YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> c#(b(x1))
   a#(b(x1)) -> b#(c(b(x1)))
   a#(b(x1)) -> c#(b(c(b(x1))))
   b#(x1) -> a#(x1)
   b#(x1) -> a#(a(x1))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> c(b(c(b(x1))))
   b(x1) -> a(a(x1))
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> c#(b(x1))
    a#(b(x1)) -> b#(c(b(x1)))
    a#(b(x1)) -> c#(b(c(b(x1))))
    b#(x1) -> a#(x1)
    b#(x1) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> c(b(c(b(x1))))
    b(x1) -> a(a(x1))
    c(c(x1)) -> x1
   graph:
    b#(x1) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(c(b(x1))))
    b#(x1) -> a#(a(x1)) -> a#(b(x1)) -> b#(c(b(x1)))
    b#(x1) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(x1))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(c(b(x1))))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> b#(c(b(x1)))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(x1))
    a#(b(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(a(x1))
    a#(b(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 8/25
    DPs:
     b#(x1) -> a#(a(x1))
     a#(b(x1)) -> b#(c(b(x1)))
     b#(x1) -> a#(x1)
    TRS:
     a(x1) -> x1
     a(b(x1)) -> c(b(c(b(x1))))
     b(x1) -> a(a(x1))
     c(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> x1
      a(b(x1)) -> c(b(c(b(x1))))
      b(x1) -> a(a(x1))
      c(c(x1)) -> x1
     interpretation:
                [0 1]     [2]
      [b](x0) = [1 2]x0 + [3],
      
      [a#](x0) = [-& 0 ]x0 + [0],
      
      [b#](x0) = [0 1]x0 + [1],
      
                [0  1 ]     [0]
      [a](x0) = [-& 0 ]x0 + [0],
      
                [-& 0 ]     [0]
      [c](x0) = [0  -&]x0 + [0]
     orientation:
      b#(x1) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(a(x1))
      
      a#(b(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = b#(c(b(x1)))
      
      b#(x1) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(x1)
      
              [0  1 ]     [0]           
      a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
      
                 [2 3]     [4]    [2 3]     [4]                 
      a(b(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = c(b(c(b(x1))))
      
              [0 1]     [2]    [0  1 ]     [1]           
      b(x1) = [1 2]x1 + [3] >= [-& 0 ]x1 + [0] = a(a(x1))
      
                      [0]           
      c(c(x1)) = x1 + [0] >= x1 = x1
     problem:
      DPs:
       a#(b(x1)) -> b#(c(b(x1)))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> c(b(c(b(x1))))
       b(x1) -> a(a(x1))
       c(c(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(b(x1)) -> b#(c(b(x1)))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> c(b(c(b(x1))))
       b(x1) -> a(a(x1))
       c(c(x1)) -> x1
      EDG Processor:
       DPs:
        a#(b(x1)) -> b#(c(b(x1)))
       TRS:
        a(x1) -> x1
        a(b(x1)) -> c(b(c(b(x1))))
        b(x1) -> a(a(x1))
        c(c(x1)) -> x1
       graph:
        
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 0/1