MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),x)
   f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
   f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
   f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
  TRS:
   f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
  ADG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
   TRS:
    f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
   graph:
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(a(),x) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
   Restore Modifier:
    DPs:
     f#(x,f(a(),y)) -> f#(a(),x)
     f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
     f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
     f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
    TRS:
     f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 12/16
     DPs:
      f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
      f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
      f#(x,f(a(),y)) -> f#(a(),x)
     TRS:
      f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x0 + x1,
       
       [h](x0) = 0,
       
       [f](x0, x1) = x1 + 1,
       
       [a] = 0
      orientation:
       f#(x,f(a(),y)) = x + y + 1 >= y + 1 = f#(f(f(a(),x),h(a())),y)
       
       f#(x,f(a(),y)) = x + y + 1 >= y + 1 = f#(a(),f(f(f(a(),x),h(a())),y))
       
       f#(x,f(a(),y)) = x + y + 1 >= x = f#(a(),x)
       
       f(x,f(a(),y)) = y + 2 >= y + 2 = f(a(),f(f(f(a(),x),h(a())),y))
      problem:
       DPs:
        f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
        f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
       TRS:
        f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0, x1) = x1,
        
        [h](x0) = 0,
        
        [f](x0, x1) = x1 + 1,
        
        [a] = 0
       orientation:
        f#(x,f(a(),y)) = y + 1 >= y = f#(f(f(a(),x),h(a())),y)
        
        f#(x,f(a(),y)) = y + 1 >= y + 1 = f#(a(),f(f(f(a(),x),h(a())),y))
        
        f(x,f(a(),y)) = y + 2 >= y + 2 = f(a(),f(f(f(a(),x),h(a())),y))
       problem:
        DPs:
         f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
        TRS:
         f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
       Open