MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),a()),x) -> f#(a(),x)
   f#(f(a(),a()),x) -> f#(b(),f(a(),x))
   f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
   f#(x,f(y,z)) -> f#(x,y)
   f#(x,f(y,z)) -> f#(f(x,y),z)
  TRS:
   f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
   f(x,f(y,z)) -> f(f(x,y),z)
  EDG Processor:
   DPs:
    f#(f(a(),a()),x) -> f#(a(),x)
    f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z)
   TRS:
    f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
    f(x,f(y,z)) -> f(f(x,y),z)
   graph:
    f#(f(a(),a()),x) -> f#(b(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(b(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x))) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x))) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),a()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(f(a(),a()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(f(x,y),z)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [f#](x0, x1) = x0 + 0,
     
     [b] = 0,
     
     [f](x0, x1) = x0 + 0,
     
     [a] = 2
    orientation:
     f#(f(a(),a()),x) = 2 >= 2 = f#(a(),x)
     
     f#(f(a(),a()),x) = 2 >= 0 = f#(b(),f(a(),x))
     
     f#(f(a(),a()),x) = 2 >= 2 = f#(a(),f(b(),f(a(),x)))
     
     f#(x,f(y,z)) = x + 0 >= x + 0 = f#(x,y)
     
     f#(x,f(y,z)) = x + 0 >= x + 0 = f#(f(x,y),z)
     
     f(f(a(),a()),x) = 2 >= 2 = f(a(),f(b(),f(a(),x)))
     
     f(x,f(y,z)) = x + 0 >= x + 0 = f(f(x,y),z)
    problem:
     DPs:
      f#(f(a(),a()),x) -> f#(a(),x)
      f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
      f(x,f(y,z)) -> f(f(x,y),z)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f#](x0, x1) = 2x0 + 2x1,
      
      [b] = 0,
      
      [f](x0, x1) = x0 + x1,
      
      [a] = 2
     orientation:
      f#(f(a(),a()),x) = 2x + 8 >= 2x + 4 = f#(a(),x)
      
      f#(f(a(),a()),x) = 2x + 8 >= 2x + 8 = f#(a(),f(b(),f(a(),x)))
      
      f#(x,f(y,z)) = 2x + 2y + 2z >= 2x + 2y = f#(x,y)
      
      f#(x,f(y,z)) = 2x + 2y + 2z >= 2x + 2y + 2z = f#(f(x,y),z)
      
      f(f(a(),a()),x) = x + 4 >= x + 4 = f(a(),f(b(),f(a(),x)))
      
      f(x,f(y,z)) = x + y + z >= x + y + z = f(f(x,y),z)
     problem:
      DPs:
       f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
       f#(x,f(y,z)) -> f#(x,y)
       f#(x,f(y,z)) -> f#(f(x,y),z)
      TRS:
       f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
       f(x,f(y,z)) -> f(f(x,y),z)
     Open