YES(?,O(n^2))

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

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
             [1 0]     [2]
   [d](x0) = [0 0]x0 + [0],
   
             [1 2]     [4]
   [f](x0) = [0 1]x0 + [8],
   
             [1 0]     [12]
   [g](x0) = [0 0]x0 + [4 ],
   
                      [1 1]     [6]
   [c](x0, x1) = x0 + [0 0]x1 + [0],
   
                  [6]
   [s](x0) = x0 + [1]
  orientation:
                  [1 0]    [1 1]    [25]    [1 0]    [1 1]    [24]               
   g(c(x,s(y))) = [0 0]x + [0 0]y + [4 ] >= [0 0]x + [0 0]y + [4 ] = g(c(s(x),y))
   
                  [1 2]    [1 1]    [18]    [1 2]    [1 1]    [17]               
   f(c(s(x),y)) = [0 1]x + [0 0]y + [9 ] >= [0 1]x + [0 0]y + [8 ] = f(c(x,s(y)))
   
             [1 4]    [24]    [1 2]    [10]             
   f(f(x)) = [0 1]x + [16] >= [0 0]x + [8 ] = f(d(f(x)))
   
          [1 2]    [4]         
   f(x) = [0 1]x + [8] >= x = x
  problem:
   
  Qed