.14 f(x, y) -> y 1.27/1.14 1.27/1.14 Polynomial Interpretation Processor: 1.27/1.14 dimension: 1 1.27/1.14 interpretation: 1.27/1.14 [g](x0) = 4x0 + 2x0x0 + 4, 1.27/1.14 1.27/1.14 [a] = 0, 1.27/1.14 1.27/1.14 [f](x0, x1) = 4x0 + x1 + 2x1x1 + 5 1.27/1.14 orientation: 1.27/1.14 f(x,x) = 5x + 2x*x + 5 >= 0 = a() 1.27/1.14 1.27/1.14 f(x,x) = 5x + 2x*x + 5 >= 4x + 2x*x + 4 = g(x) 1.27/1.14 1.27/1.14 g(x) = 4x + 2x*x + 4 >= x = x 1.27/1.14 1.27/1.14 f(x,y) = 4x + y + 2y*y + 5 >= x = x 1.27/1.14 1.27/1.14 f(x,y) = 4x + y + 2y*y + 5 >= y = y 1.27/1.14 problem: 1.27/1.14 1.27/1.14 Qed 1.27/1.14 All 0 critical pairs are joinable. 1.27/1.14 1.27/1.17 EOF