MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),a()) -> f#(a(),a())
   f#(f(a(),x),a()) -> f#(a(),f(a(),a()))
   f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
  TRS:
   f(f(a(),x),a()) -> f(f(a(),f(a(),a())),x)
  Usable Rule Processor:
   DPs:
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(a(),f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
   TRS:
    
   Restore Modifier:
    DPs:
     f#(f(a(),x),a()) -> f#(a(),a())
     f#(f(a(),x),a()) -> f#(a(),f(a(),a()))
     f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
    TRS:
     f(f(a(),x),a()) -> f(f(a(),f(a(),a())),x)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 9/9
     DPs:
      f#(f(a(),x),a()) -> f#(a(),a())
      f#(f(a(),x),a()) -> f#(a(),f(a(),a()))
      f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
     TRS:
      f(f(a(),x),a()) -> f(f(a(),f(a(),a())),x)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x0 + 1,
       
       [f](x0, x1) = x0 + 1,
       
       [a] = 1
      orientation:
       f#(f(a(),x),a()) = 3 >= 2 = f#(a(),a())
       
       f#(f(a(),x),a()) = 3 >= 2 = f#(a(),f(a(),a()))
       
       f#(f(a(),x),a()) = 3 >= 3 = f#(f(a(),f(a(),a())),x)
       
       f(f(a(),x),a()) = 3 >= 3 = f(f(a(),f(a(),a())),x)
      problem:
       DPs:
        f#(f(a(),x),a()) -> f#(f(a(),f(a(),a())),x)
       TRS:
        f(f(a(),x),a()) -> f(f(a(),f(a(),a())),x)
      Open