MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(f(f(a(),f(a(),a())),a()),x) -> f#(x,a())
   f#(f(f(a(),f(a(),a())),a()),x) -> f#(x,f(x,a()))
  TRS:
   f(f(f(a(),f(a(),a())),a()),x) -> f(x,f(x,a()))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [f#](x0, x1) = -1x0 + x1 + 1,
    
    [f](x0, x1) = x0 + 1x1 + 2,
    
    [a] = 0
   orientation:
    f#(f(f(a(),f(a(),a())),a()),x) = x + 2 >= -1x + 1 = f#(x,a())
    
    f#(f(f(a(),f(a(),a())),a()),x) = x + 2 >= x + 2 = f#(x,f(x,a()))
    
    f(f(f(a(),f(a(),a())),a()),x) = 1x + 3 >= 1x + 3 = f(x,f(x,a()))
   problem:
    DPs:
     f#(f(f(a(),f(a(),a())),a()),x) -> f#(x,f(x,a()))
    TRS:
     f(f(f(a(),f(a(),a())),a()),x) -> f(x,f(x,a()))
   Open