YES

Problem:
 a(b(x)) -> b(a(a(x)))
 b(c(x)) -> c(b(b(x)))
 c(a(x)) -> a(c(c(x)))
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
 a(u(x)) -> x
 b(v(x)) -> x
 c(w(x)) -> x

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [w](x0) = 7x0,
   
   [v](x0) = 10x0,
   
   [u](x0) = 14x0,
   
   [c](x0) = x0,
   
   [a](x0) = x0,
   
   [b](x0) = x0
  orientation:
   a(b(x)) = x >= x = b(a(a(x)))
   
   b(c(x)) = x >= x = c(b(b(x)))
   
   c(a(x)) = x >= x = a(c(c(x)))
   
   u(a(x)) = 14x >= x = x
   
   v(b(x)) = 10x >= x = x
   
   w(c(x)) = 7x >= x = x
   
   a(u(x)) = 14x >= x = x
   
   b(v(x)) = 10x >= x = x
   
   c(w(x)) = 7x >= x = x
  problem:
   a(b(x)) -> b(a(a(x)))
   b(c(x)) -> c(b(b(x)))
   c(a(x)) -> a(c(c(x)))
  String Reversal Processor:
   b(a(x)) -> a(a(b(x)))
   c(b(x)) -> b(b(c(x)))
   a(c(x)) -> c(c(a(x)))
   Bounds Processor:
    bound: 0
    enrichment: match
    automaton:
     final states: {8,5,1}
     transitions:
      a0(2) -> 9*
      a0(4) -> 1*
      a0(3) -> 4*
      b0(7) -> 5*
      b0(2) -> 3*
      b0(6) -> 7*
      c0(10) -> 8*
      c0(2) -> 6*
      c0(9) -> 10*
      f60() -> 2*
      1 -> 3*
      5 -> 6*
      8 -> 9*
    problem:
     
    Qed