2.15/1.10 YES 2.15/1.10 2.15/1.10 Proof: 2.15/1.11 This system is confluent. 2.15/1.11 By \cite{ALS94}, Theorem 4.1. 2.15/1.11 This system is of type 3 or smaller. 2.15/1.11 This system is strongly deterministic. 2.15/1.11 This system is quasi-decreasing. 2.15/1.11 By \cite{O02}, p. 214, Proposition 7.2.50. 2.15/1.11 This system is of type 3 or smaller. 2.15/1.11 This system is deterministic. 2.15/1.11 System R transformed to U(R). 2.15/1.11 This system is terminating. 2.15/1.11 Call external tool: 2.15/1.11 ./ttt2.sh 2.15/1.11 Input: 2.15/1.11 a -> c 2.15/1.11 b -> c 2.15/1.11 ?1(x, x) -> x 2.15/1.11 f(x) -> ?1(a, x) 2.15/1.11 2.15/1.11 Polynomial Interpretation Processor: 2.15/1.11 dimension: 1 2.15/1.11 interpretation: 2.15/1.11 [f](x0) = 2x0 + 6x0x0 + 7, 2.15/1.11 2.15/1.11 [?1](x0, x1) = x0 + 4x1x1 + 1, 2.15/1.11 2.15/1.11 [b] = 1, 2.15/1.11 2.15/1.11 [c] = 0, 2.15/1.11 2.15/1.11 [a] = 5 2.15/1.11 orientation: 2.15/1.11 a() = 5 >= 0 = c() 2.15/1.11 2.15/1.11 b() = 1 >= 0 = c() 2.15/1.11 2.15/1.11 ?1(x,x) = x + 4x*x + 1 >= x = x 2.15/1.11 2.15/1.11 f(x) = 2x + 6x*x + 7 >= 4x*x + 6 = ?1(a(),x) 2.15/1.11 problem: 2.15/1.11 2.15/1.11 Qed 2.15/1.11 All 0 critical pairs are joinable. 2.15/1.11 2.35/1.15 EOF