0.00/0.86 YES 0.00/0.86 0.00/0.86 Problem: 0.00/0.86 f(x, x) -> a() <= g(x) = b() 0.00/0.86 0.00/0.86 Proof: 0.00/0.86 This system is confluent. 0.00/0.86 By \cite{ALS94}, Theorem 4.1. 0.00/0.86 This system is of type 3 or smaller. 0.00/0.86 This system is strongly deterministic. 0.00/0.86 All 0 critical pairs are joinable. 0.00/0.86 This system is quasi-decreasing. 0.00/0.86 By \cite{A14}, Theorem 11.5.9. 0.00/0.86 This system is of type 3 or smaller. 0.00/0.86 This system is deterministic. 0.00/0.86 System R transformed to V(R) + Emb. 0.00/0.86 This system is terminating. 0.00/0.86 Call external tool: 0.00/0.86 ./ttt2.sh 0.00/0.86 Input: 0.00/0.86 f(x, x) -> a() 0.00/0.86 f(x, x) -> g(x) 0.00/0.86 g(x) -> x 0.00/0.86 f(x, y) -> x 0.00/0.86 f(x, y) -> y 0.00/0.86 0.00/0.86 Polynomial Interpretation Processor: 0.00/0.86 dimension: 1 0.00/0.86 interpretation: 0.00/0.86 [g](x0) = 2x0 + 2x0x0 + 4, 0.00/0.86 0.00/0.86 [a] = 0, 0.00/0.86 0.00/0.86 [f](x0, x1) = x0 + x1 + 2x0x0 + 5 0.00/0.86 orientation: 0.00/0.86 f(x,x) = 2x + 2x*x + 5 >= 0 = a() 0.00/0.86 0.00/0.86 f(x,x) = 2x + 2x*x + 5 >= 2x + 2x*x + 4 = g(x) 0.00/0.86 0.00/0.86 g(x) = 2x + 2x*x + 4 >= x = x 0.00/0.86 0.00/0.86 f(x,y) = x + 2x*x + y + 5 >= x = x 0.00/0.86 0.00/0.86 f(x,y) = x + 2x*x + y + 5 >= y = y 0.00/0.86 problem: 0.00/0.86 0.00/0.86 Qed 0.00/0.86 0.00/0.91 EOF