3.38/1.79 YES 3.38/1.79 3.38/1.79 Proof: 3.45/1.79 This system is confluent. 3.45/1.79 By \cite{ALS94}, Theorem 4.1. 3.45/1.79 This system is of type 3 or smaller. 3.45/1.79 This system is strongly deterministic. 3.45/1.79 This system is quasi-decreasing. 3.45/1.79 By \cite{A14}, Theorem 11.5.9. 3.45/1.79 This system is of type 3 or smaller. 3.45/1.79 This system is deterministic. 3.45/1.79 System R transformed to V(R) + Emb. 3.45/1.79 This system is terminating. 3.45/1.79 Call external tool: 3.45/1.79 ./ttt2.sh 3.45/1.79 Input: 3.45/1.79 (VAR x) 3.45/1.79 (RULES 3.45/1.79 f(x) -> x 3.45/1.79 g(x) -> C 3.45/1.79 g(x) -> A 3.45/1.79 A -> B 3.45/1.79 g(x) -> x 3.45/1.79 f(x) -> x 3.45/1.79 ) 3.45/1.79 3.45/1.79 Polynomial Interpretation Processor: 3.45/1.79 dimension: 1 3.45/1.79 interpretation: 3.45/1.79 [B] = 0, 3.45/1.79 3.45/1.79 [A] = 2, 3.45/1.79 3.45/1.79 [C] = 0, 3.45/1.79 3.45/1.79 [g](x0) = 2x0 + 3, 3.45/1.79 3.45/1.79 [f](x0) = x0 + 2 3.45/1.79 orientation: 3.45/1.79 f(x) = x + 2 >= x = x 3.45/1.79 3.45/1.79 g(x) = 2x + 3 >= 0 = C() 3.45/1.79 3.45/1.79 g(x) = 2x + 3 >= 2 = A() 3.45/1.79 3.45/1.79 A() = 2 >= 0 = B() 3.45/1.79 3.45/1.79 g(x) = 2x + 3 >= x = x 3.45/1.79 problem: 3.45/1.79 3.45/1.79 Qed 3.45/1.79 All 0 critical pairs are joinable. 3.45/1.79 3.47/1.82 EOF