YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(x1) -> a(x1)
  c(a(b(x1))) -> b(a(b(c(c(x1)))))
  DP Processor:
   DPs:
    b#(x1) -> a#(x1)
    c#(a(b(x1))) -> c#(x1)
    c#(a(b(x1))) -> c#(c(x1))
    c#(a(b(x1))) -> b#(c(c(x1)))
    c#(a(b(x1))) -> a#(b(c(c(x1))))
    c#(a(b(x1))) -> b#(a(b(c(c(x1)))))
   TRS:
    a(x1) -> x1
    b(x1) -> a(x1)
    c(a(b(x1))) -> b(a(b(c(c(x1)))))
   TDG Processor:
    DPs:
     b#(x1) -> a#(x1)
     c#(a(b(x1))) -> c#(x1)
     c#(a(b(x1))) -> c#(c(x1))
     c#(a(b(x1))) -> b#(c(c(x1)))
     c#(a(b(x1))) -> a#(b(c(c(x1))))
     c#(a(b(x1))) -> b#(a(b(c(c(x1)))))
    TRS:
     a(x1) -> x1
     b(x1) -> a(x1)
     c(a(b(x1))) -> b(a(b(c(c(x1)))))
    graph:
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> b#(a(b(c(c(x1)))))
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(b(c(c(x1))))
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> b#(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))) -> b#(a(b(c(c(x1)))))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(b(c(c(x1))))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> b#(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)
     c#(a(b(x1))) -> b#(c(c(x1))) -> b#(x1) -> a#(x1)
     c#(a(b(x1))) -> b#(a(b(c(c(x1))))) -> b#(x1) -> a#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 12/36
     DPs:
      c#(a(b(x1))) -> c#(c(x1))
      c#(a(b(x1))) -> c#(x1)
     TRS:
      a(x1) -> x1
      b(x1) -> a(x1)
      c(a(b(x1))) -> b(a(b(c(c(x1)))))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(x1) -> a(x1)
       c(a(b(x1))) -> b(a(b(c(c(x1)))))
      interpretation:
                 [0 1]     [0]
       [b](x0) = [0 0]x0 + [3],
       
       [c#](x0) = [0 0]x0 + [2],
       
                 [0  1 ]     [0 ]
       [a](x0) = [-& 0 ]x0 + [-&],
       
                 [0 0]     [0]
       [c](x0) = [0 0]x0 + [0]
      orientation:
       c#(a(b(x1))) = [1 1]x1 + [4] >= [0 0]x1 + [2] = c#(c(x1))
       
       c#(a(b(x1))) = [1 1]x1 + [4] >= [0 0]x1 + [2] = c#(x1)
       
               [0  1 ]     [0 ]           
       a(x1) = [-& 0 ]x1 + [-&] >= x1 = x1
       
               [0 1]     [0]    [0  1 ]     [0 ]        
       b(x1) = [0 0]x1 + [3] >= [-& 0 ]x1 + [-&] = a(x1)
       
                     [1 1]     [4]    [1 1]     [4]                    
       c(a(b(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = b(a(b(c(c(x1)))))
      problem:
       DPs:
        
       TRS:
        a(x1) -> x1
        b(x1) -> a(x1)
        c(a(b(x1))) -> b(a(b(c(c(x1)))))
      Qed