0.00/0.77 YES 0.00/0.77 0.00/0.77 Problem: 0.00/0.77 a() -> c() 0.00/0.77 b() -> c() 0.00/0.77 f(x) -> x <= a() = x 0.00/0.77 0.00/0.77 Proof: 0.00/0.77 This system is confluent. 0.00/0.77 By \cite{ALS94}, Theorem 4.1. 0.00/0.77 This system is of type 3 or smaller. 0.00/0.77 This system is strongly deterministic. 0.00/0.77 All 0 critical pairs are joinable. 0.00/0.77 This system is quasi-decreasing. 0.00/0.77 By \cite{A14}, Theorem 11.5.9. 0.00/0.77 This system is of type 3 or smaller. 0.00/0.77 This system is deterministic. 0.00/0.77 System R transformed to V(R) + Emb. 0.00/0.77 This system is terminating. 0.00/0.77 Call external tool: 0.00/0.77 ./ttt2.sh 0.00/0.77 Input: 0.00/0.77 a() -> c() 0.00/0.77 b() -> c() 0.00/0.77 f(x) -> x 0.00/0.77 f(x) -> a() 0.00/0.77 f(x) -> x 0.00/0.77 0.00/0.77 Polynomial Interpretation Processor: 0.00/0.77 dimension: 1 0.00/0.77 interpretation: 0.00/0.77 [f](x0) = 4x0 + 3x0x0 + 4, 0.00/0.77 0.00/0.77 [b] = 1, 0.00/0.77 0.00/0.77 [c] = 0, 0.00/0.77 0.00/0.77 [a] = 2 0.00/0.77 orientation: 0.00/0.77 a() = 2 >= 0 = c() 0.00/0.77 0.00/0.77 b() = 1 >= 0 = c() 0.00/0.77 0.00/0.77 f(x) = 4x + 3x*x + 4 >= x = x 0.00/0.77 0.00/0.77 f(x) = 4x + 3x*x + 4 >= 2 = a() 0.00/0.77 problem: 0.00/0.77 0.00/0.77 Qed 0.00/0.77 0.00/0.80 EOF