3.40/1.71 YES 3.40/1.71 3.40/1.71 Proof: 3.40/1.71 This system is confluent. 3.40/1.71 Removed infeasible rules from system R. 3.40/1.71 By \cite{ALS94}, Theorem 4.1. 3.40/1.71 This system is of type 3 or smaller. 3.40/1.71 This system is strongly deterministic. 3.40/1.71 This system is quasi-decreasing. 3.40/1.71 By \cite{A14}, Theorem 11.5.9. 3.40/1.71 This system is of type 3 or smaller. 3.40/1.71 This system is deterministic. 3.40/1.71 System R transformed to V(R) + Emb. 3.40/1.71 This system is terminating. 3.40/1.71 Call external tool: 3.40/1.71 ./ttt2.sh 3.40/1.71 Input: 3.40/1.71 (VAR x y) 3.40/1.71 (RULES 3.40/1.71 f(x, y) -> x 3.40/1.71 f(x, y) -> g(y) 3.40/1.71 f(x, y) -> g(x) 3.40/1.71 g(x) -> x 3.40/1.71 f(x, y) -> x 3.40/1.71 f(x, y) -> y 3.40/1.71 ) 3.40/1.71 3.40/1.71 Polynomial Interpretation Processor: 3.40/1.71 dimension: 1 3.40/1.71 interpretation: 3.40/1.71 [g](x0) = x0 + 1, 3.40/1.71 3.40/1.71 [f](x0, x1) = x0 + 4x1 + x0x0 + 2 3.40/1.71 orientation: 3.40/1.71 f(x,y) = x + x*x + 4y + 2 >= x = x 3.40/1.71 3.40/1.71 f(x,y) = x + x*x + 4y + 2 >= y + 1 = g(y) 3.40/1.71 3.40/1.71 f(x,y) = x + x*x + 4y + 2 >= x + 1 = g(x) 3.40/1.71 3.40/1.71 g(x) = x + 1 >= x = x 3.40/1.71 3.40/1.71 f(x,y) = x + x*x + 4y + 2 >= y = y 3.40/1.71 problem: 3.40/1.71 3.40/1.71 Qed 3.40/1.71 All 0 critical pairs are joinable. 3.40/1.71 3.40/1.76 EOF