0.00/0.76 YES 0.00/0.76 0.00/0.76 Problem: 0.00/0.76 f(x) -> g(y) <= x = y 0.00/0.76 0.00/0.76 Proof: 0.00/0.76 This system is confluent. 0.00/0.76 By \cite{ALS94}, Theorem 4.1. 0.00/0.76 This system is of type 3 or smaller. 0.00/0.76 This system is strongly deterministic. 0.00/0.76 All 0 critical pairs are joinable. 0.00/0.76 This system is quasi-decreasing. 0.00/0.76 By \cite{O02}, p. 214, Proposition 7.2.50. 0.00/0.76 This system is of type 3 or smaller. 0.00/0.76 This system is deterministic. 0.00/0.76 System R transformed to U(R). 0.00/0.76 This system is terminating. 0.00/0.76 Call external tool: 0.00/0.76 ./ttt2.sh 0.00/0.76 Input: 0.00/0.76 ?1(y, x) -> g(y) 0.00/0.76 f(x) -> ?1(x, x) 0.00/0.76 0.00/0.76 Polynomial Interpretation Processor: 0.00/0.76 dimension: 1 0.00/0.76 interpretation: 0.00/0.76 [f](x0) = 6x0x0 + 4, 0.00/0.76 0.00/0.76 [g](x0) = -1x0 + 2x0x0, 0.00/0.76 0.00/0.76 [?1](x0, x1) = 2x0x0 + 4x1x1 + 1 0.00/0.76 orientation: 0.00/0.77 ?1(y,x) = 4x*x + 2y*y + 1 >= -1y + 2y*y = g(y) 0.00/0.77 0.00/0.77 f(x) = 6x*x + 4 >= 6x*x + 1 = ?1(x,x) 0.00/0.77 problem: 0.00/0.77 0.00/0.77 Qed 0.00/0.77 0.00/0.88 EOF