3.95/1.84 MAYBE 3.95/1.84 3.95/1.84 Proof: 3.95/1.84 ConCon could not decide confluence of the system. 3.95/1.84 \cite{ALS94}, Theorem 4.1 does not apply. 3.95/1.84 This system is of type 3 or smaller. 3.95/1.84 This system is strongly deterministic. 3.95/1.84 This system is quasi-decreasing. 3.95/1.84 By \cite{A14}, Theorem 11.5.9. 3.95/1.84 This system is of type 3 or smaller. 3.95/1.84 This system is deterministic. 3.95/1.84 System R transformed to V(R) + Emb. 3.95/1.84 This system is terminating. 3.95/1.84 Call external tool: 3.95/1.84 ./ttt2.sh 3.95/1.84 Input: 3.95/1.84 (VAR x y) 3.95/1.84 (RULES 3.95/1.84 a -> t(c) 3.95/1.84 a -> t(d) 3.95/1.84 f(x, y) -> x 3.95/1.84 g(x, x) -> h(x, x) 3.95/1.84 h(x, y) -> x 3.95/1.84 h(x, y) -> y 3.95/1.84 g(x, y) -> x 3.95/1.84 g(x, y) -> y 3.95/1.84 t(x) -> x 3.95/1.84 f(x, y) -> x 3.95/1.84 f(x, y) -> y 3.95/1.84 ) 3.95/1.84 3.95/1.84 Polynomial Interpretation Processor: 3.95/1.84 dimension: 1 3.95/1.84 interpretation: 3.95/1.84 [h](x0, x1) = 2x0 + x1 + 4, 3.95/1.84 3.95/1.84 [g](x0, x1) = x0 + 2x1 + 5, 3.95/1.84 3.95/1.84 [f](x0, x1) = x0 + x1 + 7x1x1 + 4, 3.95/1.84 3.95/1.84 [d] = 0, 3.95/1.84 3.95/1.84 [t](x0) = 4x0 + 4, 3.95/1.84 3.95/1.84 [c] = 0, 3.95/1.84 3.95/1.84 [a] = 5 3.95/1.84 orientation: 3.95/1.84 a() = 5 >= 4 = t(c()) 3.95/1.84 3.95/1.84 a() = 5 >= 4 = t(d()) 3.95/1.84 3.95/1.84 f(x,y) = x + y + 7y*y + 4 >= x = x 3.95/1.84 3.95/1.84 g(x,x) = 3x + 5 >= 3x + 4 = h(x,x) 3.95/1.84 3.95/1.84 h(x,y) = 2x + y + 4 >= x = x 3.95/1.84 3.95/1.84 h(x,y) = 2x + y + 4 >= y = y 3.95/1.84 3.95/1.84 g(x,y) = x + 2y + 5 >= x = x 3.95/1.84 3.95/1.84 g(x,y) = x + 2y + 5 >= y = y 3.95/1.84 3.95/1.84 t(x) = 4x + 4 >= x = x 3.95/1.84 3.95/1.84 f(x,y) = x + y + 7y*y + 4 >= y = y 3.95/1.84 problem: 3.95/1.84 3.95/1.84 Qed 3.95/1.84 ConCon could not decide whether all 2 critical pairs are joinable or not. 3.95/1.84 Overlap: (rule1: a -> t(d), rule2: a -> t(c), pos: ε, mgu: {}) 3.95/1.84 CP: t(c) = t(d) 3.95/1.84 ConCon could not decide context-joinability of this critical pair. 3.95/1.84 3.95/1.87 EOF