MAYBE

Problem:
 f(f(s(x),0()),f(y,z)) -> f(f(y,z),f(y,s(z)))
 f(f(s(x),s(y)),f(z,w)) -> f(f(x,y),f(z,w))

Proof:
 DP Processor:
  DPs:
   f#(f(s(x),0()),f(y,z)) -> f#(y,s(z))
   f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
   f#(f(s(x),s(y)),f(z,w)) -> f#(x,y)
   f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
  TRS:
   f(f(s(x),0()),f(y,z)) -> f(f(y,z),f(y,s(z)))
   f(f(s(x),s(y)),f(z,w)) -> f(f(x,y),f(z,w))
  EDG Processor:
   DPs:
    f#(f(s(x),0()),f(y,z)) -> f#(y,s(z))
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y)
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
   TRS:
    f(f(s(x),0()),f(y,z)) -> f(f(y,z),f(y,s(z)))
    f(f(s(x),s(y)),f(z,w)) -> f(f(x,y),f(z,w))
   graph:
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z))) ->
    f#(f(s(x),0()),f(y,z)) -> f#(y,s(z))
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z))) ->
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z))) ->
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y)
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z))) ->
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w)) ->
    f#(f(s(x),0()),f(y,z)) -> f#(y,s(z))
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w)) ->
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w)) ->
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y)
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w)) ->
    f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y) ->
    f#(f(s(x),0()),f(y,z)) -> f#(y,s(z))
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y) ->
    f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y) ->
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y)
    f#(f(s(x),s(y)),f(z,w)) -> f#(x,y) -> f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
     f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
     f#(f(s(x),s(y)),f(z,w)) -> f#(x,y)
    TRS:
     f(f(s(x),0()),f(y,z)) -> f(f(y,z),f(y,s(z)))
     f(f(s(x),s(y)),f(z,w)) -> f(f(x,y),f(z,w))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x0 + x1,
      
      [f](x0, x1) = 1x0 + 1x1 + 1,
      
      [0] = 0,
      
      [s](x0) = x0
     orientation:
      f#(f(s(x),0()),f(y,z)) = 1x + 1y + 1z + 1 >= 1y + 1z + 1 = f#(f(y,z),f(y,s(z)))
      
      f#(f(s(x),s(y)),f(z,w)) = 1w + 1x + 1y + 1z + 1 >= 1w + 1x + 1y + 1z + 1 = f#(f(x,y),f(z,w))
      
      f#(f(s(x),s(y)),f(z,w)) = 1w + 1x + 1y + 1z + 1 >= x + y = f#(x,y)
      
      f(f(s(x),0()),f(y,z)) = 2x + 2y + 2z + 2 >= 2y + 2z + 2 = f(f(y,z),f(y,s(z)))
      
      f(f(s(x),s(y)),f(z,w)) = 2w + 2x + 2y + 2z + 2 >= 2w + 2x + 2y + 2z + 2 = f(f(x,y),f(z,w))
     problem:
      DPs:
       f#(f(s(x),0()),f(y,z)) -> f#(f(y,z),f(y,s(z)))
       f#(f(s(x),s(y)),f(z,w)) -> f#(f(x,y),f(z,w))
      TRS:
       f(f(s(x),0()),f(y,z)) -> f(f(y,z),f(y,s(z)))
       f(f(s(x),s(y)),f(z,w)) -> f(f(x,y),f(z,w))
     Open