0.00/0.86 YES 0.00/0.86 0.00/0.86 Problem: 0.00/0.86 f(x) -> e() <= d() = l() 0.00/0.86 h(x, x) -> A() 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{O02}, p. 214, Proposition 7.2.50. 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 U(R). 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 ?1(l(), x) -> e() 0.00/0.86 f(x) -> ?1(d(), x) 0.00/0.86 h(x, x) -> A() 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 [A] = 0, 0.00/0.86 0.00/0.86 [h](x0, x1) = 2x0 + 4x1 + 1, 0.00/0.86 0.00/0.86 [d] = 0, 0.00/0.86 0.00/0.86 [f](x0) = 2x0x0 + 4, 0.00/0.86 0.00/0.86 [e] = 0, 0.00/0.86 0.00/0.86 [?1](x0, x1) = 2x0 + x1x1 + 1, 0.00/0.86 0.00/0.86 [l] = 4 0.00/0.86 orientation: 0.00/0.86 ?1(l(),x) = x*x + 9 >= 0 = e() 0.00/0.86 0.00/0.86 f(x) = 2x*x + 4 >= x*x + 1 = ?1(d(),x) 0.00/0.86 0.00/0.86 h(x,x) = 6x + 1 >= 0 = A() 0.00/0.86 problem: 0.00/0.86 0.00/0.86 Qed 0.00/0.86 0.00/0.87 EOF