MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),a()) -> f#(a(),a())
   f#(f(a(),x),a()) -> f#(x,f(a(),a()))
   f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
   f#(f(a(),x),a()) -> f#(f(f(x,f(a(),a())),a()),a())
  TRS:
   f(f(a(),x),a()) -> f(f(f(x,f(a(),a())),a()),a())
  Restore Modifier:
   DPs:
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(x,f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
    f#(f(a(),x),a()) -> f#(f(f(x,f(a(),a())),a()),a())
   TRS:
    f(f(a(),x),a()) -> f(f(f(x,f(a(),a())),a()),a())
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 16/16
    DPs:
     f#(f(a(),x),a()) -> f#(a(),a())
     f#(f(a(),x),a()) -> f#(x,f(a(),a()))
     f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
     f#(f(a(),x),a()) -> f#(f(f(x,f(a(),a())),a()),a())
    TRS:
     f(f(a(),x),a()) -> f(f(f(x,f(a(),a())),a()),a())
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x1,
      
      [f](x0, x1) = 0,
      
      [a] = 1
     orientation:
      f#(f(a(),x),a()) = 1 >= 1 = f#(a(),a())
      
      f#(f(a(),x),a()) = 1 >= 0 = f#(x,f(a(),a()))
      
      f#(f(a(),x),a()) = 1 >= 1 = f#(f(x,f(a(),a())),a())
      
      f#(f(a(),x),a()) = 1 >= 1 = f#(f(f(x,f(a(),a())),a()),a())
      
      f(f(a(),x),a()) = 0 >= 0 = f(f(f(x,f(a(),a())),a()),a())
     problem:
      DPs:
       f#(f(a(),x),a()) -> f#(a(),a())
       f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
       f#(f(a(),x),a()) -> f#(f(f(x,f(a(),a())),a()),a())
      TRS:
       f(f(a(),x),a()) -> f(f(f(x,f(a(),a())),a()),a())
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x0,
       
       [f](x0, x1) = 1,
       
       [a] = 0
      orientation:
       f#(f(a(),x),a()) = 1 >= 0 = f#(a(),a())
       
       f#(f(a(),x),a()) = 1 >= 1 = f#(f(x,f(a(),a())),a())
       
       f#(f(a(),x),a()) = 1 >= 1 = f#(f(f(x,f(a(),a())),a()),a())
       
       f(f(a(),x),a()) = 1 >= 1 = f(f(f(x,f(a(),a())),a()),a())
      problem:
       DPs:
        f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
        f#(f(a(),x),a()) -> f#(f(f(x,f(a(),a())),a()),a())
       TRS:
        f(f(a(),x),a()) -> f(f(f(x,f(a(),a())),a()),a())
      Open