MAYBE

Problem:
 a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
 a(a(x)) -> f(b(),a(f(a(x),b())))
 f(a(x),b()) -> f(b(),a(x))

Proof:
 DP Processor:
  DPs:
   a#(a(f(b(),a(x)))) -> a#(a(x))
   a#(a(f(b(),a(x)))) -> a#(a(a(x)))
   a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
   a#(a(x)) -> f#(a(x),b())
   a#(a(x)) -> a#(f(a(x),b()))
   a#(a(x)) -> f#(b(),a(f(a(x),b())))
   f#(a(x),b()) -> f#(b(),a(x))
  TRS:
   a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
   a(a(x)) -> f(b(),a(f(a(x),b())))
   f(a(x),b()) -> f(b(),a(x))
  EDG Processor:
   DPs:
    a#(a(f(b(),a(x)))) -> a#(a(x))
    a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(x)) -> f#(a(x),b())
    a#(a(x)) -> a#(f(a(x),b()))
    a#(a(x)) -> f#(b(),a(f(a(x),b())))
    f#(a(x),b()) -> f#(b(),a(x))
   TRS:
    a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
    a(a(x)) -> f(b(),a(f(a(x),b())))
    f(a(x),b()) -> f(b(),a(x))
   graph:
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b()) ->
    f#(a(x),b()) -> f#(b(),a(x))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(f(b(),a(x)))) -> a#(a(x))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) -> a#(a(x)) -> f#(a(x),b())
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(x)) -> a#(f(a(x),b()))
    a#(a(f(b(),a(x)))) -> a#(a(a(x))) ->
    a#(a(x)) -> f#(b(),a(f(a(x),b())))
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(f(b(),a(x)))) -> a#(a(x))
    a#(a(f(b(),a(x)))) -> a#(a(x)) ->
    a#(a(f(b(),a(x)))) -> a#(a(a(x)))
    a#(a(f(b(),a(x)))) -> a#(a(x)) ->
    a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> f#(a(x),b())
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> a#(f(a(x),b()))
    a#(a(f(b(),a(x)))) -> a#(a(x)) -> a#(a(x)) -> f#(b(),a(f(a(x),b())))
    a#(a(x)) -> f#(a(x),b()) -> f#(a(x),b()) -> f#(b(),a(x))
   Restore Modifier:
    DPs:
     a#(a(f(b(),a(x)))) -> a#(a(x))
     a#(a(f(b(),a(x)))) -> a#(a(a(x)))
     a#(a(f(b(),a(x)))) -> f#(a(a(a(x))),b())
     a#(a(x)) -> f#(a(x),b())
     a#(a(x)) -> a#(f(a(x),b()))
     a#(a(x)) -> f#(b(),a(f(a(x),b())))
     f#(a(x),b()) -> f#(b(),a(x))
    TRS:
     a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
     a(a(x)) -> f(b(),a(f(a(x),b())))
     f(a(x),b()) -> f(b(),a(x))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 14/49
     DPs:
      a#(a(f(b(),a(x)))) -> a#(a(a(x)))
      a#(a(f(b(),a(x)))) -> a#(a(x))
     TRS:
      a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
      a(a(x)) -> f(b(),a(f(a(x),b())))
      f(a(x),b()) -> f(b(),a(x))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0,
       
       [f](x0, x1) = x0 + x1,
       
       [a](x0) = x0 + 1,
       
       [b] = 0
      orientation:
       a#(a(f(b(),a(x)))) = x + 2 >= x + 2 = a#(a(a(x)))
       
       a#(a(f(b(),a(x)))) = x + 2 >= x + 1 = a#(a(x))
       
       a(a(f(b(),a(x)))) = x + 3 >= x + 3 = f(a(a(a(x))),b())
       
       a(a(x)) = x + 2 >= x + 2 = f(b(),a(f(a(x),b())))
       
       f(a(x),b()) = x + 1 >= x + 1 = f(b(),a(x))
      problem:
       DPs:
        a#(a(f(b(),a(x)))) -> a#(a(a(x)))
       TRS:
        a(a(f(b(),a(x)))) -> f(a(a(a(x))),b())
        a(a(x)) -> f(b(),a(f(a(x),b())))
        f(a(x),b()) -> f(b(),a(x))
      Open