YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> a#(a(a(x1)))
   a#(a(b(x1))) -> b#(c(a(a(a(x1)))))
   a#(a(b(x1))) -> b#(b(c(a(a(a(x1))))))
  TRS:
   a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
   b(c(a(x1))) -> x1
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(a(x1)))
    a#(a(b(x1))) -> b#(c(a(a(a(x1)))))
    a#(a(b(x1))) -> b#(b(c(a(a(a(x1))))))
   TRS:
    a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
    b(c(a(x1))) -> x1
   graph:
    a#(a(b(x1))) -> a#(a(a(x1))) ->
    a#(a(b(x1))) -> b#(b(c(a(a(a(x1))))))
    a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1))) -> b#(c(a(a(a(x1)))))
    a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(c(a(a(a(x1))))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(c(a(a(a(x1)))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(c(a(a(a(x1))))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(c(a(a(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 15/25
    DPs:
     a#(a(b(x1))) -> a#(a(a(x1)))
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
    TRS:
     a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
     b(c(a(x1))) -> x1
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [a#](x0) = x0 + 0,
      
      [c](x0) = -2x0 + 14,
      
      [a](x0) = 1x0 + 0,
      
      [b](x0) = 1x0 + 15
     orientation:
      a#(a(b(x1))) = 2x1 + 16 >= 2x1 + 1 = a#(a(a(x1)))
      
      a#(a(b(x1))) = 2x1 + 16 >= x1 + 0 = a#(x1)
      
      a#(a(b(x1))) = 2x1 + 16 >= 1x1 + 0 = a#(a(x1))
      
      a(a(b(x1))) = 3x1 + 17 >= 3x1 + 16 = b(b(c(a(a(a(x1))))))
      
      b(c(a(x1))) = x1 + 15 >= x1 = x1
     problem:
      DPs:
       a#(a(b(x1))) -> a#(a(a(x1)))
      TRS:
       a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
       b(c(a(x1))) -> x1
     EDG Processor:
      DPs:
       a#(a(b(x1))) -> a#(a(a(x1)))
      TRS:
       a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
       b(c(a(x1))) -> x1
      graph:
       a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1)))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [a#](x0) = x0 + 0,
        
        [c](x0) = -12x0 + 4,
        
        [a](x0) = 4x0 + -4,
        
        [b](x0) = 8x0 + 12
       orientation:
        a#(a(b(x1))) = 12x1 + 16 >= 8x1 + 0 = a#(a(a(x1)))
        
        a(a(b(x1))) = 16x1 + 20 >= 16x1 + 20 = b(b(c(a(a(a(x1))))))
        
        b(c(a(x1))) = x1 + 12 >= x1 = x1
       problem:
        DPs:
         
        TRS:
         a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
         b(c(a(x1))) -> x1
       Qed