YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(b(x1))) -> a#(x1)
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> b#(b(x1))
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(b(a(x1)))
  TRS:
   b(b(b(x1))) -> a(x1)
   a(a(a(x1))) -> b(b(x1))
   a(a(x1)) -> a(b(a(x1)))
  TDG Processor:
   DPs:
    b#(b(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(b(x1))
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
   TRS:
    b(b(b(x1))) -> a(x1)
    a(a(a(x1))) -> b(b(x1))
    a(a(x1)) -> a(b(a(x1)))
   graph:
    a#(a(a(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(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))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(b(x1))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(x1)
    a#(a(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1)
    b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(b(x1))
    b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
   Root-Labeling Processor:
    DPs:
     b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
     b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
     b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
     a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
     a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
     a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
     a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
     a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
     a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(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)))
     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(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))))
    TRS:
     f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
     f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
     f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
     b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
     b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
     b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
     a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
     a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
     a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
     f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
     f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
     f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
     b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
     b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
     b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
     a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
     a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
     a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
     a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
     a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
     a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
    TDG Processor:
     DPs:
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(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)))
      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(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))))
     TRS:
      f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
      f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
      f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
      b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
      b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
      b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
      a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
      a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
      a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
      f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
      f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
      f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
      b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
      b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
      b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
      a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
      a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
      a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
      a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
      a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
      a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
     graph:
      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(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(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(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(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(f4)(x1))) -> b{#,(f4)}(f4(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(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(b)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(b)(x1))) -> b{#,(f4)}(f4(a)(a(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(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(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)(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(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(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(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(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(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(f4)(x1))) -> b{#,(f4)}(f4(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(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(f4)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(f4)(x1))) -> b{#,(f4)}(f4(a)(a(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(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(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)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1)) ->
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(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(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(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(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(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(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(f4)(x1))) -> b{#,(f4)}(f4(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(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> a{#,(f4)}(f4(b)(b(a)(a(a)(x1)))) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
      a{#,(f4)}(f4(a)(a(a)(x1))) -> b{#,(f4)}(f4(a)(a(a)(x1))) ->
      b{#,(f4)}(f4(b)(b(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(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)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1))
      b{#,(f4)}(f4(b)(b(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(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(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(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(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(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(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
      b{#,(f4)}(f4(b)(b(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(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(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(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(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(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(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
      b{#,(f4)}(f4(b)(b(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)(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)(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)(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)(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)(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)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(a)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
      b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1)) ->
      a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(f4)(x1))
     Polynomial Interpretation Processor:
      dimension: 1
      interpretation:
       [a(b)](x0) = x0,
       
       [b(f4)](x0) = x0 + 1,
       
       [b{#,(f4)}](x0) = x0,
       
       [f4(f4)](x0) = x0,
       
       [b(b)](x0) = x0,
       
       [a(f4)](x0) = x0 + 1,
       
       [f4(a)](x0) = x0,
       
       [b(a)](x0) = x0,
       
       [a{#,(f4)}](x0) = x0,
       
       [a(a)](x0) = x0,
       
       [f4(b)](x0) = x0
      orientation:
       b{#,(f4)}(f4(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 = a{#,(f4)}(f4(f4)(x1))
       
       b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a{#,(f4)}(f4(b)(x1))
       
       b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a{#,(f4)}(f4(a)(x1))
       
       a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 = b{#,(f4)}(f4(f4)(x1))
       
       a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(b)(x1))
       
       a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(a)(x1))
       
       a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(b)(b(f4)(x1)))
       
       a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(b)(b(b)(x1)))
       
       a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f4)}(f4(b)(b(a)(x1)))
       
       a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(f4)(x1)))
       
       a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(b)(x1)))
       
       a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = b{#,(f4)}(f4(a)(a(a)(x1)))
       
       a{#,(f4)}(f4(a)(a(f4)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
       
       a{#,(f4)}(f4(a)(a(b)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
       
       a{#,(f4)}(f4(a)(a(a)(x1))) = x1 >= x1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
       
       f4(b)(b(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 + 1 = f4(a)(a(f4)(x1))
       
       f4(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = f4(a)(a(b)(x1))
       
       f4(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = f4(a)(a(a)(x1))
       
       b(b)(b(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 + 1 = b(a)(a(f4)(x1))
       
       b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(x1))
       
       b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(a)(x1))
       
       a(b)(b(b)(b(b)(b(f4)(x1)))) = x1 + 1 >= x1 + 1 = a(a)(a(f4)(x1))
       
       a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(x1))
       
       a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1))
       
       f4(a)(a(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = f4(b)(b(b)(b(f4)(x1)))
       
       f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = f4(b)(b(b)(b(b)(x1)))
       
       f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = f4(b)(b(b)(b(a)(x1)))
       
       b(a)(a(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(b)(b(f4)(x1)))
       
       b(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(b)(b(b)(x1)))
       
       b(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(x1)))
       
       a(a)(a(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = a(b)(b(b)(b(f4)(x1)))
       
       a(a)(a(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a(b)(b(b)(b(b)(x1)))
       
       a(a)(a(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a(b)(b(b)(b(a)(x1)))
       
       a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(f4)(x1)))
       
       a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(x1)))
       
       a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(a)(x1)))
      problem:
       DPs:
        b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) -> a{#,(f4)}(f4(b)(x1))
        b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) -> a{#,(f4)}(f4(a)(x1))
        a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(x1))
        a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(a)(x1))
        a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> b{#,(f4)}(f4(b)(b(f4)(x1)))
        a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) -> b{#,(f4)}(f4(b)(b(b)(x1)))
        a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> b{#,(f4)}(f4(b)(b(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)))
        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(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))))
       TRS:
        f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
        f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
        f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
        b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
        b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
        b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
        a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
        a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
        a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
        f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
        f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
        f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
        b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
        b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
        b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
        a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
        a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
        a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
        a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
        a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
        a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
      Polynomial Interpretation Processor:
       dimension: 1
       usable rules:
        f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
        f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
        f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
        b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
        b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
        b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
        a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
        a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
        a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
        f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
        f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
        f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
        b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
        b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
        b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
        a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
        a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
        a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
        a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
        a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
        a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
       interpretation:
        [a(b)](x0) = x0 + 1,
        
        [b(f4)](x0) = 0,
        
        [b{#,(f4)}](x0) = x0,
        
        [b(b)](x0) = x0 + 1,
        
        [a(f4)](x0) = 0,
        
        [f4(a)](x0) = x0,
        
        [b(a)](x0) = x0,
        
        [a{#,(f4)}](x0) = x0,
        
        [a(a)](x0) = x0 + 1,
        
        [f4(b)](x0) = x0
       orientation:
        b{#,(f4)}(f4(b)(b(b)(b(b)(x1)))) = x1 + 2 >= x1 = a{#,(f4)}(f4(b)(x1))
        
        b{#,(f4)}(f4(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 = a{#,(f4)}(f4(a)(x1))
        
        a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 = b{#,(f4)}(f4(b)(x1))
        
        a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 2 >= x1 = b{#,(f4)}(f4(a)(x1))
        
        a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = 1 >= 0 = b{#,(f4)}(f4(b)(b(f4)(x1)))
        
        a{#,(f4)}(f4(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f4)}(f4(b)(b(b)(x1)))
        
        a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 2 >= x1 = b{#,(f4)}(f4(b)(b(a)(x1)))
        
        a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = b{#,(f4)}(f4(a)(a(f4)(x1)))
        
        a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(b)(x1)))
        
        a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f4)}(f4(a)(a(a)(x1)))
        
        a{#,(f4)}(f4(a)(a(f4)(x1))) = 0 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
        
        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(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
        
        f4(b)(b(b)(b(b)(b(f4)(x1)))) = 2 >= 0 = f4(a)(a(f4)(x1))
        
        f4(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 1 = f4(a)(a(b)(x1))
        
        f4(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 1 = f4(a)(a(a)(x1))
        
        b(b)(b(b)(b(b)(b(f4)(x1)))) = 3 >= 0 = b(a)(a(f4)(x1))
        
        b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 1 = b(a)(a(b)(x1))
        
        b(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(a)(x1))
        
        a(b)(b(b)(b(b)(b(f4)(x1)))) = 3 >= 1 = a(a)(a(f4)(x1))
        
        a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 2 = a(a)(a(b)(x1))
        
        a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 2 = a(a)(a(a)(x1))
        
        f4(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 1 = f4(b)(b(b)(b(f4)(x1)))
        
        f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 2 = f4(b)(b(b)(b(b)(x1)))
        
        f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 1 = f4(b)(b(b)(b(a)(x1)))
        
        b(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 2 = b(b)(b(b)(b(f4)(x1)))
        
        b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(b)(x1)))
        
        b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 2 = b(b)(b(b)(b(a)(x1)))
        
        a(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 2 = a(b)(b(b)(b(f4)(x1)))
        
        a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 4 >= x1 + 3 = a(b)(b(b)(b(b)(x1)))
        
        a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(b)(b(a)(x1)))
        
        a(a)(a(f4)(x1)) = 1 >= 1 = a(b)(b(a)(a(f4)(x1)))
        
        a(a)(a(b)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(b)(x1)))
        
        a(a)(a(a)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(a)(x1)))
       problem:
        DPs:
         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)))
         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(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))))
        TRS:
         f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
         f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
         f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
         b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
         b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
         b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
         a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
         a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
         a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
         f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
         f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
         f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
         b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
         b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
         b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
         a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
         a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
         a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
         a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
         a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
         a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
       SCC Processor:
        #sccs: 1
        #rules: 3
        #arcs: 99/36
        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:
         f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
         f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
         f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
         b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
         b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
         b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
         a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
         a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
         a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
         f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
         f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
         f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
         b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
         b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
         b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
         a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
         a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
         a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
         a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
         a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
         a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
        Polynomial Interpretation Processor:
         dimension: 1
         usable rules:
          f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
          f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
          f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
          b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
          b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
          b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
          a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
          a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
          a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
          f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
          f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
          f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
          b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
          b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
          b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
          a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
          a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
          a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
          a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
          a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
          a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
         interpretation:
          [a(b)](x0) = 1,
          
          [b(f4)](x0) = 0,
          
          [b(b)](x0) = 1,
          
          [a(f4)](x0) = 0,
          
          [f4(a)](x0) = 1,
          
          [b(a)](x0) = x0,
          
          [a{#,(f4)}](x0) = x0,
          
          [a(a)](x0) = 1,
          
          [f4(b)](x0) = x0
         orientation:
          a{#,(f4)}(f4(a)(a(b)(x1))) = 1 >= 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
          
          a{#,(f4)}(f4(a)(a(f4)(x1))) = 1 >= 0 = a{#,(f4)}(f4(b)(b(a)(a(f4)(x1))))
          
          a{#,(f4)}(f4(a)(a(a)(x1))) = 1 >= 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
          
          f4(b)(b(b)(b(b)(b(f4)(x1)))) = 1 >= 1 = f4(a)(a(f4)(x1))
          
          f4(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = f4(a)(a(b)(x1))
          
          f4(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = f4(a)(a(a)(x1))
          
          b(b)(b(b)(b(b)(b(f4)(x1)))) = 1 >= 0 = b(a)(a(f4)(x1))
          
          b(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = b(a)(a(b)(x1))
          
          b(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = b(a)(a(a)(x1))
          
          a(b)(b(b)(b(b)(b(f4)(x1)))) = 1 >= 1 = a(a)(a(f4)(x1))
          
          a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a(a)(a(b)(x1))
          
          a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a(a)(a(a)(x1))
          
          f4(a)(a(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = f4(b)(b(b)(b(f4)(x1)))
          
          f4(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = f4(b)(b(b)(b(b)(x1)))
          
          f4(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = f4(b)(b(b)(b(a)(x1)))
          
          b(a)(a(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = b(b)(b(b)(b(f4)(x1)))
          
          b(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b(b)(b(b)(b(b)(x1)))
          
          b(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(x1)))
          
          a(a)(a(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = a(b)(b(b)(b(f4)(x1)))
          
          a(a)(a(a)(a(a)(a(b)(x1)))) = 1 >= 1 = a(b)(b(b)(b(b)(x1)))
          
          a(a)(a(a)(a(a)(a(a)(x1)))) = 1 >= 1 = a(b)(b(b)(b(a)(x1)))
          
          a(a)(a(f4)(x1)) = 1 >= 1 = a(b)(b(a)(a(f4)(x1)))
          
          a(a)(a(b)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(x1)))
          
          a(a)(a(a)(x1)) = 1 >= 1 = a(b)(b(a)(a(a)(x1)))
         problem:
          DPs:
           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))))
          TRS:
           f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
           f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
           f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
           b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
           b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
           b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
           a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
           a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
           a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
           f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
           f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
           f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
           b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
           b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
           b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
           a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
           a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
           a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
           a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
           a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
           a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
         Polynomial Interpretation Processor:
          dimension: 1
          usable rules:
           f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
           f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
           f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
           b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
           b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
           b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
           a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
           a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
           a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
           f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
           f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
           f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
           b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
           b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
           b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
           a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
           a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
           a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
           a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
           a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
           a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
          interpretation:
           [a(b)](x0) = x0 + 1,
           
           [b(f4)](x0) = 0,
           
           [b(b)](x0) = x0 + 1,
           
           [a(f4)](x0) = 0,
           
           [f4(a)](x0) = x0 + 1,
           
           [b(a)](x0) = x0,
           
           [a{#,(f4)}](x0) = x0,
           
           [a(a)](x0) = x0 + 1,
           
           [f4(b)](x0) = x0
          orientation:
           a{#,(f4)}(f4(a)(a(b)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(b)(x1))))
           
           a{#,(f4)}(f4(a)(a(a)(x1))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(b)(b(a)(a(a)(x1))))
           
           f4(b)(b(b)(b(b)(b(f4)(x1)))) = 2 >= 1 = f4(a)(a(f4)(x1))
           
           f4(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 2 = f4(a)(a(b)(x1))
           
           f4(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 2 >= x1 + 2 = f4(a)(a(a)(x1))
           
           b(b)(b(b)(b(b)(b(f4)(x1)))) = 3 >= 0 = b(a)(a(f4)(x1))
           
           b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 1 = b(a)(a(b)(x1))
           
           b(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 1 = b(a)(a(a)(x1))
           
           a(b)(b(b)(b(b)(b(f4)(x1)))) = 3 >= 1 = a(a)(a(f4)(x1))
           
           a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 2 = a(a)(a(b)(x1))
           
           a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 2 = a(a)(a(a)(x1))
           
           f4(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 1 = f4(b)(b(b)(b(f4)(x1)))
           
           f4(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 4 >= x1 + 2 = f4(b)(b(b)(b(b)(x1)))
           
           f4(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 1 = f4(b)(b(b)(b(a)(x1)))
           
           b(a)(a(a)(a(a)(a(f4)(x1)))) = 2 >= 2 = b(b)(b(b)(b(f4)(x1)))
           
           b(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 3 = b(b)(b(b)(b(b)(x1)))
           
           b(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 2 = b(b)(b(b)(b(a)(x1)))
           
           a(a)(a(a)(a(a)(a(f4)(x1)))) = 3 >= 2 = a(b)(b(b)(b(f4)(x1)))
           
           a(a)(a(a)(a(a)(a(b)(x1)))) = x1 + 4 >= x1 + 3 = a(b)(b(b)(b(b)(x1)))
           
           a(a)(a(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 2 = a(b)(b(b)(b(a)(x1)))
           
           a(a)(a(f4)(x1)) = 1 >= 1 = a(b)(b(a)(a(f4)(x1)))
           
           a(a)(a(b)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(b)(x1)))
           
           a(a)(a(a)(x1)) = x1 + 2 >= x1 + 2 = a(b)(b(a)(a(a)(x1)))
          problem:
           DPs:
            
           TRS:
            f4(b)(b(b)(b(b)(b(f4)(x1)))) -> f4(a)(a(f4)(x1))
            f4(b)(b(b)(b(b)(b(b)(x1)))) -> f4(a)(a(b)(x1))
            f4(b)(b(b)(b(b)(b(a)(x1)))) -> f4(a)(a(a)(x1))
            b(b)(b(b)(b(b)(b(f4)(x1)))) -> b(a)(a(f4)(x1))
            b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(x1))
            b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(a)(x1))
            a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(f4)(x1))
            a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(x1))
            a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(x1))
            f4(a)(a(a)(a(a)(a(f4)(x1)))) -> f4(b)(b(b)(b(f4)(x1)))
            f4(a)(a(a)(a(a)(a(b)(x1)))) -> f4(b)(b(b)(b(b)(x1)))
            f4(a)(a(a)(a(a)(a(a)(x1)))) -> f4(b)(b(b)(b(a)(x1)))
            b(a)(a(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(f4)(x1)))
            b(a)(a(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(b)(x1)))
            b(a)(a(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(x1)))
            a(a)(a(a)(a(a)(a(f4)(x1)))) -> a(b)(b(b)(b(f4)(x1)))
            a(a)(a(a)(a(a)(a(b)(x1)))) -> a(b)(b(b)(b(b)(x1)))
            a(a)(a(a)(a(a)(a(a)(x1)))) -> a(b)(b(b)(b(a)(x1)))
            a(a)(a(f4)(x1)) -> a(b)(b(a)(a(f4)(x1)))
            a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(x1)))
            a(a)(a(a)(x1)) -> a(b)(b(a)(a(a)(x1)))
          Qed