4.74/2.18 MAYBE 4.74/2.18 4.74/2.18 Proof: 4.74/2.18 ConCon could not decide confluence of the system. 4.74/2.18 \cite{ALS94}, Theorem 4.1 does not apply. 4.74/2.18 This system is of type 3 or smaller. 4.74/2.18 This system is strongly deterministic. 4.74/2.18 This system is quasi-decreasing. 4.74/2.18 By \cite{A14}, Theorem 11.5.9. 4.74/2.18 This system is of type 3 or smaller. 4.74/2.18 This system is deterministic. 4.74/2.18 System R transformed to V(R) + Emb. 4.88/2.18 This system is terminating. 4.88/2.18 Call external tool: 4.88/2.18 ./ttt2.sh 4.88/2.18 Input: 4.88/2.18 (VAR x y z) 4.88/2.18 (RULES 4.88/2.18 f(x) -> x 4.88/2.18 g(d, x, x) -> A 4.88/2.18 h(x, x) -> g(x, x, f(k)) 4.88/2.18 c -> e' 4.88/2.18 a -> c 4.88/2.18 a -> d 4.88/2.18 b -> c 4.88/2.18 b -> d 4.88/2.18 c -> e 4.88/2.18 c -> l 4.88/2.18 k -> l 4.88/2.18 k -> m 4.88/2.18 d -> m 4.88/2.18 h(x, y) -> x 4.88/2.18 h(x, y) -> y 4.88/2.18 g(x, y, z) -> x 4.88/2.18 g(x, y, z) -> y 4.88/2.18 g(x, y, z) -> z 4.88/2.18 f(x) -> x 4.88/2.18 ) 4.88/2.18 4.88/2.18 Polynomial Interpretation Processor: 4.88/2.18 dimension: 1 4.88/2.18 interpretation: 4.88/2.18 [m] = 0, 4.88/2.18 4.88/2.18 [l] = 0, 4.88/2.18 4.88/2.18 [e] = 0, 4.88/2.18 4.88/2.18 [b] = 4, 4.88/2.18 4.88/2.18 [a] = 4, 4.88/2.18 4.88/2.18 [e'] = 0, 4.88/2.18 4.88/2.18 [c] = 1, 4.88/2.18 4.88/2.18 [k] = 1, 4.88/2.18 4.88/2.18 [h](x0, x1) = x0 + 6x1 + x1x1 + 7, 4.88/2.18 4.88/2.18 [A] = 0, 4.88/2.18 4.88/2.18 [g](x0, x1, x2) = x0 + 6x1 + x2 + 1, 4.88/2.18 4.88/2.18 [d] = 1, 4.88/2.18 4.88/2.18 [f](x0) = 4x0 + 1 4.88/2.18 orientation: 4.88/2.18 f(x) = 4x + 1 >= x = x 4.88/2.18 4.88/2.18 g(d(),x,x) = 7x + 2 >= 0 = A() 4.88/2.18 4.88/2.18 h(x,x) = 7x + x*x + 7 >= 7x + 6 = g(x,x,f(k())) 4.88/2.18 4.88/2.18 c() = 1 >= 0 = e'() 4.88/2.18 4.88/2.18 a() = 4 >= 1 = c() 4.88/2.18 4.88/2.18 a() = 4 >= 1 = d() 4.88/2.18 4.88/2.18 b() = 4 >= 1 = c() 4.88/2.18 4.88/2.18 b() = 4 >= 1 = d() 4.88/2.18 4.88/2.18 c() = 1 >= 0 = e() 4.88/2.18 4.88/2.18 c() = 1 >= 0 = l() 4.88/2.18 4.88/2.18 k() = 1 >= 0 = l() 4.88/2.18 4.88/2.18 k() = 1 >= 0 = m() 4.88/2.18 4.88/2.18 d() = 1 >= 0 = m() 4.88/2.18 4.88/2.19 h(x,y) = x + 6y + y*y + 7 >= x = x 4.88/2.19 4.88/2.19 h(x,y) = x + 6y + y*y + 7 >= y = y 4.88/2.19 4.88/2.19 g(x,y,z) = x + 6y + z + 1 >= x = x 4.88/2.19 4.88/2.19 g(x,y,z) = x + 6y + z + 1 >= y = y 4.88/2.19 4.88/2.19 g(x,y,z) = x + 6y + z + 1 >= z = z 4.88/2.19 problem: 4.88/2.19 4.88/2.19 Qed 4.88/2.19 ConCon could not decide whether all 13 critical pairs are joinable or not. 4.88/2.19 Overlap: (rule1: g(d, y, y) -> A, rule2: d -> m, pos: 1, mgu: {}) 4.88/2.19 CP: g(m, y, y) = A 4.88/2.19 ConCon could not decide context-joinability of this critical pair. 4.88/2.19 4.88/2.19 EOF