YES

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

Proof:
 DP Processor:
  DPs:
   not#(x) -> xor#(x,true())
   or#(x,y) -> xor#(x,y)
   or#(x,y) -> and#(x,y)
   or#(x,y) -> xor#(and(x,y),xor(x,y))
   implies#(x,y) -> xor#(x,true())
   implies#(x,y) -> and#(x,y)
   implies#(x,y) -> xor#(and(x,y),xor(x,true()))
   and#(xor(x,y),z) -> and#(y,z)
   and#(xor(x,y),z) -> and#(x,z)
   and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
  TRS:
   not(x) -> xor(x,true())
   or(x,y) -> xor(and(x,y),xor(x,y))
   implies(x,y) -> xor(and(x,y),xor(x,true()))
   and(x,true()) -> x
   and(x,false()) -> false()
   and(x,x) -> x
   xor(x,false()) -> x
   xor(x,x) -> false()
   and(xor(x,y),z) -> xor(and(x,z),and(y,z))
  LPO Processor:
   argument filtering:
    pi(not) = [0]
    pi(true) = []
    pi(xor) = [0,1]
    pi(or) = [0,1]
    pi(and) = [0,1]
    pi(implies) = [0,1]
    pi(false) = []
    pi(not#) = [0]
    pi(xor#) = 0
    pi(or#) = [0,1]
    pi(and#) = [0,1]
    pi(implies#) = [0,1]
   precedence:
    or# ~ implies > or > implies# > and# > and ~ not > xor > xor# ~ not# ~ false ~ true
   problem:
    DPs:
     
    TRS:
     not(x) -> xor(x,true())
     or(x,y) -> xor(and(x,y),xor(x,y))
     implies(x,y) -> xor(and(x,y),xor(x,true()))
     and(x,true()) -> x
     and(x,false()) -> false()
     and(x,x) -> x
     xor(x,false()) -> x
     xor(x,x) -> false()
     and(xor(x,y),z) -> xor(and(x,z),and(y,z))
   Qed