YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   b#(c(x1)) -> a#(b(b(x1)))
   b#(c(x1)) -> a#(a(b(b(x1))))
  TRS:
   a(b(x1)) -> x1
   a(c(x1)) -> c(c(x1))
   b(c(x1)) -> a(a(b(b(x1))))
  TDG Processor:
   DPs:
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> a#(b(b(x1)))
    b#(c(x1)) -> a#(a(b(b(x1))))
   TRS:
    a(b(x1)) -> x1
    a(c(x1)) -> c(c(x1))
    b(c(x1)) -> a(a(b(b(x1))))
   graph:
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(b(b(x1))))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(b(b(x1)))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(b(b(x1))))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(b(x1)))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     b#(c(x1)) -> b#(b(x1))
     b#(c(x1)) -> b#(x1)
    TRS:
     a(b(x1)) -> x1
     a(c(x1)) -> c(c(x1))
     b(c(x1)) -> a(a(b(b(x1))))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0) = -2x0 + 0,
      
      [c](x0) = 1x0 + 3,
      
      [a](x0) = 1x0 + 1,
      
      [b](x0) = -1x0 + 0
     orientation:
      b#(c(x1)) = -1x1 + 1 >= -3x1 + 0 = b#(b(x1))
      
      b#(c(x1)) = -1x1 + 1 >= -2x1 + 0 = b#(x1)
      
      a(b(x1)) = x1 + 1 >= x1 = x1
      
      a(c(x1)) = 2x1 + 4 >= 2x1 + 4 = c(c(x1))
      
      b(c(x1)) = x1 + 2 >= x1 + 2 = a(a(b(b(x1))))
     problem:
      DPs:
       
      TRS:
       a(b(x1)) -> x1
       a(c(x1)) -> c(c(x1))
       b(c(x1)) -> a(a(b(b(x1))))
     Qed