3.09/1.64 YES 3.09/1.64 3.09/1.64 Proof: 3.09/1.64 This system is confluent. 3.09/1.64 Inlined conditions in System R. 3.09/1.64 By \cite{ALS94}, Theorem 4.1. 3.09/1.64 This system is of type 3 or smaller. 3.09/1.64 This system is strongly deterministic. 3.09/1.64 This system is quasi-decreasing. 3.09/1.64 By \cite{O02}, p. 214, Proposition 7.2.50. 3.09/1.64 This system is of type 3 or smaller. 3.09/1.64 This system is deterministic. 3.09/1.64 System R transformed to U(R). 3.09/1.64 This system is terminating. 3.09/1.64 Call external tool: 3.09/1.64 ./ttt2.sh 3.09/1.64 Input: 3.09/1.64 (VAR x) 3.09/1.64 (RULES 3.09/1.64 f(x) -> g(x) 3.09/1.64 a -> c 3.09/1.64 b -> c 3.09/1.64 ) 3.09/1.64 3.09/1.64 Polynomial Interpretation Processor: 3.09/1.64 dimension: 1 3.09/1.64 interpretation: 3.09/1.64 [b] = 1, 3.09/1.64 3.09/1.64 [c] = 0, 3.09/1.64 3.09/1.64 [a] = 1, 3.09/1.64 3.09/1.64 [g](x0) = -3x0 + 4x0x0, 3.09/1.64 3.09/1.64 [f](x0) = 6x0 + 4x0x0 + 1 3.09/1.64 orientation: 3.09/1.64 f(x) = 6x + 4x*x + 1 >= -3x + 4x*x = g(x) 3.09/1.64 3.09/1.64 a() = 1 >= 0 = c() 3.09/1.64 3.09/1.64 b() = 1 >= 0 = c() 3.09/1.64 problem: 3.09/1.64 3.09/1.64 Qed 3.09/1.64 All 0 critical pairs are joinable. 3.09/1.64 3.09/1.67 EOF