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
     usable rules:
      a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
      b(c(a(x1))) -> x1
     interpretation:
      [a](x0) = 1x0 + 1,
      
      [a#](x0) = 1x0 + 0,
      
      [b](x0) = 2x0 + 8,
      
      [c](x0) = -3x0 + 2
     orientation:
      a#(a(b(x1))) = 4x1 + 10 >= 3x1 + 3 = a#(a(a(x1)))
      
      a#(a(b(x1))) = 4x1 + 10 >= 1x1 + 0 = a#(x1)
      
      a#(a(b(x1))) = 4x1 + 10 >= 2x1 + 2 = a#(a(x1))
      
      a(a(b(x1))) = 4x1 + 10 >= 4x1 + 10 = b(b(c(a(a(a(x1))))))
      
      b(c(a(x1))) = x1 + 8 >= x1 = x1
     problem:
      DPs:
       
      TRS:
       a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
       b(c(a(x1))) -> x1
     Qed