3.57/1.51 MAYBE 3.57/1.51 3.57/1.51 Proof: 3.57/1.51 ConCon could not decide confluence of the system. 3.57/1.51 \cite{ALS94}, Theorem 4.1 does not apply. 3.57/1.51 This system is of type 3 or smaller. 3.57/1.51 This system is strongly deterministic. 3.57/1.51 This system is quasi-decreasing. 3.57/1.51 By \cite{A14}, Theorem 11.5.9. 3.57/1.51 This system is of type 3 or smaller. 3.57/1.51 This system is deterministic. 3.57/1.51 System R transformed to V(R) + Emb. 3.57/1.51 This system is terminating. 3.57/1.51 Call external tool: 3.57/1.51 ./ttt2.sh 3.57/1.51 Input: 3.57/1.51 f(x) -> x 3.57/1.51 g(d, x, x) -> A 3.57/1.51 h(x, x) -> g(x, x, f(k)) 3.57/1.51 c -> e' 3.57/1.51 a -> c 3.57/1.51 a -> d 3.57/1.51 b -> c 3.57/1.51 b -> d 3.57/1.51 c -> e 3.57/1.51 c -> l 3.57/1.51 k -> l 3.57/1.51 k -> m 3.57/1.51 d -> m 3.57/1.51 h(x, y) -> x 3.57/1.51 h(x, y) -> y 3.57/1.51 g(x, y, z) -> x 3.57/1.51 g(x, y, z) -> y 3.57/1.51 g(x, y, z) -> z 3.57/1.51 f(x) -> x 3.57/1.51 3.57/1.51 Polynomial Interpretation Processor: 3.57/1.51 dimension: 1 3.57/1.51 interpretation: 3.57/1.51 [m] = 0, 3.57/1.51 3.57/1.51 [l] = 0, 3.57/1.51 3.57/1.51 [e] = 0, 3.57/1.51 3.57/1.51 [b] = 4, 3.57/1.51 3.57/1.51 [a] = 4, 3.57/1.51 3.57/1.51 [e'] = 0, 3.57/1.51 3.57/1.51 [c] = 1, 3.57/1.51 3.57/1.51 [k] = 1, 3.57/1.51 3.57/1.51 [h](x0, x1) = x0 + 6x1 + x1x1 + 7, 3.57/1.51 3.57/1.51 [A] = 0, 3.57/1.51 3.57/1.51 [g](x0, x1, x2) = x0 + 6x1 + x2 + 1, 3.57/1.51 3.57/1.51 [d] = 1, 3.57/1.51 3.57/1.51 [f](x0) = 4x0 + 1 3.57/1.51 orientation: 3.57/1.51 f(x) = 4x + 1 >= x = x 3.57/1.51 3.57/1.51 g(d(),x,x) = 7x + 2 >= 0 = A() 3.57/1.51 3.57/1.51 h(x,x) = 7x + x*x + 7 >= 7x + 6 = g(x,x,f(k())) 3.57/1.51 3.57/1.51 c() = 1 >= 0 = e'() 3.57/1.51 3.57/1.51 a() = 4 >= 1 = c() 3.57/1.51 3.57/1.51 a() = 4 >= 1 = d() 3.57/1.51 3.57/1.51 b() = 4 >= 1 = c() 3.57/1.51 3.57/1.51 b() = 4 >= 1 = d() 3.57/1.51 3.57/1.51 c() = 1 >= 0 = e() 3.57/1.51 3.57/1.51 c() = 1 >= 0 = l() 3.57/1.51 3.57/1.51 k() = 1 >= 0 = l() 3.57/1.51 3.57/1.51 k() = 1 >= 0 = m() 3.57/1.51 3.57/1.51 d() = 1 >= 0 = m() 3.57/1.51 3.57/1.51 h(x,y) = x + 6y + y*y + 7 >= x = x 3.57/1.52 3.57/1.52 h(x,y) = x + 6y + y*y + 7 >= y = y 3.57/1.52 3.57/1.52 g(x,y,z) = x + 6y + z + 1 >= x = x 3.57/1.52 3.57/1.52 g(x,y,z) = x + 6y + z + 1 >= y = y 3.57/1.52 3.57/1.52 g(x,y,z) = x + 6y + z + 1 >= z = z 3.57/1.52 problem: 3.57/1.52 3.57/1.52 Qed 3.57/1.52 This critical pair is not trivial. 3.57/1.52 3.93/1.55 EOF