3.46/1.41 MAYBE 3.46/1.41 3.46/1.41 Proof: 3.46/1.41 ConCon could not decide confluence of the system. 3.46/1.41 \cite{ALS94}, Theorem 4.1 does not apply. 3.46/1.42 This system is of type 3 or smaller. 3.46/1.42 This system is strongly deterministic. 3.46/1.42 This system is quasi-decreasing. 3.46/1.42 By \cite{A14}, Theorem 11.5.9. 3.46/1.42 This system is of type 3 or smaller. 3.46/1.42 This system is deterministic. 3.46/1.42 System R transformed to V(R) + Emb. 3.46/1.42 This system is terminating. 3.46/1.42 Call external tool: 3.46/1.42 ./ttt2.sh 3.46/1.42 Input: 3.46/1.42 f(x) -> c(x, g(x)) 3.46/1.42 f(x) -> g(x) 3.46/1.42 a -> b 3.46/1.42 g(a) -> h(b) 3.46/1.42 h(x) -> x 3.46/1.42 c(x, y) -> x 3.46/1.42 c(x, y) -> y 3.46/1.42 g(x) -> x 3.46/1.42 f(x) -> x 3.46/1.42 3.46/1.42 Matrix Interpretation Processor: dim=1 3.46/1.42 3.46/1.42 interpretation: 3.46/1.42 [h](x0) = x0 + 1, 3.46/1.42 3.46/1.42 [b] = 3, 3.46/1.42 3.46/1.42 [a] = 5, 3.46/1.42 3.46/1.42 [c](x0, x1) = x0 + x1 + 2, 3.46/1.42 3.46/1.42 [g](x0) = 4x0, 3.46/1.42 3.46/1.42 [f](x0) = 5x0 + 2 3.46/1.42 orientation: 3.46/1.42 f(x) = 5x + 2 >= 5x + 2 = c(x,g(x)) 3.46/1.42 3.46/1.42 f(x) = 5x + 2 >= 4x = g(x) 3.46/1.42 3.46/1.42 a() = 5 >= 3 = b() 3.46/1.42 3.46/1.42 g(a()) = 20 >= 4 = h(b()) 3.46/1.42 3.46/1.42 h(x) = x + 1 >= x = x 3.46/1.42 3.46/1.42 c(x,y) = x + y + 2 >= x = x 3.46/1.42 3.46/1.42 c(x,y) = x + y + 2 >= y = y 3.46/1.42 3.46/1.42 g(x) = 4x >= x = x 3.46/1.42 3.46/1.42 f(x) = 5x + 2 >= x = x 3.46/1.42 problem: 3.46/1.42 f(x) -> c(x,g(x)) 3.46/1.42 g(x) -> x 3.46/1.42 Matrix Interpretation Processor: dim=1 3.46/1.42 3.46/1.42 interpretation: 3.46/1.42 [c](x0, x1) = 2x0 + 2x1, 3.46/1.42 3.46/1.42 [g](x0) = 2x0 + 2, 3.46/1.42 3.46/1.42 [f](x0) = 6x0 + 4 3.46/1.42 orientation: 3.46/1.42 f(x) = 6x + 4 >= 6x + 4 = c(x,g(x)) 3.46/1.42 3.46/1.42 g(x) = 2x + 2 >= x = x 3.46/1.42 problem: 3.46/1.42 f(x) -> c(x,g(x)) 3.46/1.42 Matrix Interpretation Processor: dim=1 3.46/1.42 3.46/1.42 interpretation: 3.46/1.42 [c](x0, x1) = x0 + x1, 3.46/1.42 3.46/1.42 [g](x0) = 4x0, 3.46/1.42 3.46/1.42 [f](x0) = 5x0 + 1 3.46/1.42 orientation: 3.46/1.42 f(x) = 5x + 1 >= 5x = c(x,g(x)) 3.46/1.42 problem: 3.46/1.42 3.46/1.42 Qed 3.46/1.42 This critical pair is not joinable. 3.46/1.42 3.46/1.44 EOF