MAYBE

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

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