1.66/1.28 MAYBE 1.66/1.28 1.66/1.28 Proof: 1.66/1.28 ConCon could not decide confluence of the system. 1.66/1.28 \cite{ALS94}, Theorem 4.1 does not apply. 1.66/1.28 This system is of type 3 or smaller. 1.66/1.28 This system is strongly deterministic. 1.66/1.28 This system is quasi-decreasing. 1.66/1.28 By \cite{A14}, Theorem 11.5.9. 1.66/1.28 This system is of type 3 or smaller. 1.66/1.28 This system is deterministic. 1.66/1.28 System R transformed to V(R) + Emb. 1.66/1.28 This system is terminating. 1.66/1.28 Call external tool: 1.66/1.28 ./ttt2.sh 1.66/1.28 Input: 1.66/1.28 a -> t(c) 1.66/1.28 a -> t(d) 1.66/1.28 f(x, y) -> x 1.66/1.28 g(x, x) -> h(x, x) 1.66/1.28 h(x, y) -> x 1.66/1.28 h(x, y) -> y 1.66/1.28 g(x, y) -> x 1.66/1.28 g(x, y) -> y 1.66/1.28 t(x) -> x 1.66/1.28 f(x, y) -> x 1.66/1.28 f(x, y) -> y 1.66/1.28 1.66/1.28 Polynomial Interpretation Processor: 1.66/1.28 dimension: 1 1.66/1.28 interpretation: 1.66/1.28 [h](x0, x1) = 2x0 + x1 + 4, 1.66/1.28 1.66/1.28 [g](x0, x1) = x0 + 2x1 + 5, 1.66/1.28 1.66/1.28 [f](x0, x1) = x0 + x1 + 7x1x1 + 4, 1.66/1.28 1.66/1.28 [d] = 0, 1.66/1.28 1.66/1.28 [t](x0) = 4x0 + 4, 1.66/1.28 1.66/1.28 [c] = 0, 1.66/1.28 1.66/1.28 [a] = 5 1.66/1.28 orientation: 1.66/1.28 a() = 5 >= 4 = t(c()) 2.95/1.28 2.95/1.28 a() = 5 >= 4 = t(d()) 2.95/1.28 2.95/1.28 f(x,y) = x + y + 7y*y + 4 >= x = x 2.95/1.28 2.95/1.28 g(x,x) = 3x + 5 >= 3x + 4 = h(x,x) 2.95/1.29 2.95/1.29 h(x,y) = 2x + y + 4 >= x = x 2.95/1.29 2.95/1.29 h(x,y) = 2x + y + 4 >= y = y 2.95/1.29 2.95/1.29 g(x,y) = x + 2y + 5 >= x = x 2.95/1.29 2.95/1.29 g(x,y) = x + 2y + 5 >= y = y 2.95/1.29 2.95/1.29 t(x) = 4x + 4 >= x = x 2.95/1.29 2.95/1.29 f(x,y) = x + y + 7y*y + 4 >= y = y 2.95/1.29 problem: 2.95/1.29 2.95/1.29 Qed 2.95/1.29 This critical pair is not infeasible. 2.95/1.29 This critical pair is unconditional. 2.95/1.29 2.95/1.32 EOF