(COMMENT generated from Maude module 'RENAMED-BOOL' by 'nosorts' transformation)
(VAR A B C U' U X Z Y)
(THEORY (AC _xor_)
(AC _or_)
(AC _and_))
(RULES
U11(tt,U',U) -> U12(equal(_isNotEqualTo_(U,U'),true))

U12(tt) -> false

U21(tt,B,U') -> U22(equal(_isNotEqualTo_(B,true),true),U')

U22(tt,U') -> U'

_and_(A,A) -> A

_and_(A,_xor_(B,C)) -> _xor_(_and_(A,B),_and_(A,C))

_and_(false,A) -> false

_and_(true,A) -> A

_implies_(A,B) -> not_(_xor_(A,_and_(A,B)))

_isEqualTo_(U,U') -> U11(tt,U',U)

_isEqualTo_(U,U) -> true

_isNotEqualTo_(U,U') -> if_then_else_fi(_isEqualTo_(U,U'),false,true)

_isNotEqualTo_(U,U) -> false

_or_(A,B) -> _xor_(_and_(A,B),_xor_(A,B))

_xor_(A,A) -> false

_xor_(false,A) -> A

and(tt,X) -> X

equal(X,X) -> tt

if_then_else_fi(B,U,U') -> U21(tt,B,U')

if_then_else_fi(true,U,U') -> U

not_(A) -> _xor_(A,true)

not_(false) -> true

not_(true) -> false
)