YES

Problem:
 a(b(x1)) -> C(x1)
 b(c(x1)) -> A(x1)
 c(a(x1)) -> B(x1)
 A(C(x1)) -> b(x1)
 C(B(x1)) -> a(x1)
 B(A(x1)) -> c(x1)
 a(a(a(a(a(x1))))) -> A(A(A(x1)))
 A(A(A(A(x1)))) -> a(a(a(a(x1))))
 b(b(b(b(b(x1))))) -> B(B(B(x1)))
 B(B(B(B(x1)))) -> b(b(b(b(x1))))
 c(c(c(c(c(x1))))) -> C(C(C(x1)))
 C(C(C(C(x1)))) -> c(c(c(c(x1))))
 B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
 A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
 C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
 B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
 A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
 C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
 a(A(x1)) -> x1
 A(a(x1)) -> x1
 b(B(x1)) -> x1
 B(b(x1)) -> x1
 c(C(x1)) -> x1
 C(c(x1)) -> x1

Proof:
 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:
   a(b(x1)) = x1 + 4 >= x1 + 3 = C(x1)
   
   b(c(x1)) = x1 + 4 >= x1 + 3 = A(x1)
   
   c(a(x1)) = x1 + 4 >= x1 + 3 = B(x1)
   
   A(C(x1)) = x1 + 6 >= x1 + 2 = b(x1)
   
   C(B(x1)) = x1 + 6 >= x1 + 2 = a(x1)
   
   B(A(x1)) = x1 + 6 >= x1 + 2 = c(x1)
   
   a(a(a(a(a(x1))))) = x1 + 10 >= x1 + 9 = A(A(A(x1)))
   
   A(A(A(A(x1)))) = x1 + 12 >= x1 + 8 = a(a(a(a(x1))))
   
   b(b(b(b(b(x1))))) = x1 + 10 >= x1 + 9 = B(B(B(x1)))
   
   B(B(B(B(x1)))) = x1 + 12 >= x1 + 8 = b(b(b(b(x1))))
   
   c(c(c(c(c(x1))))) = x1 + 10 >= x1 + 9 = C(C(C(x1)))
   
   C(C(C(C(x1)))) = x1 + 12 >= x1 + 8 = c(c(c(c(x1))))
   
   B(a(a(a(a(x1))))) = x1 + 11 >= x1 + 11 = c(A(A(A(x1))))
   
   A(A(A(b(x1)))) = x1 + 11 >= x1 + 11 = a(a(a(a(C(x1)))))
   
   C(b(b(b(b(x1))))) = x1 + 11 >= x1 + 11 = a(B(B(B(x1))))
   
   B(B(B(c(x1)))) = x1 + 11 >= x1 + 11 = b(b(b(b(A(x1)))))
   
   A(c(c(c(c(x1))))) = x1 + 11 >= x1 + 11 = b(C(C(C(x1))))
   
   C(C(C(a(x1)))) = x1 + 11 >= x1 + 11 = c(c(c(c(B(x1)))))
   
   a(A(x1)) = x1 + 5 >= x1 = x1
   
   A(a(x1)) = x1 + 5 >= x1 = x1
   
   b(B(x1)) = x1 + 5 >= x1 = x1
   
   B(b(x1)) = x1 + 5 >= x1 = x1
   
   c(C(x1)) = x1 + 5 >= x1 = x1
   
   C(c(x1)) = x1 + 5 >= x1 = x1
  problem:
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
  Bounds Processor:
   bound: 0
   enrichment: match
   automaton:
    final states: {22,19,15,11,6,1}
    transitions:
     B0(2) -> 12*
     B0(12) -> 13*
     B0(13) -> 14*
     c0(5) -> 1*
     c0(12) -> 23*
     c0(23) -> 24*
     c0(25) -> 22*
     c0(24) -> 25*
     C0(7) -> 20*
     C0(2) -> 7*
     C0(20) -> 21*
     a0(14) -> 11*
     a0(10) -> 6*
     a0(9) -> 10*
     a0(8) -> 9*
     a0(7) -> 8*
     A0(4) -> 5*
     A0(2) -> 3*
     A0(3) -> 4*
     b0(17) -> 18*
     b0(3) -> 16*
     b0(21) -> 19*
     b0(18) -> 15*
     b0(16) -> 17*
     f60() -> 2*
     19 -> 3*
     11 -> 7*
     22 -> 7,20,21
     6 -> 3,4,5
     1 -> 12*
     15 -> 12,13,14
   problem:
    
   Qed