YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(b(a(x1)))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
  TRS:
   a(a(x1)) -> a(b(a(x1)))
   b(b(x1)) -> a(a(x1))
   a(b(b(a(x1)))) -> x1
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
   TRS:
    a(a(x1)) -> a(b(a(x1)))
    b(b(x1)) -> a(a(x1))
    a(b(b(a(x1)))) -> x1
   graph:
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
   Root-Labeling Processor:
    DPs:
     a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
     a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
     a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
     a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
     a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
     a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
     b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1))
     b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
     b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1))
     b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
     b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
     b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1)))
    TRS:
     a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
     a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
     a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
     f4(b)(b(b)(b(f4)(x1))) -> f4(a)(a(a)(a(f4)(x1)))
     f4(b)(b(b)(b(a)(x1))) -> f4(a)(a(a)(a(a)(x1)))
     f4(b)(b(b)(b(b)(x1))) -> f4(a)(a(a)(a(b)(x1)))
     a(b)(b(b)(b(f4)(x1))) -> a(a)(a(a)(a(f4)(x1)))
     a(b)(b(b)(b(a)(x1))) -> a(a)(a(a)(a(a)(x1)))
     a(b)(b(b)(b(b)(x1))) -> a(a)(a(a)(a(b)(x1)))
     b(b)(b(b)(b(f4)(x1))) -> b(a)(a(a)(a(f4)(x1)))
     b(b)(b(b)(b(a)(x1))) -> b(a)(a(a)(a(a)(x1)))
     b(b)(b(b)(b(b)(x1))) -> b(a)(a(a)(a(b)(x1)))
     f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> f4(f4)(x1)
     f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(a)(x1)
     f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(x1)
     a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(f4)(x1)
     a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(a)(x1)
     a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(x1)
     b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1)
     b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(a)(x1)
     b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
    TDG Processor:
     DPs:
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1)))
     TRS:
      a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
      a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
      a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
      f4(b)(b(b)(b(f4)(x1))) -> f4(a)(a(a)(a(f4)(x1)))
      f4(b)(b(b)(b(a)(x1))) -> f4(a)(a(a)(a(a)(x1)))
      f4(b)(b(b)(b(b)(x1))) -> f4(a)(a(a)(a(b)(x1)))
      a(b)(b(b)(b(f4)(x1))) -> a(a)(a(a)(a(f4)(x1)))
      a(b)(b(b)(b(a)(x1))) -> a(a)(a(a)(a(a)(x1)))
      a(b)(b(b)(b(b)(x1))) -> a(a)(a(a)(a(b)(x1)))
      b(b)(b(b)(b(f4)(x1))) -> b(a)(a(a)(a(f4)(x1)))
      b(b)(b(b)(b(a)(x1))) -> b(a)(a(a)(a(a)(x1)))
      b(b)(b(b)(b(b)(x1))) -> b(a)(a(a)(a(b)(x1)))
      f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> f4(f4)(x1)
      f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(a)(x1)
      f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(x1)
      a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(f4)(x1)
      a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(a)(x1)
      a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(x1)
      b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1)
      b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(a)(x1)
      b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
     graph:
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
     Polynomial Interpretation Processor:
      dimension: 1
      interpretation:
       [b(b)](x0) = x0,
       
       [b{#,(f4)}](x0) = x0 + 1,
       
       [a{#,(f4)}](x0) = x0 + 1,
       
       [a(b)](x0) = x0,
       
       [a(f4)](x0) = x0 + 1,
       
       [f4(f4)](x0) = x0,
       
       [b(a)](x0) = x0,
       
       [f4(b)](x0) = x0,
       
       [a(a)](x0) = x0,
       
       [b(f4)](x0) = x0 + 1,
       
       [f4(a)](x0) = x0
      orientation:
       a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f4)}(f4(a)(a(f4)(x1)))
       
       a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(a)(x1)))
       
       a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(x1)))
       
       a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
       
       a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
       
       a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
       
       b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(f4)(x1))
       
       b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(x1))
       
       b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(x1))
       
       b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(a)(a(f4)(x1)))
       
       b{#,(f4)}(f4(b)(b(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(a(a)(x1)))
       
       b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(a(b)(x1)))
       
       a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(f4)(x1)))
       
       a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1)))
       
       a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1)))
       
       f4(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = f4(a)(a(a)(a(f4)(x1)))
       
       f4(b)(b(b)(b(a)(x1))) = x1 >= x1 = f4(a)(a(a)(a(a)(x1)))
       
       f4(b)(b(b)(b(b)(x1))) = x1 >= x1 = f4(a)(a(a)(a(b)(x1)))
       
       a(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = a(a)(a(a)(a(f4)(x1)))
       
       a(b)(b(b)(b(a)(x1))) = x1 >= x1 = a(a)(a(a)(a(a)(x1)))
       
       a(b)(b(b)(b(b)(x1))) = x1 >= x1 = a(a)(a(a)(a(b)(x1)))
       
       b(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 + 1 = b(a)(a(a)(a(f4)(x1)))
       
       b(b)(b(b)(b(a)(x1))) = x1 >= x1 = b(a)(a(a)(a(a)(x1)))
       
       b(b)(b(b)(b(b)(x1))) = x1 >= x1 = b(a)(a(a)(a(b)(x1)))
       
       f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = f4(f4)(x1)
       
       f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = f4(a)(x1)
       
       f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = f4(b)(x1)
       
       a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 + 1 = a(f4)(x1)
       
       a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(a)(x1)
       
       a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(x1)
       
       b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 + 1 = b(f4)(x1)
       
       b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(a)(x1)
       
       b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(x1)
      problem:
       DPs:
        a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
        a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
        a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
        a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
        a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
        a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
        b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
        b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(b)(x1))
        b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
        b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
        b{#,(f4)}(f4(b)(b(b)(x1))) -> a{#,(f4)}(f4(a)(a(b)(x1)))
       TRS:
        a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
        a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
        a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
        f4(b)(b(b)(b(f4)(x1))) -> f4(a)(a(a)(a(f4)(x1)))
        f4(b)(b(b)(b(a)(x1))) -> f4(a)(a(a)(a(a)(x1)))
        f4(b)(b(b)(b(b)(x1))) -> f4(a)(a(a)(a(b)(x1)))
        a(b)(b(b)(b(f4)(x1))) -> a(a)(a(a)(a(f4)(x1)))
        a(b)(b(b)(b(a)(x1))) -> a(a)(a(a)(a(a)(x1)))
        a(b)(b(b)(b(b)(x1))) -> a(a)(a(a)(a(b)(x1)))
        b(b)(b(b)(b(f4)(x1))) -> b(a)(a(a)(a(f4)(x1)))
        b(b)(b(b)(b(a)(x1))) -> b(a)(a(a)(a(a)(x1)))
        b(b)(b(b)(b(b)(x1))) -> b(a)(a(a)(a(b)(x1)))
        f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(a)(x1)
        f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(x1)
        a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(f4)(x1)
        a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(a)(x1)
        a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(x1)
        b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(f4)(x1)
        b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(a)(x1)
        b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
      Polynomial Interpretation Processor:
       dimension: 1
       interpretation:
        [b(b)](x0) = x0 + 1,
        
        [b{#,(f4)}](x0) = x0,
        
        [a{#,(f4)}](x0) = x0,
        
        [a(b)](x0) = x0,
        
        [a(f4)](x0) = x0,
        
        [b(a)](x0) = x0,
        
        [f4(b)](x0) = x0,
        
        [a(a)](x0) = x0,
        
        [b(f4)](x0) = x0,
        
        [f4(a)](x0) = x0
       orientation:
        a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(f4)(x1)))
        
        a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(x1)))
        
        a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1)))
        
        a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
        
        a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
        
        a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
        
        b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(x1))
        
        b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(b)(x1))
        
        b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(f4)(x1)))
        
        b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(x1)))
        
        b{#,(f4)}(f4(b)(b(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(a(b)(x1)))
        
        a(a)(a(f4)(x1)) = x1 >= x1 = a(b)(b(a)(a(f4)(x1)))
        
        a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1)))
        
        a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1)))
        
        f4(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 = f4(a)(a(a)(a(f4)(x1)))
        
        f4(b)(b(b)(b(a)(x1))) = x1 + 1 >= x1 = f4(a)(a(a)(a(a)(x1)))
        
        f4(b)(b(b)(b(b)(x1))) = x1 + 2 >= x1 = f4(a)(a(a)(a(b)(x1)))
        
        a(b)(b(b)(b(f4)(x1))) = x1 + 1 >= x1 = a(a)(a(a)(a(f4)(x1)))
        
        a(b)(b(b)(b(a)(x1))) = x1 + 1 >= x1 = a(a)(a(a)(a(a)(x1)))
        
        a(b)(b(b)(b(b)(x1))) = x1 + 2 >= x1 = a(a)(a(a)(a(b)(x1)))
        
        b(b)(b(b)(b(f4)(x1))) = x1 + 2 >= x1 = b(a)(a(a)(a(f4)(x1)))
        
        b(b)(b(b)(b(a)(x1))) = x1 + 2 >= x1 = b(a)(a(a)(a(a)(x1)))
        
        b(b)(b(b)(b(b)(x1))) = x1 + 3 >= x1 = b(a)(a(a)(a(b)(x1)))
        
        f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 1 >= x1 = f4(a)(x1)
        
        f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 = f4(b)(x1)
        
        a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = a(f4)(x1)
        
        a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 1 >= x1 = a(a)(x1)
        
        a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 = a(b)(x1)
        
        b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = b(f4)(x1)
        
        b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 1 >= x1 = b(a)(x1)
        
        b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 1 >= x1 + 1 = b(b)(x1)
       problem:
        DPs:
         a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
         a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
         a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
         a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
         a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
         a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
         b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
         b{#,(f4)}(f4(b)(b(f4)(x1))) -> a{#,(f4)}(f4(a)(a(f4)(x1)))
         b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
        TRS:
         a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
         a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
         a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
         b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
       Polynomial Interpretation Processor:
        dimension: 1
        interpretation:
         [b(b)](x0) = x0,
         
         [b{#,(f4)}](x0) = x0,
         
         [a{#,(f4)}](x0) = x0,
         
         [a(b)](x0) = x0,
         
         [a(f4)](x0) = x0,
         
         [b(a)](x0) = x0,
         
         [f4(b)](x0) = x0,
         
         [a(a)](x0) = x0,
         
         [b(f4)](x0) = x0 + 1,
         
         [f4(a)](x0) = x0
        orientation:
         a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(f4)(x1)))
         
         a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(x1)))
         
         a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1)))
         
         a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
         
         a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
         
         a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
         
         b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(x1))
         
         b{#,(f4)}(f4(b)(b(f4)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(a(f4)(x1)))
         
         b{#,(f4)}(f4(b)(b(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(x1)))
         
         a(a)(a(f4)(x1)) = x1 >= x1 = a(b)(b(a)(a(f4)(x1)))
         
         a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1)))
         
         a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1)))
         
         b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(x1)
        problem:
         DPs:
          a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
          a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
          a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
          a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
          a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
          a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
          b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(x1))
          b{#,(f4)}(f4(b)(b(a)(x1))) -> a{#,(f4)}(f4(a)(a(a)(x1)))
         TRS:
          a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
          a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
          a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
          b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
        Polynomial Interpretation Processor:
         dimension: 1
         usable rules:
          
         interpretation:
          [b(b)](x0) = 0,
          
          [b{#,(f4)}](x0) = x0,
          
          [a{#,(f4)}](x0) = 0,
          
          [a(b)](x0) = 0,
          
          [a(f4)](x0) = 0,
          
          [b(a)](x0) = 0,
          
          [f4(b)](x0) = 1,
          
          [a(a)](x0) = 0,
          
          [f4(a)](x0) = 0
         orientation:
          a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(f4)(x1)))
          
          a{#,(f4)}(f4(a)(a(a)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(a)(x1)))
          
          a{#,(f4)}(f4(a)(a(b)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(b)(x1)))
          
          a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
          
          a{#,(f4)}(f4(a)(a(a)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
          
          a{#,(f4)}(f4(a)(a(b)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
          
          b{#,(f4)}(f4(b)(b(a)(x1))) = 1 >= 0 = a{#,(f4)}(f4(a)(x1))
          
          b{#,(f4)}(f4(b)(b(a)(x1))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(x1)))
          
          a(a)(a(f4)(x1)) = 0 >= 0 = a(b)(b(a)(a(f4)(x1)))
          
          a(a)(a(a)(x1)) = 0 >= 0 = a(b)(b(a)(a(a)(x1)))
          
          a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(x1)))
          
          b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = b(b)(x1)
         problem:
          DPs:
           a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1)))
           a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1)))
           a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1)))
           a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
           a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
           a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
          TRS:
           a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
           a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
           a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
           b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
         SCC Processor:
          #sccs: 1
          #rules: 3
          #arcs: 72/36
          DPs:
           a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
           a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
           a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
          TRS:
           a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
           a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
           a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
           b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(x1)
          Polynomial Interpretation Processor:
           dimension: 1
           interpretation:
            [b(b)](x0) = x0 + 1,
            
            [a{#,(f4)}](x0) = x0,
            
            [a(b)](x0) = x0 + 1,
            
            [a(f4)](x0) = x0,
            
            [b(a)](x0) = x0,
            
            [f4(b)](x0) = x0,
            
            [a(a)](x0) = x0 + 1,
            
            [f4(a)](x0) = x0
           orientation:
            a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
            
            a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
            
            a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
            
            a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(f4)(x1)))
            
            a(a)(a(a)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(a)(x1)))
            
            a(a)(a(b)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(b)(x1)))
            
            b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 3 >= x1 + 1 = b(b)(x1)
           problem:
            DPs:
             a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
             a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
             a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
            TRS:
             a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
             a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
             a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
           Polynomial Interpretation Processor:
            dimension: 1
            interpretation:
             [a{#,(f4)}](x0) = x0,
             
             [a(b)](x0) = x0,
             
             [a(f4)](x0) = x0 + 1,
             
             [b(a)](x0) = x0,
             
             [f4(b)](x0) = x0,
             
             [a(a)](x0) = x0,
             
             [f4(a)](x0) = x0 + 1
            orientation:
             a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
             
             a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
             
             a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
             
             a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(f4)(x1)))
             
             a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1)))
             
             a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1)))
            problem:
             DPs:
              
             TRS:
              a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
              a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
              a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
            Qed