NO

Problem:
 not(true()) -> false()
 not(false()) -> true()
 or(true(),y) -> true()
 or(x,true()) -> true()
 or(false(),false()) -> false()
 and(true(),true()) -> true()
 and(x,true()) -> x
 and(true(),y) -> y
 and(false(),false()) -> false()
 not(and(x,y)) -> or(not(x),not(y))
 not(or(x,y)) -> and(not(x),not(y))

Proof:
 Nonconfluence Processor:
  terms: false() *<- not(or(true(),y)) ->* and(false(),not(y))
  Qed