2.39/1.20 MAYBE 2.39/1.20 2.39/1.20 Proof: 2.39/1.20 ConCon could not decide confluence of the system. 2.39/1.20 \cite{ALS94}, Theorem 4.1 does not apply. 2.44/1.20 This system is of type 3 or smaller. 2.44/1.20 This system is strongly deterministic. 2.44/1.20 This system is quasi-decreasing. 2.44/1.20 By \cite{O02}, p. 214, Proposition 7.2.50. 2.44/1.20 This system is of type 3 or smaller. 2.44/1.20 This system is deterministic. 2.44/1.20 System R transformed to U(R). 2.44/1.20 This system is terminating. 2.44/1.20 Call external tool: 2.44/1.20 ./ttt2.sh 2.44/1.20 Input: 2.44/1.20 a -> c 2.44/1.20 a -> d 2.44/1.20 b -> c 2.44/1.20 b -> d 2.44/1.20 g(x, x) -> h(x, x) 2.44/1.20 ?1(c, x) -> x 2.44/1.20 f(x) -> ?1(x, x) 2.44/1.20 2.44/1.20 Polynomial Interpretation Processor: 2.44/1.20 dimension: 1 2.44/1.20 interpretation: 2.44/1.21 [f](x0) = x0 + 4x0x0 + 2, 2.44/1.21 2.44/1.21 [?1](x0, x1) = x1 + 4x0x0 + 1, 2.44/1.21 2.44/1.21 [h](x0, x1) = 2x0 + -4x1 + x0x0 + 5x1x1, 2.44/1.21 2.44/1.21 [g](x0, x1) = 2x0 + 2x1 + 6x1x1 + 1, 2.44/1.21 2.44/1.21 [b] = 1, 2.44/1.21 2.44/1.21 [d] = 0, 2.44/1.21 2.44/1.21 [c] = 0, 2.44/1.21 2.44/1.21 [a] = 1 2.44/1.21 orientation: 2.44/1.21 a() = 1 >= 0 = c() 2.44/1.21 2.44/1.21 a() = 1 >= 0 = d() 2.44/1.21 2.44/1.21 b() = 1 >= 0 = c() 2.44/1.21 2.44/1.21 b() = 1 >= 0 = d() 2.44/1.21 2.44/1.21 g(x,x) = 4x + 6x*x + 1 >= -2x + 6x*x = h(x,x) 2.44/1.21 2.44/1.21 ?1(c(),x) = x + 1 >= x = x 2.44/1.21 2.44/1.21 f(x) = x + 4x*x + 2 >= x + 4x*x + 1 = ?1(x,x) 2.44/1.21 problem: 2.44/1.21 2.44/1.21 Qed 2.44/1.21 This critical pair is not unfeasible. 2.44/1.21 ConCon could not decide whether all 4 critical pairs are joinable or not. 2.44/1.21 Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {}) 2.44/1.21 CP: c = d 2.44/1.21 This critical pair is not unfeasible. 2.44/1.21 2.46/1.23 EOF