3.16/1.62 YES 3.16/1.62 3.16/1.62 Proof: 3.16/1.62 This system is confluent. 3.16/1.62 By \cite{ALS94}, Theorem 4.1. 3.16/1.62 This system is of type 3 or smaller. 3.16/1.62 This system is strongly deterministic. 3.16/1.62 This system is quasi-decreasing. 3.16/1.62 By \cite{O02}, p. 214, Proposition 7.2.50. 3.16/1.62 This system is of type 3 or smaller. 3.16/1.62 This system is deterministic. 3.16/1.62 System R transformed to optimized U(R). 3.16/1.62 This system is terminating. 3.16/1.62 Call external tool: 3.16/1.62 ./ttt2.sh 3.16/1.62 Input: 3.16/1.62 (VAR x y) 3.16/1.62 (RULES 3.16/1.62 f(x) -> ?1(x, x) 3.16/1.62 ?1(y, x) -> g(y) 3.16/1.62 ) 3.16/1.62 3.16/1.62 Polynomial Interpretation Processor: 3.16/1.62 dimension: 1 3.16/1.62 interpretation: 3.16/1.62 [g](x0) = -2x0 + 3x0x0, 3.16/1.62 3.16/1.62 [?1](x0, x1) = -2x0 + 4x0x0 + x1x1 + 4, 3.16/1.62 3.16/1.62 [f](x0) = 5x0x0 + 5 3.16/1.62 orientation: 3.16/1.62 f(x) = 5x*x + 5 >= -2x + 5x*x + 4 = ?1(x,x) 3.16/1.62 3.16/1.62 ?1(y,x) = x*x + -2y + 4y*y + 4 >= -2y + 3y*y = g(y) 3.16/1.62 problem: 3.16/1.62 3.16/1.63 Qed 3.16/1.63 All 0 critical pairs are joinable. 3.16/1.63 3.16/1.67 EOF