YES

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

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