(COMMENT generated from Maude module 'RENAMED-BOOL' by 'nokinds' transformation)
(VAR A B C U' U V1 V2 X Z Y)
(THEORY (AC _xor_)
(AC _or_)
(AC _and_))
(RULES
U101(tt,A,B) -> _xor_(_and_(A,B),_xor_(A,B))

U11(tt,A) -> A

U111(tt) -> false

U121(tt,A) -> A

U131(tt,B,U') -> U132(equal(_isNotEqualTo_(B,true),true),U')

U132(tt,U') -> U'

U141(tt,U) -> U

U151(tt,A) -> _xor_(A,true)

U21(tt,A,B,C) -> _xor_(_and_(A,B),_and_(A,C))

U31(tt) -> false

U41(tt,A) -> A

U51(tt,A,B) -> not_(_xor_(A,_and_(A,B)))

U61(tt,U',U) -> U62(equal(_isNotEqualTo_(U,U'),true))

U62(tt) -> false

U71(tt) -> true

U81(tt,U',U) -> if_then_else_fi(_isEqualTo_(U,U'),false,true)

U91(tt) -> false

_and_(A,A) -> U11(isBool(A),A)

_and_(A,_xor_(B,C)) -> U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C)

_and_(false,A) -> U31(isBool(A))

_and_(true,A) -> U41(isBool(A),A)

_implies_(A,B) -> U51(and(isBool(A),isBool(B)),A,B)

_isEqualTo_(U,U') -> U61(and(isS(U'),isS(U)),U',U)

_isEqualTo_(U,U) -> U71(isS(U))

_isNotEqualTo_(U,U') -> U81(and(isS(U'),isS(U)),U',U)

_isNotEqualTo_(U,U) -> U91(isS(U))

_or_(A,B) -> U101(and(isBool(A),isBool(B)),A,B)

_xor_(A,A) -> U111(isBool(A))

_xor_(false,A) -> U121(isBool(A),A)

and(tt,X) -> X

equal(X,X) -> tt

if_then_else_fi(B,U,U') -> U131(and(isBool(B),and(isS(U'),isS(U))),B,U')

if_then_else_fi(true,U,U') -> U141(and(isS(U'),isS(U)),U)

isBool(false) -> tt

isBool(true) -> tt

isBool(_and_(V1,V2)) -> and(isBool(V1),isBool(V2))

isBool(_implies_(V1,V2)) -> and(isBool(V1),isBool(V2))

isBool(_isEqualTo_(V1,V2)) -> and(isUniversal(V1),isUniversal(V2))

isBool(_isNotEqualTo_(V1,V2)) -> and(isUniversal(V1),isUniversal(V2))

isBool(_or_(V1,V2)) -> and(isBool(V1),isBool(V2))

isBool(_xor_(V1,V2)) -> and(isBool(V1),isBool(V2))

isBool(not_(V1)) -> isBool(V1)

not_(A) -> U151(isBool(A),A)

not_(false) -> true

not_(true) -> false
)