10.46/3.09 YES 10.92/3.10 10.92/3.10 Problem: 10.92/3.10 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 10.92/3.10 b(a(b(b(x1)))) -> b(b(b(b(x1)))) 10.92/3.10 a(b(b(a(x1)))) -> b(a(a(a(x1)))) 10.92/3.10 b(a(b(a(x1)))) -> a(a(a(a(x1)))) 10.92/3.10 10.92/3.10 Proof: 10.92/3.10 String Reversal Processor: 10.92/3.10 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 10.92/3.10 b(b(a(b(x1)))) -> b(b(b(b(x1)))) 10.92/3.10 a(b(b(a(x1)))) -> a(a(a(b(x1)))) 10.92/3.10 a(b(a(b(x1)))) -> a(a(a(a(x1)))) 10.92/3.10 Matrix Interpretation Processor: dim=4 10.92/3.10 10.92/3.10 interpretation: 10.92/3.10 [1 1 0 0] [0] 10.92/3.10 [0 0 1 0] [0] 10.92/3.10 [a](x0) = [0 0 0 0]x0 + [1] 10.92/3.10 [0 1 0 1] [0], 10.92/3.10 10.92/3.10 [1 0 0 0] [0] 10.92/3.10 [0 1 1 1] [0] 10.92/3.10 [b](x0) = [0 0 0 0]x0 + [1] 10.92/3.10 [0 0 0 0] [0] 10.92/3.10 orientation: 10.92/3.10 [1 1 1 1] [1] [1 1 1 1] [0] 10.92/3.10 [0 1 1 1] [3] [0 1 1 1] [3] 10.92/3.10 b(a(b(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(a(b(x1)))) 10.92/3.10 [0 0 0 0] [0] [0 0 0 0] [0] 10.92/3.10 10.92/3.10 [1 1 1 1] [0] [1 0 0 0] [0] 10.92/3.10 [0 1 1 1] [3] [0 1 1 1] [3] 10.92/3.10 b(b(a(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(b(b(x1)))) 10.92/3.10 [0 0 0 0] [0] [0 0 0 0] [0] 10.92/3.10 10.92/3.10 [1 2 1 1] [2] [1 1 1 1] [2] 10.92/3.10 [0 0 0 0] [1] [0 0 0 0] [1] 10.92/3.10 a(b(b(a(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = a(a(a(b(x1)))) 10.92/3.10 [0 1 1 1] [2] [0 1 1 1] [2] 10.92/3.10 10.92/3.10 [1 2 2 2] [2] [1 1 1 0] [2] 10.92/3.10 [0 0 0 0] [1] [0 0 0 0] [1] 10.92/3.10 a(b(a(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = a(a(a(a(x1)))) 10.92/3.10 [0 1 1 1] [2] [0 1 1 1] [2] 10.92/3.10 problem: 10.92/3.10 b(b(a(b(x1)))) -> b(b(b(b(x1)))) 10.92/3.10 a(b(b(a(x1)))) -> a(a(a(b(x1)))) 10.92/3.10 a(b(a(b(x1)))) -> a(a(a(a(x1)))) 10.92/3.10 String Reversal Processor: 10.92/3.10 b(a(b(b(x1)))) -> b(b(b(b(x1)))) 10.92/3.10 a(b(b(a(x1)))) -> b(a(a(a(x1)))) 10.92/3.10 b(a(b(a(x1)))) -> a(a(a(a(x1)))) 10.92/3.10 Bounds Processor: 10.92/3.10 bound: 0 10.92/3.10 enrichment: match 10.92/3.10 automaton: 10.92/3.10 final states: {10,6,1} 10.92/3.10 transitions: 10.92/3.10 f20() -> 2* 10.92/3.10 b0(5) -> 1* 10.92/3.10 b0(2) -> 3* 10.92/3.10 b0(9) -> 6* 10.92/3.10 b0(4) -> 5* 10.92/3.10 b0(3) -> 4* 10.92/3.10 a0(7) -> 8* 10.92/3.10 a0(2) -> 7* 10.92/3.10 a0(9) -> 10* 10.92/3.10 a0(8) -> 9* 10.92/3.10 1 -> 3* 10.92/3.10 6 -> 7* 10.92/3.10 10 -> 3* 10.92/3.10 problem: 10.92/3.10 10.92/3.10 Qed 10.92/3.10 EOF