8.01/2.34 YES 8.01/2.34 8.01/2.34 Problem: 8.01/2.34 strict: 8.01/2.34 b(c(c(x1))) -> a(c(b(x1))) 8.01/2.34 c(a(a(x1))) -> c(b(b(x1))) 8.01/2.34 a(b(a(x1))) -> c(b(a(x1))) 8.01/2.34 weak: 8.01/2.34 a(b(c(x1))) -> a(a(c(x1))) 8.01/2.34 c(a(a(x1))) -> c(a(b(x1))) 8.01/2.34 a(b(c(x1))) -> c(c(c(x1))) 8.01/2.34 8.01/2.34 Proof: 8.01/2.34 Matrix Interpretation Processor: dim=2 8.01/2.34 8.01/2.34 interpretation: 8.01/2.34 [1 2] [0] 8.01/2.34 [a](x0) = [0 0]x0 + [1], 8.01/2.34 8.01/2.34 [1 0] [0] 8.01/2.34 [b](x0) = [0 0]x0 + [1], 8.01/2.34 8.01/2.34 [1 0] [1] 8.01/2.34 [c](x0) = [0 0]x0 + [0] 8.01/2.34 orientation: 8.01/2.34 [1 0] [2] [1 0] [1] 8.01/2.34 b(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(c(b(x1))) 8.01/2.34 8.01/2.34 [1 2] [3] [1 0] [1] 8.01/2.34 c(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(b(b(x1))) 8.01/2.34 8.01/2.34 [1 2] [2] [1 2] [1] 8.01/2.34 a(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(b(a(x1))) 8.01/2.34 8.01/2.34 [1 0] [3] [1 0] [3] 8.01/2.34 a(b(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(a(c(x1))) 8.01/2.34 8.01/2.34 [1 2] [3] [1 0] [3] 8.01/2.34 c(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(a(b(x1))) 8.01/2.34 8.01/2.34 [1 0] [3] [1 0] [3] 8.01/2.34 a(b(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(c(c(x1))) 8.01/2.34 problem: 8.01/2.34 strict: 8.01/2.34 8.01/2.34 weak: 8.01/2.34 a(b(c(x1))) -> a(a(c(x1))) 8.01/2.34 c(a(a(x1))) -> c(a(b(x1))) 8.01/2.34 a(b(c(x1))) -> c(c(c(x1))) 8.01/2.34 Qed 8.01/2.35 EOF