YES

Problem:
 a(b(x1)) -> x1
 a(c(x1)) -> b(c(a(a(x1))))
 c(b(x1)) -> a(c(x1))

Proof:
 String Reversal Processor:
  b(a(x1)) -> x1
  c(a(x1)) -> a(a(c(b(x1))))
  b(c(x1)) -> c(a(x1))
  DP Processor:
   DPs:
    c#(a(x1)) -> b#(x1)
    c#(a(x1)) -> c#(b(x1))
    b#(c(x1)) -> c#(a(x1))
   TRS:
    b(a(x1)) -> x1
    c(a(x1)) -> a(a(c(b(x1))))
    b(c(x1)) -> c(a(x1))
   TDG Processor:
    DPs:
     c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> c#(b(x1))
     b#(c(x1)) -> c#(a(x1))
    TRS:
     b(a(x1)) -> x1
     c(a(x1)) -> a(a(c(b(x1))))
     b(c(x1)) -> c(a(x1))
    graph:
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(a(x1))
     b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> c#(b(x1))
     b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> b#(x1)
    CDG Processor:
     DPs:
      c#(a(x1)) -> b#(x1)
      c#(a(x1)) -> c#(b(x1))
      b#(c(x1)) -> c#(a(x1))
     TRS:
      b(a(x1)) -> x1
      c(a(x1)) -> a(a(c(b(x1))))
      b(c(x1)) -> c(a(x1))
     graph:
      c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
      c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
      b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> b#(x1)
      b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> c#(b(x1))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 4/9
      DPs:
       c#(a(x1)) -> c#(b(x1))
      TRS:
       b(a(x1)) -> x1
       c(a(x1)) -> a(a(c(b(x1))))
       b(c(x1)) -> c(a(x1))
      Bounds Processor:
       bound: 1
       enrichment: match-dp
       automaton:
        final states: {1}
        transitions:
         c{#,1}(24) -> 25*
         b1(36) -> 37*
         b1(23) -> 24*
         f60() -> 2*
         c{#,0}(3) -> 1*
         b0(10) -> 11*
         b0(2) -> 3*
         c0(26) -> 27*
         c0(11) -> 12*
         c0(8) -> 9*
         a0(27) -> 28*
         a0(12) -> 13*
         a0(7) -> 8*
         a0(28) -> 29*
         a0(13) -> 14*
         2 -> 11,7,3
         7 -> 10*
         9 -> 11,3
         12 -> 24*
         13 -> 23*
         14 -> 12,24,26,9,3
         24 -> 26*
         25 -> 1*
         27 -> 37,24
         28 -> 36*
         29 -> 27,12,24
         37 -> 24*
       problem:
        DPs:
         
        TRS:
         b(a(x1)) -> x1
         c(a(x1)) -> a(a(c(b(x1))))
         b(c(x1)) -> c(a(x1))
       Qed