3.87/1.75 YES 3.87/1.75 3.87/1.75 Proof: 3.87/1.75 This system is confluent. 3.87/1.75 Removed infeasible rules from system R. 3.87/1.75 By \cite{ALS94}, Theorem 4.1. 3.87/1.75 This system is of type 3 or smaller. 3.87/1.75 This system is strongly deterministic. 3.87/1.75 This system is quasi-decreasing. 3.87/1.75 By \cite{O02}, p. 214, Proposition 7.2.50. 3.87/1.75 This system is of type 3 or smaller. 3.87/1.75 This system is deterministic. 3.87/1.75 System R transformed to U(R). 3.87/1.75 This system is terminating. 3.87/1.75 Call external tool: 3.87/1.75 ./ttt2.sh 3.87/1.75 Input: 3.87/1.75 (VAR x) 3.87/1.75 (RULES 3.87/1.75 h(x, x) -> A 3.87/1.75 ) 3.87/1.75 3.87/1.75 Polynomial Interpretation Processor: 3.87/1.75 dimension: 1 3.87/1.75 interpretation: 3.87/1.75 [A] = 0, 3.87/1.75 3.87/1.75 [h](x0, x1) = 3x0 + -3x1 + 5x1x1 + 1 3.87/1.75 orientation: 3.87/1.75 h(x,x) = 5x*x + 1 >= 0 = A() 3.87/1.75 problem: 3.87/1.75 3.87/1.75 Qed 3.87/1.76 All 0 critical pairs are joinable. 3.87/1.76 4.86/2.04 EOF