NO

1 decompositions
 #1 -----------
   1: not(true()) -> false()
   2: not(false()) -> true()
   3: or(true(),x1) -> true()
   4: or(x2,true()) -> true()
   5: or(false(),false()) -> false()
   6: implies(true(),x3) -> x3
   8: implies(x5,x6) -> or(not(x5),x6)

unjoinable peak
    x16
*<- implies(true(),x16) ->*
    or(false(),x16)
NOTE: input TRS is reduced

original is
   1: not(true()) -> false()
   2: not(false()) -> true()
   3: or(true(),x1) -> true()
   4: or(x2,true()) -> true()
   5: or(false(),false()) -> false()
   6: implies(true(),x3) -> x3
   7: implies(false(),x4) -> true()
   8: implies(x5,x6) -> or(not(x5),x6)

reduced to
   1: not(true()) -> false()
   2: not(false()) -> true()
   3: or(true(),x1) -> true()
   4: or(x2,true()) -> true()
   5: or(false(),false()) -> false()
   6: implies(true(),x3) -> x3
   8: implies(x5,x6) -> or(not(x5),x6)