YES

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

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