0.00/0.76 YES 0.00/0.76 0.00/0.76 Problem: 0.00/0.76 f(x) -> a() <= x = b() 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 optimized 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(b(), x) -> a() 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) = 7x0x0 + 2, 0.00/0.76 0.00/0.76 [a] = 0, 0.00/0.76 0.00/0.76 [?1](x0, x1) = -1x0 + 4x0x0 + 2x1x1, 0.00/0.76 0.00/0.76 [b] = 3 0.00/0.76 orientation: 0.00/0.77 ?1(b(),x) = 2x*x + 33 >= 0 = a() 0.00/0.77 0.00/0.77 f(x) = 7x*x + 2 >= -1x + 6x*x = ?1(x,x) 0.00/0.77 problem: 0.00/0.77 0.00/0.77 Qed 0.00/0.77 0.00/0.77 EOF