2.06/1.12 YES 2.06/1.12 2.06/1.12 Proof: 2.06/1.12 This system is confluent. 2.06/1.12 By \cite{ALS94}, Theorem 4.1. 2.06/1.12 This system is of type 3 or smaller. 2.06/1.12 This system is strongly deterministic. 2.06/1.12 This system is quasi-decreasing. 2.06/1.12 By \cite{O02}, p. 214, Proposition 7.2.50. 2.06/1.12 This system is of type 3 or smaller. 2.06/1.12 This system is deterministic. 2.06/1.12 System R transformed to optimized U(R). 2.06/1.12 This system is terminating. 2.06/1.12 Call external tool: 2.06/1.12 ./ttt2.sh 2.06/1.12 Input: 2.06/1.12 a -> c 2.06/1.12 b -> c 2.06/1.12 f(x) -> ?1(a, x) 2.06/1.12 ?1(x, x) -> x 2.06/1.12 2.06/1.12 Polynomial Interpretation Processor: 2.06/1.12 dimension: 1 2.06/1.12 interpretation: 2.06/1.12 [?1](x0, x1) = 2x0 + -1x1 + 2x1x1 + 1, 2.06/1.12 2.06/1.12 [f](x0) = 4x0x0 + 6, 2.06/1.12 2.06/1.12 [b] = 4, 2.06/1.12 2.06/1.12 [c] = 0, 2.06/1.12 2.06/1.12 [a] = 2 2.06/1.12 orientation: 2.06/1.12 a() = 2 >= 0 = c() 2.06/1.12 2.06/1.12 b() = 4 >= 0 = c() 2.06/1.12 2.06/1.12 f(x) = 4x*x + 6 >= -1x + 2x*x + 5 = ?1(a(),x) 2.06/1.12 2.06/1.12 ?1(x,x) = x + 2x*x + 1 >= x = x 2.06/1.12 problem: 2.06/1.12 2.06/1.12 Qed 2.06/1.12 All 0 critical pairs are joinable. 2.06/1.12 2.06/1.14 EOF