7.18/2.19 YES 7.18/2.19 7.18/2.19 Problem: 7.18/2.19 a(b(c(x1))) -> c(b(a(x1))) 7.18/2.19 C(B(A(x1))) -> A(B(C(x1))) 7.18/2.19 b(a(C(x1))) -> C(a(b(x1))) 7.18/2.19 c(A(B(x1))) -> B(A(c(x1))) 7.18/2.19 A(c(b(x1))) -> b(c(A(x1))) 7.18/2.19 B(C(a(x1))) -> a(C(B(x1))) 7.18/2.19 a(A(x1)) -> x1 7.18/2.19 A(a(x1)) -> x1 7.18/2.19 b(B(x1)) -> x1 7.18/2.19 B(b(x1)) -> x1 7.18/2.19 c(C(x1)) -> x1 7.18/2.19 C(c(x1)) -> x1 7.18/2.19 7.18/2.19 Proof: 7.18/2.19 Matrix Interpretation Processor: dim=1 7.18/2.19 7.18/2.19 interpretation: 7.18/2.19 [C](x0) = x0 + 2, 7.18/2.19 7.18/2.19 [B](x0) = x0 + 1, 7.18/2.19 7.18/2.19 [A](x0) = x0 + 3, 7.18/2.19 7.18/2.19 [a](x0) = x0 + 10, 7.18/2.19 7.18/2.19 [b](x0) = x0, 7.18/2.19 7.18/2.19 [c](x0) = x0 + 5 7.18/2.19 orientation: 7.18/2.19 a(b(c(x1))) = x1 + 15 >= x1 + 15 = c(b(a(x1))) 7.18/2.19 7.18/2.19 C(B(A(x1))) = x1 + 6 >= x1 + 6 = A(B(C(x1))) 7.18/2.19 7.18/2.19 b(a(C(x1))) = x1 + 12 >= x1 + 12 = C(a(b(x1))) 7.18/2.19 7.18/2.19 c(A(B(x1))) = x1 + 9 >= x1 + 9 = B(A(c(x1))) 7.18/2.19 7.18/2.19 A(c(b(x1))) = x1 + 8 >= x1 + 8 = b(c(A(x1))) 7.18/2.19 7.18/2.19 B(C(a(x1))) = x1 + 13 >= x1 + 13 = a(C(B(x1))) 7.18/2.19 7.18/2.19 a(A(x1)) = x1 + 13 >= x1 = x1 7.18/2.19 7.18/2.19 A(a(x1)) = x1 + 13 >= x1 = x1 7.18/2.19 7.18/2.19 b(B(x1)) = x1 + 1 >= x1 = x1 7.18/2.19 7.18/2.19 B(b(x1)) = x1 + 1 >= x1 = x1 7.18/2.19 7.18/2.19 c(C(x1)) = x1 + 7 >= x1 = x1 7.18/2.19 7.18/2.19 C(c(x1)) = x1 + 7 >= x1 = x1 7.18/2.19 problem: 7.18/2.19 a(b(c(x1))) -> c(b(a(x1))) 7.18/2.19 C(B(A(x1))) -> A(B(C(x1))) 7.18/2.19 b(a(C(x1))) -> C(a(b(x1))) 7.18/2.19 c(A(B(x1))) -> B(A(c(x1))) 7.18/2.19 A(c(b(x1))) -> b(c(A(x1))) 7.18/2.19 B(C(a(x1))) -> a(C(B(x1))) 7.18/2.19 String Reversal Processor: 7.18/2.19 c(b(a(x1))) -> a(b(c(x1))) 7.18/2.19 A(B(C(x1))) -> C(B(A(x1))) 7.18/2.19 C(a(b(x1))) -> b(a(C(x1))) 7.18/2.19 B(A(c(x1))) -> c(A(B(x1))) 7.18/2.19 b(c(A(x1))) -> A(c(b(x1))) 7.18/2.19 a(C(B(x1))) -> B(C(a(x1))) 7.18/2.19 Bounds Processor: 7.18/2.19 bound: 0 7.18/2.19 enrichment: match 7.18/2.19 automaton: 7.18/2.19 final states: {17,14,11,8,5,1} 7.18/2.19 transitions: 7.18/2.19 f60() -> 2* 7.18/2.19 a0(2) -> 18* 7.18/2.19 a0(9) -> 10* 7.18/2.19 a0(4) -> 1* 7.18/2.19 b0(10) -> 8* 7.18/2.19 b0(2) -> 15* 7.18/2.19 b0(3) -> 4* 7.18/2.19 c0(15) -> 16* 7.18/2.19 c0(2) -> 3* 7.18/2.19 c0(13) -> 11* 7.18/2.19 C0(7) -> 5* 7.18/2.19 C0(2) -> 9* 7.18/2.19 C0(18) -> 19* 7.18/2.19 B0(2) -> 12* 7.18/2.19 B0(19) -> 17* 7.18/2.19 B0(6) -> 7* 7.18/2.19 A0(12) -> 13* 7.18/2.19 A0(2) -> 6* 7.18/2.19 A0(16) -> 14* 7.18/2.19 1 -> 3,16 7.18/2.19 5 -> 6,13 7.18/2.19 8 -> 9,19 7.18/2.19 11 -> 12,7 7.18/2.19 14 -> 15,4 7.18/2.19 17 -> 18,10 7.18/2.19 problem: 7.18/2.19 7.18/2.19 Qed 7.18/2.20 EOF