0.00/0.80 YES 0.00/0.80 0.00/0.80 Problem: 0.00/0.80 f(x) -> x <= x = a() 0.00/0.80 g(x) -> h(x, x) 0.00/0.80 h(x, y) -> i(x) 0.00/0.80 0.00/0.80 Proof: 0.00/0.80 This system is confluent. 0.00/0.80 By \cite{ALS94}, Theorem 4.1. 0.00/0.80 This system is of type 3 or smaller. 0.00/0.80 This system is strongly deterministic. 0.00/0.80 All 0 critical pairs are joinable. 0.00/0.80 This system is quasi-decreasing. 0.00/0.80 By \cite{O02}, p. 214, Proposition 7.2.50. 0.00/0.80 This system is of type 3 or smaller. 0.00/0.80 This system is deterministic. 0.00/0.80 System R transformed to U(R). 0.00/0.80 This system is terminating. 0.00/0.80 Call external tool: 0.00/0.80 ./ttt2.sh 0.00/0.80 Input: 0.00/0.80 ?1(a(), x) -> x 0.00/0.80 f(x) -> ?1(x, x) 0.00/0.80 g(x) -> h(x, x) 0.00/0.80 h(x, y) -> i(x) 0.00/0.80 0.00/0.80 Polynomial Interpretation Processor: 0.00/0.80 dimension: 1 0.00/0.80 interpretation: 0.00/0.80 [i](x0) = 2x0, 0.00/0.80 0.00/0.80 [h](x0, x1) = 2x0 + 2x1x1 + 4, 0.00/0.80 0.00/0.80 [g](x0) = 4x0 + 2x0x0 + 5, 0.00/0.80 0.00/0.80 [f](x0) = 7x0x0 + 1, 0.00/0.80 0.00/0.80 [?1](x0, x1) = -6x0 + x1 + 7x0x0, 0.00/0.80 0.00/0.80 [a] = 2 0.00/0.80 orientation: 0.00/0.80 ?1(a(),x) = x + 16 >= x = x 0.00/0.80 0.00/0.80 f(x) = 7x*x + 1 >= -5x + 7x*x = ?1(x,x) 0.00/0.80 0.00/0.80 g(x) = 4x + 2x*x + 5 >= 2x + 2x*x + 4 = h(x,x) 0.00/0.80 0.00/0.80 h(x,y) = 2x + 2y*y + 4 >= 2x = i(x) 0.00/0.80 problem: 0.00/0.80 0.00/0.80 Qed 0.00/0.80 0.00/0.83 EOF