YES

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

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