MAYBE

Problem:
 f(f(0(),x),1()) -> f(g(f(x,x)),x)
 f(g(x),y) -> g(f(x,y))

Proof:
 DP Processor:
  DPs:
   f#(f(0(),x),1()) -> f#(x,x)
   f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
   f#(g(x),y) -> f#(x,y)
  TRS:
   f(f(0(),x),1()) -> f(g(f(x,x)),x)
   f(g(x),y) -> g(f(x,y))
  EDG Processor:
   DPs:
    f#(f(0(),x),1()) -> f#(x,x)
    f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
    f#(g(x),y) -> f#(x,y)
   TRS:
    f(f(0(),x),1()) -> f(g(f(x,x)),x)
    f(g(x),y) -> g(f(x,y))
   graph:
    f#(g(x),y) -> f#(x,y) -> f#(f(0(),x),1()) -> f#(x,x)
    f#(g(x),y) -> f#(x,y) -> f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
    f#(g(x),y) -> f#(x,y) -> f#(g(x),y) -> f#(x,y)
    f#(f(0(),x),1()) -> f#(g(f(x,x)),x) -> f#(g(x),y) -> f#(x,y)
    f#(f(0(),x),1()) -> f#(x,x) -> f#(g(x),y) -> f#(x,y)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [f#](x0, x1) = x0 + -16,
     
     [g](x0) = x0 + 0,
     
     [1] = 0,
     
     [f](x0, x1) = x0 + 6x1 + -4,
     
     [0] = 0
    orientation:
     f#(f(0(),x),1()) = 6x + 0 >= x + -16 = f#(x,x)
     
     f#(f(0(),x),1()) = 6x + 0 >= 6x + 0 = f#(g(f(x,x)),x)
     
     f#(g(x),y) = x + 0 >= x + -16 = f#(x,y)
     
     f(f(0(),x),1()) = 6x + 6 >= 6x + 0 = f(g(f(x,x)),x)
     
     f(g(x),y) = x + 6y + 0 >= x + 6y + 0 = g(f(x,y))
    problem:
     DPs:
      f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
      f#(g(x),y) -> f#(x,y)
     TRS:
      f(f(0(),x),1()) -> f(g(f(x,x)),x)
      f(g(x),y) -> g(f(x,y))
    Open