YES

1 decompositions
 #0 -----------
   1: not(T()) -> F()
   2: not(F()) -> T()
   3: not(not(x)) -> x
   4: exor(x,T()) -> not(x)
   5: exor(x,F()) -> x
   6: exor(not(x),y) -> not(exor(x,y))
   7: exor(exor(x,y),z) -> exor(x,exor(y,z))
   8: exor(x,y) -> exor(y,x)

@Jouannaud and Kirchner's criterion
--- R
   1: not(T()) -> F()
   2: not(F()) -> T()
   3: not(not(x)) -> x
   4: exor(x,T()) -> not(x)
   5: exor(x,F()) -> x
   6: exor(not(x),y) -> not(exor(x,y))
   7: exor(exor(x,y),z) -> exor(x,exor(y,z))
   8: exor(x,y) -> exor(y,x)

--- S
   1: not(T()) -> F()
   2: not(F()) -> T()
   3: not(not(x)) -> x
   4: exor(x,T()) -> not(x)
   5: exor(x,F()) -> x
   6: exor(not(x),y) -> not(exor(x,y))
   7: exor(exor(x,y),z) -> exor(x,exor(y,z))
   8: exor(x,y) -> exor(y,x)