MAYBE

Problem:
 f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
 f(s(x),y,z) -> f(x,s(c(y)),c(z))
 f(c(x),x,y) -> c(y)
 g(x,y) -> x
 g(x,y) -> y

Proof:
 DP Processor:
  DPs:
   f#(x,c(x),c(y)) -> f#(y,x,y)
   f#(x,c(x),c(y)) -> f#(y,y,f(y,x,y))
   f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
  TRS:
   f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
   f(s(x),y,z) -> f(x,s(c(y)),c(z))
   f(c(x),x,y) -> c(y)
   g(x,y) -> x
   g(x,y) -> y
  Usable Rule Processor:
   DPs:
    f#(x,c(x),c(y)) -> f#(y,x,y)
    f#(x,c(x),c(y)) -> f#(y,y,f(y,x,y))
    f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
   TRS:
    f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
    f(s(x),y,z) -> f(x,s(c(y)),c(z))
    f(c(x),x,y) -> c(y)
   EDG Processor:
    DPs:
     f#(x,c(x),c(y)) -> f#(y,x,y)
     f#(x,c(x),c(y)) -> f#(y,y,f(y,x,y))
     f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
    TRS:
     f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
     f(s(x),y,z) -> f(x,s(c(y)),c(z))
     f(c(x),x,y) -> c(y)
    graph:
     f#(s(x),y,z) -> f#(x,s(c(y)),c(z)) ->
     f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
     f#(x,c(x),c(y)) -> f#(y,y,f(y,x,y)) ->
     f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
     f#(x,c(x),c(y)) -> f#(y,x,y) -> f#(x,c(x),c(y)) -> f#(y,x,y)
     f#(x,c(x),c(y)) -> f#(y,x,y) ->
     f#(x,c(x),c(y)) -> f#(y,y,f(y,x,y))
     f#(x,c(x),c(y)) -> f#(y,x,y) -> f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
    Restore Modifier:
     DPs:
      f#(x,c(x),c(y)) -> f#(y,x,y)
      f#(x,c(x),c(y)) -> f#(y,y,f(y,x,y))
      f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
     TRS:
      f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
      f(s(x),y,z) -> f(x,s(c(y)),c(z))
      f(c(x),x,y) -> c(y)
      g(x,y) -> x
      g(x,y) -> y
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 5/9
      DPs:
       f#(x,c(x),c(y)) -> f#(y,x,y)
      TRS:
       f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
       f(s(x),y,z) -> f(x,s(c(y)),c(z))
       f(c(x),x,y) -> c(y)
       g(x,y) -> x
       g(x,y) -> y
      Open
      
      DPs:
       f#(s(x),y,z) -> f#(x,s(c(y)),c(z))
      TRS:
       f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
       f(s(x),y,z) -> f(x,s(c(y)),c(z))
       f(c(x),x,y) -> c(y)
       g(x,y) -> x
       g(x,y) -> y
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0, x1, x2) = x0,
        
        [g](x0, x1) = x0 + x1,
        
        [s](x0) = x0 + 1,
        
        [f](x0, x1, x2) = 0,
        
        [c](x0) = 0
       orientation:
        f#(s(x),y,z) = x + 1 >= x = f#(x,s(c(y)),c(z))
        
        f(x,c(x),c(y)) = 0 >= 0 = f(y,y,f(y,x,y))
        
        f(s(x),y,z) = 0 >= 0 = f(x,s(c(y)),c(z))
        
        f(c(x),x,y) = 0 >= 0 = c(y)
        
        g(x,y) = x + y >= x = x
        
        g(x,y) = x + y >= y = y
       problem:
        DPs:
         
        TRS:
         f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
         f(s(x),y,z) -> f(x,s(c(y)),c(z))
         f(c(x),x,y) -> c(y)
         g(x,y) -> x
         g(x,y) -> y
       Qed