3.67/1.76 YES 3.67/1.76 3.67/1.76 Proof: 3.67/1.76 This system is confluent. 3.67/1.76 Removed infeasible rules from system R. 3.67/1.76 By \cite{ALS94}, Theorem 4.1. 3.67/1.76 This system is of type 3 or smaller. 3.67/1.76 This system is strongly deterministic. 3.67/1.76 This system is quasi-decreasing. 3.67/1.76 By \cite{O02}, p. 214, Proposition 7.2.50. 3.67/1.76 This system is of type 3 or smaller. 3.67/1.76 This system is deterministic. 3.67/1.76 System R transformed to optimized U(R). 3.67/1.76 This system is terminating. 3.67/1.76 Call external tool: 3.67/1.76 ./ttt2.sh 3.67/1.76 Input: 3.67/1.76 (VAR x) 3.67/1.76 (RULES 3.67/1.76 h(x, x) -> A 3.67/1.76 ) 3.67/1.76 3.67/1.76 Polynomial Interpretation Processor: 3.67/1.76 dimension: 1 3.67/1.76 interpretation: 3.67/1.76 [A] = 0, 3.67/1.76 3.67/1.76 [h](x0, x1) = 3x0 + -3x1 + 5x1x1 + 1 3.67/1.76 orientation: 3.67/1.76 h(x,x) = 5x*x + 1 >= 0 = A() 3.67/1.76 problem: 3.67/1.76 3.67/1.76 Qed 3.67/1.76 All 0 critical pairs are joinable. 3.67/1.76 4.97/2.11 EOF