16.06/4.43 YES 16.06/4.43 16.06/4.43 Problem: 16.06/4.43 strict: 16.06/4.43 c(c(c(x1))) -> c(b(c(x1))) 16.06/4.43 b(b(c(x1))) -> a(c(b(x1))) 16.06/4.43 b(a(b(x1))) -> c(c(b(x1))) 16.06/4.43 weak: 16.06/4.43 b(a(a(x1))) -> a(a(b(x1))) 16.06/4.43 b(b(a(x1))) -> a(b(c(x1))) 16.06/4.43 b(b(a(x1))) -> a(a(c(x1))) 16.06/4.43 16.06/4.43 Proof: 16.06/4.43 Matrix Interpretation Processor: dim=1 16.06/4.43 16.06/4.43 interpretation: 16.06/4.43 [a](x0) = 3x0 + 2, 16.06/4.43 16.06/4.43 [b](x0) = 3x0, 16.06/4.43 16.06/4.43 [c](x0) = 3x0 + 1 16.06/4.43 orientation: 16.06/4.43 c(c(c(x1))) = 27x1 + 13 >= 27x1 + 10 = c(b(c(x1))) 16.06/4.43 16.06/4.43 b(b(c(x1))) = 27x1 + 9 >= 27x1 + 5 = a(c(b(x1))) 16.06/4.43 16.06/4.43 b(a(b(x1))) = 27x1 + 6 >= 27x1 + 4 = c(c(b(x1))) 16.06/4.43 16.06/4.43 b(a(a(x1))) = 27x1 + 24 >= 27x1 + 8 = a(a(b(x1))) 16.06/4.43 16.06/4.43 b(b(a(x1))) = 27x1 + 18 >= 27x1 + 11 = a(b(c(x1))) 16.06/4.43 16.06/4.43 b(b(a(x1))) = 27x1 + 18 >= 27x1 + 17 = a(a(c(x1))) 16.06/4.43 problem: 16.06/4.43 strict: 16.06/4.43 16.06/4.43 weak: 16.06/4.43 16.06/4.43 Qed 16.06/4.44 EOF