23.93/6.41 YES 23.93/6.42 23.93/6.42 Problem: 23.93/6.42 strict: 23.93/6.42 b(c(a(x1))) -> a(b(a(x1))) 23.93/6.42 a(a(a(x1))) -> c(c(c(x1))) 23.93/6.42 a(a(a(x1))) -> a(b(a(x1))) 23.93/6.42 weak: 23.93/6.42 c(c(a(x1))) -> c(a(c(x1))) 23.93/6.42 b(a(b(x1))) -> b(c(c(x1))) 23.93/6.42 c(a(b(x1))) -> a(c(b(x1))) 23.93/6.42 23.93/6.42 Proof: 23.93/6.42 String Reversal Processor: 23.93/6.42 strict: 23.93/6.42 a(c(b(x1))) -> a(b(a(x1))) 23.93/6.42 a(a(a(x1))) -> c(c(c(x1))) 23.93/6.42 a(a(a(x1))) -> a(b(a(x1))) 23.93/6.42 weak: 23.93/6.42 a(c(c(x1))) -> c(a(c(x1))) 23.93/6.42 b(a(b(x1))) -> c(c(b(x1))) 23.93/6.42 b(a(c(x1))) -> b(c(a(x1))) 23.93/6.42 Arctic Interpretation Processor: 23.93/6.42 dimension: 2 23.93/6.42 interpretation: 23.93/6.42 [1 0] 23.93/6.42 [b](x0) = [2 2]x0, 23.93/6.42 23.93/6.42 [0 0 ] 23.93/6.42 [c](x0) = [-& -&]x0, 23.93/6.42 23.93/6.42 [1 0 ] 23.93/6.42 [a](x0) = [-& -&]x0 23.93/6.42 orientation: 23.93/6.42 [3 3 ] [3 2 ] 23.93/6.42 a(c(b(x1))) = [-& -&]x1 >= [-& -&]x1 = a(b(a(x1))) 23.93/6.42 23.93/6.42 [3 2 ] [0 0 ] 23.93/6.42 a(a(a(x1))) = [-& -&]x1 >= [-& -&]x1 = c(c(c(x1))) 23.93/6.42 23.93/6.42 [3 2 ] [3 2 ] 23.93/6.42 a(a(a(x1))) = [-& -&]x1 >= [-& -&]x1 = a(b(a(x1))) 23.93/6.42 23.93/6.42 [1 1 ] [1 1 ] 23.93/6.42 a(c(c(x1))) = [-& -&]x1 >= [-& -&]x1 = c(a(c(x1))) 23.93/6.42 23.93/6.42 [3 3] [2 2 ] 23.93/6.42 b(a(b(x1))) = [4 4]x1 >= [-& -&]x1 = c(c(b(x1))) 23.93/6.42 23.93/6.42 [2 2] [2 1] 23.93/6.42 b(a(c(x1))) = [3 3]x1 >= [3 2]x1 = b(c(a(x1))) 23.93/6.42 problem: 23.93/6.42 strict: 23.93/6.42 a(c(b(x1))) -> a(b(a(x1))) 23.93/6.42 a(a(a(x1))) -> a(b(a(x1))) 23.93/6.42 weak: 23.93/6.42 a(c(c(x1))) -> c(a(c(x1))) 23.93/6.42 b(a(c(x1))) -> b(c(a(x1))) 23.93/6.42 Arctic Interpretation Processor: 23.93/6.42 dimension: 1 23.93/6.42 interpretation: 23.93/6.42 [b](x0) = x0, 23.93/6.42 23.93/6.42 [c](x0) = 4x0, 23.93/6.42 23.93/6.42 [a](x0) = x0 23.93/6.42 orientation: 23.93/6.42 a(c(b(x1))) = 4x1 >= x1 = a(b(a(x1))) 23.93/6.42 23.93/6.42 a(a(a(x1))) = x1 >= x1 = a(b(a(x1))) 23.93/6.42 23.93/6.42 a(c(c(x1))) = 8x1 >= 8x1 = c(a(c(x1))) 23.93/6.42 23.93/6.42 b(a(c(x1))) = 4x1 >= 4x1 = b(c(a(x1))) 23.93/6.42 problem: 23.93/6.42 strict: 23.93/6.42 a(a(a(x1))) -> a(b(a(x1))) 23.93/6.42 weak: 23.93/6.42 a(c(c(x1))) -> c(a(c(x1))) 23.93/6.42 b(a(c(x1))) -> b(c(a(x1))) 23.93/6.42 String Reversal Processor: 23.93/6.42 strict: 23.93/6.42 a(a(a(x1))) -> a(b(a(x1))) 23.93/6.42 weak: 23.93/6.42 c(c(a(x1))) -> c(a(c(x1))) 23.93/6.42 c(a(b(x1))) -> a(c(b(x1))) 23.93/6.42 Arctic Interpretation Processor: 23.93/6.42 dimension: 1 23.93/6.42 interpretation: 23.93/6.42 [b](x0) = x0, 23.93/6.42 23.93/6.42 [c](x0) = 3x0, 23.93/6.42 23.93/6.42 [a](x0) = 8x0 23.93/6.42 orientation: 23.93/6.42 a(a(a(x1))) = 24x1 >= 16x1 = a(b(a(x1))) 23.93/6.42 23.93/6.42 c(c(a(x1))) = 14x1 >= 14x1 = c(a(c(x1))) 23.93/6.42 23.93/6.42 c(a(b(x1))) = 11x1 >= 11x1 = a(c(b(x1))) 23.93/6.42 problem: 23.93/6.42 strict: 23.93/6.42 23.93/6.42 weak: 23.93/6.42 c(c(a(x1))) -> c(a(c(x1))) 23.93/6.42 c(a(b(x1))) -> a(c(b(x1))) 23.93/6.42 Qed 23.97/6.42 EOF