YES Proof: This system is confluent. By \cite{GNG13}, Theorem 9. This system is deterministic. This system is weakly left-linear. System R transformed to optimized U(R). This system is not orthogonal. Call external tool: csi - trs 30 Input: ?1(y, x, y) -> G(x) F(x, y) -> ?1(x, x, y) a -> b sorted: (order) 0:?1(y,x,y) -> G(x) F(x,y) -> ?1(x,x,y) 1:a() -> b() ----- sorts [0>1, 1>2, 2>5, 3>4] sort attachment (strict) ?1 : 5 x 5 x 5 -> 1 G : 5 -> 2 F : 5 x 5 -> 0 a : 3 b : 4 ----- 0:?1(y,x,y) -> G(x) F(x,y) -> ?1(x,x,y) Church Rosser Transformation Processor (kb): ?1(y,x,y) -> G(x) F(x,y) -> ?1(x,x,y) critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [G](x0) = x0, [?1](x0, x1, x2) = x0 + x1 + x2 + 2, [F](x0, x1) = 2x0 + 4x1 + 3 orientation: ?1(y,x,y) = x + 2y + 2 >= x = G(x) F(x,y) = 2x + 4y + 3 >= 2x + y + 2 = ?1(x,x,y) problem: Qed 1:a() -> b() Uncurry Processor: a() -> b() Ground Confluence Processor: confluent by decision procedure. This system is not normal. This system is oriented. This system is of type 3 or smaller. This system is not right-stable. This system is conditional.