YES Problem: a(a(b(b(x1)))) -> C(C(x1)) b(b(c(c(x1)))) -> A(A(x1)) c(c(a(a(x1)))) -> B(B(x1)) A(A(C(C(x1)))) -> b(b(x1)) C(C(B(B(x1)))) -> a(a(x1)) B(B(A(A(x1)))) -> c(c(x1)) a(a(a(a(a(a(a(a(a(a(x1)))))))))) -> A(A(A(A(A(A(x1)))))) A(A(A(A(A(A(A(A(x1)))))))) -> a(a(a(a(a(a(a(a(x1)))))))) b(b(b(b(b(b(b(b(b(b(x1)))))))))) -> B(B(B(B(B(B(x1)))))) B(B(B(B(B(B(B(B(x1)))))))) -> b(b(b(b(b(b(b(b(x1)))))))) c(c(c(c(c(c(c(c(c(c(x1)))))))))) -> C(C(C(C(C(C(x1)))))) C(C(C(C(C(C(C(C(x1)))))))) -> c(c(c(c(c(c(c(c(x1)))))))) B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> c(c(A(A(A(A(A(A(x1)))))))) A(A(A(A(A(A(b(b(x1)))))))) -> a(a(a(a(a(a(a(a(C(C(x1)))))))))) C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> a(a(B(B(B(B(B(B(x1)))))))) B(B(B(B(B(B(c(c(x1)))))))) -> b(b(b(b(b(b(b(b(A(A(x1)))))))))) A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> b(b(C(C(C(C(C(C(x1)))))))) C(C(C(C(C(C(a(a(x1)))))))) -> c(c(c(c(c(c(c(c(B(B(x1)))))))))) a(a(A(A(x1)))) -> x1 A(A(a(a(x1)))) -> x1 b(b(B(B(x1)))) -> x1 B(B(b(b(x1)))) -> x1 c(c(C(C(x1)))) -> x1 C(C(c(c(x1)))) -> x1 Proof: String Reversal Processor: b(b(a(a(x1)))) -> C(C(x1)) c(c(b(b(x1)))) -> A(A(x1)) a(a(c(c(x1)))) -> B(B(x1)) C(C(A(A(x1)))) -> b(b(x1)) B(B(C(C(x1)))) -> a(a(x1)) A(A(B(B(x1)))) -> c(c(x1)) a(a(a(a(a(a(a(a(a(a(x1)))))))))) -> A(A(A(A(A(A(x1)))))) A(A(A(A(A(A(A(A(x1)))))))) -> a(a(a(a(a(a(a(a(x1)))))))) b(b(b(b(b(b(b(b(b(b(x1)))))))))) -> B(B(B(B(B(B(x1)))))) B(B(B(B(B(B(B(B(x1)))))))) -> b(b(b(b(b(b(b(b(x1)))))))) c(c(c(c(c(c(c(c(c(c(x1)))))))))) -> C(C(C(C(C(C(x1)))))) C(C(C(C(C(C(C(C(x1)))))))) -> c(c(c(c(c(c(c(c(x1)))))))) a(a(a(a(a(a(a(a(B(B(x1)))))))))) -> A(A(A(A(A(A(c(c(x1)))))))) b(b(A(A(A(A(A(A(x1)))))))) -> C(C(a(a(a(a(a(a(a(a(x1)))))))))) b(b(b(b(b(b(b(b(C(C(x1)))))))))) -> B(B(B(B(B(B(a(a(x1)))))))) c(c(B(B(B(B(B(B(x1)))))))) -> A(A(b(b(b(b(b(b(b(b(x1)))))))))) c(c(c(c(c(c(c(c(A(A(x1)))))))))) -> C(C(C(C(C(C(b(b(x1)))))))) a(a(C(C(C(C(C(C(x1)))))))) -> B(B(c(c(c(c(c(c(c(c(x1)))))))))) A(A(a(a(x1)))) -> x1 a(a(A(A(x1)))) -> x1 B(B(b(b(x1)))) -> x1 b(b(B(B(x1)))) -> x1 C(C(c(c(x1)))) -> x1 c(c(C(C(x1)))) -> x1 Matrix Interpretation Processor: dim=1 interpretation: [A](x0) = x0 + 3, [a](x0) = x0 + 2, [c](x0) = x0 + 2, [B](x0) = x0 + 3, [b](x0) = x0 + 2, [C](x0) = x0 + 3 orientation: b(b(a(a(x1)))) = x1 + 8 >= x1 + 6 = C(C(x1)) c(c(b(b(x1)))) = x1 + 8 >= x1 + 6 = A(A(x1)) a(a(c(c(x1)))) = x1 + 8 >= x1 + 6 = B(B(x1)) C(C(A(A(x1)))) = x1 + 12 >= x1 + 4 = b(b(x1)) B(B(C(C(x1)))) = x1 + 12 >= x1 + 4 = a(a(x1)) A(A(B(B(x1)))) = x1 + 12 >= x1 + 4 = c(c(x1)) a(a(a(a(a(a(a(a(a(a(x1)))))))))) = x1 + 20 >= x1 + 18 = A(A(A(A(A(A(x1)))))) A(A(A(A(A(A(A(A(x1)))))))) = x1 + 24 >= x1 + 16 = a(a(a(a(a(a(a(a(x1)))))))) b(b(b(b(b(b(b(b(b(b(x1)))))))))) = x1 + 20 >= x1 + 18 = B(B(B(B(B(B(x1)))))) B(B(B(B(B(B(B(B(x1)))))))) = x1 + 24 >= x1 + 16 = b(b(b(b(b(b(b(b(x1)))))))) c(c(c(c(c(c(c(c(c(c(x1)))))))))) = x1 + 20 >= x1 + 18 = C(C(C(C(C(C(x1)))))) C(C(C(C(C(C(C(C(x1)))))))) = x1 + 24 >= x1 + 16 = c(c(c(c(c(c(c(c(x1)))))))) a(a(a(a(a(a(a(a(B(B(x1)))))))))) = x1 + 22 >= x1 + 22 = A(A(A(A(A(A(c(c(x1)))))))) b(b(A(A(A(A(A(A(x1)))))))) = x1 + 22 >= x1 + 22 = C(C(a(a(a(a(a(a(a(a(x1)))))))))) b(b(b(b(b(b(b(b(C(C(x1)))))))))) = x1 + 22 >= x1 + 22 = B(B(B(B(B(B(a(a(x1)))))))) c(c(B(B(B(B(B(B(x1)))))))) = x1 + 22 >= x1 + 22 = A(A(b(b(b(b(b(b(b(b(x1)))))))))) c(c(c(c(c(c(c(c(A(A(x1)))))))))) = x1 + 22 >= x1 + 22 = C(C(C(C(C(C(b(b(x1)))))))) a(a(C(C(C(C(C(C(x1)))))))) = x1 + 22 >= x1 + 22 = B(B(c(c(c(c(c(c(c(c(x1)))))))))) A(A(a(a(x1)))) = x1 + 10 >= x1 = x1 a(a(A(A(x1)))) = x1 + 10 >= x1 = x1 B(B(b(b(x1)))) = x1 + 10 >= x1 = x1 b(b(B(B(x1)))) = x1 + 10 >= x1 = x1 C(C(c(c(x1)))) = x1 + 10 >= x1 = x1 c(c(C(C(x1)))) = x1 + 10 >= x1 = x1 problem: a(a(a(a(a(a(a(a(B(B(x1)))))))))) -> A(A(A(A(A(A(c(c(x1)))))))) b(b(A(A(A(A(A(A(x1)))))))) -> C(C(a(a(a(a(a(a(a(a(x1)))))))))) b(b(b(b(b(b(b(b(C(C(x1)))))))))) -> B(B(B(B(B(B(a(a(x1)))))))) c(c(B(B(B(B(B(B(x1)))))))) -> A(A(b(b(b(b(b(b(b(b(x1)))))))))) c(c(c(c(c(c(c(c(A(A(x1)))))))))) -> C(C(C(C(C(C(b(b(x1)))))))) a(a(C(C(C(C(C(C(x1)))))))) -> B(B(c(c(c(c(c(c(c(c(x1)))))))))) String Reversal Processor: B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> c(c(A(A(A(A(A(A(x1)))))))) A(A(A(A(A(A(b(b(x1)))))))) -> a(a(a(a(a(a(a(a(C(C(x1)))))))))) C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> a(a(B(B(B(B(B(B(x1)))))))) B(B(B(B(B(B(c(c(x1)))))))) -> b(b(b(b(b(b(b(b(A(A(x1)))))))))) A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> b(b(C(C(C(C(C(C(x1)))))))) C(C(C(C(C(C(a(a(x1)))))))) -> c(c(c(c(c(c(c(c(B(B(x1)))))))))) Bounds Processor: bound: 0 enrichment: match automaton: final states: {42,36,28,20,10,1} transitions: B0(2) -> 21* B0(23) -> 24* B0(24) -> 25* B0(22) -> 23* B0(21) -> 22* B0(25) -> 26* c0(47) -> 48* c0(44) -> 45* c0(22) -> 43* c0(45) -> 46* c0(8) -> 9* c0(43) -> 44* c0(48) -> 49* c0(49) -> 42* c0(9) -> 1* c0(46) -> 47* C0(38) -> 39* C0(39) -> 40* C0(11) -> 12* C0(12) -> 37* C0(37) -> 38* C0(2) -> 11* a0(12) -> 13* a0(17) -> 18* a0(14) -> 15* a0(13) -> 14* a0(15) -> 16* a0(27) -> 20* a0(18) -> 19* a0(26) -> 27* a0(19) -> 10* a0(16) -> 17* A0(4) -> 5* A0(2) -> 3* A0(5) -> 6* A0(3) -> 4* A0(6) -> 7* A0(7) -> 8* b0(33) -> 34* b0(29) -> 30* b0(35) -> 28* b0(30) -> 31* b0(41) -> 36* b0(4) -> 29* b0(32) -> 33* b0(40) -> 41* b0(34) -> 35* b0(31) -> 32* f60() -> 2* 42 -> 11,12,37,38,39,40 28 -> 21,22,23,24,25,26 36 -> 3,4 1 -> 21,22 20 -> 11,12 10 -> 3,4,5,6,7,8 problem: Qed