1.12/1.16	MAYBE
1.12/1.16	Input TRS:
1.12/1.16	    AC symbols: _or_ _xor_ _and_
1.12/1.16	    1: U101(tt(),A,B) -> _xor_(_and_(A,B),_xor_(A,B))
1.12/1.16	    2: U11(tt(),A) -> A
1.12/1.16	    3: U111(tt()) -> false()
1.12/1.16	    4: U121(tt(),A) -> A
1.12/1.16	    5: U131(tt(),B,U') -> U132(equal(_isNotEqualTo_(B,true()),true()),U')
1.12/1.16	    6: U132(tt(),U') -> U'
1.12/1.16	    7: U141(tt(),U) -> U
1.12/1.16	    8: U151(tt(),A) -> _xor_(A,true())
1.12/1.16	    9: U21(tt(),A,B,C) -> _xor_(_and_(A,B),_and_(A,C))
1.12/1.16	    10: U31(tt()) -> false()
1.12/1.16	    11: U41(tt(),A) -> A
1.12/1.16	    12: U51(tt(),A,B) -> not_(_xor_(A,_and_(A,B)))
1.12/1.16	    13: U61(tt(),U',U) -> U62(equal(_isNotEqualTo_(U,U'),true()))
1.12/1.16	    14: U62(tt()) -> false()
1.12/1.16	    15: U71(tt()) -> true()
1.12/1.16	    16: U81(tt(),U',U) -> if_then_else_fi(_isEqualTo_(U,U'),false(),true())
1.12/1.16	    17: U91(tt()) -> false()
1.12/1.16	    18: _and_(A,A) -> U11(isBool(A),A)
1.12/1.16	    19: _and_(A,_xor_(B,C)) -> U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C)
1.12/1.16	    20: _and_(false(),A) -> U31(isBool(A))
1.12/1.16	    21: _and_(true(),A) -> U41(isBool(A),A)
1.12/1.16	    22: _implies_(A,B) -> U51(and(isBool(A),isBool(B)),A,B)
1.12/1.16	    23: _isEqualTo_(U,U') -> U61(and(isS(U'),isS(U)),U',U)
1.12/1.16	    24: _isEqualTo_(U,U) -> U71(isS(U))
1.12/1.16	    25: _isNotEqualTo_(U,U') -> U81(and(isS(U'),isS(U)),U',U)
1.12/1.16	    26: _isNotEqualTo_(U,U) -> U91(isS(U))
1.12/1.16	    27: _or_(A,B) -> U101(and(isBool(A),isBool(B)),A,B)
1.12/1.16	    28: _xor_(A,A) -> U111(isBool(A))
1.12/1.16	    29: _xor_(false(),A) -> U121(isBool(A),A)
1.12/1.16	    30: and(tt(),X) -> X
1.12/1.16	    31: equal(X,X) -> tt()
1.12/1.16	    32: if_then_else_fi(B,U,U') -> U131(and(isBool(B),and(isS(U'),isS(U))),B,U')
1.12/1.16	    33: if_then_else_fi(true(),U,U') -> U141(and(isS(U'),isS(U)),U)
1.12/1.16	    34: isBool(false()) -> tt()
1.12/1.16	    35: isBool(true()) -> tt()
1.12/1.16	    36: isBool(_and_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	    37: isBool(_implies_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	    38: isBool(_isEqualTo_(V1,V2)) -> and(isUniversal(V1),isUniversal(V2))
1.12/1.16	    39: isBool(_isNotEqualTo_(V1,V2)) -> and(isUniversal(V1),isUniversal(V2))
1.12/1.16	    40: isBool(_or_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	    41: isBool(_xor_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	    42: isBool(not_(V1)) -> isBool(V1)
1.12/1.16	    43: not_(A) -> U151(isBool(A),A)
1.12/1.16	    44: not_(false()) -> true()
1.12/1.16	    45: not_(true()) -> false()
1.12/1.16	Number of strict rules: 45
1.12/1.16	Direct POLO(bPol) ... failed.
1.12/1.16	Uncurrying and U71 U91
1.12/1.16	AC symbols: _or_ _xor_ _and_
1.12/1.16	1: U101(tt(),A,B) -> _xor_(_and_(A,B),_xor_(A,B))
1.12/1.16	2: U11(tt(),A) -> A
1.12/1.16	3: U111(tt()) -> false()
1.12/1.16	4: U121(tt(),A) -> A
1.12/1.16	5: U131(tt(),B,U') -> U132(equal(_isNotEqualTo_(B,true()),true()),U')
1.12/1.16	6: U132(tt(),U') -> U'
1.12/1.16	7: U141(tt(),U) -> U
1.12/1.16	8: U151(tt(),A) -> _xor_(A,true())
1.12/1.16	9: U21(tt(),A,B,C) -> _xor_(_and_(A,B),_and_(A,C))
1.12/1.16	10: U31(tt()) -> false()
1.12/1.16	11: U41(tt(),A) -> A
1.12/1.16	12: U51(tt(),A,B) -> not_(_xor_(A,_and_(A,B)))
1.12/1.16	13: U61(tt(),U',U) -> U62(equal(_isNotEqualTo_(U,U'),true()))
1.12/1.16	14: U62(tt()) -> false()
1.12/1.16	15: U71^1_tt() -> true()
1.12/1.16	16: U81(tt(),U',U) -> if_then_else_fi(_isEqualTo_(U,U'),false(),true())
1.12/1.16	17: U91^1_tt() -> false()
1.12/1.16	18: _and_(A,A) -> U11(isBool(A),A)
1.12/1.16	19: _and_(A,_xor_(B,C)) -> U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C)
1.12/1.16	20: _and_(false(),A) -> U31(isBool(A))
1.12/1.16	21: _and_(true(),A) -> U41(isBool(A),A)
1.12/1.16	22: _implies_(A,B) -> U51(and(isBool(A),isBool(B)),A,B)
1.12/1.16	23: _isEqualTo_(U,U') -> U61(and^1_isS(U',isS(U)),U',U)
1.12/1.16	24: _isEqualTo_(U,U) -> U71^1_isS(U)
1.12/1.16	25: _isNotEqualTo_(U,U') -> U81(and^1_isS(U',isS(U)),U',U)
1.12/1.16	26: _isNotEqualTo_(U,U) -> U91^1_isS(U)
1.12/1.16	27: _or_(A,B) -> U101(and(isBool(A),isBool(B)),A,B)
1.12/1.16	28: _xor_(A,A) -> U111(isBool(A))
1.12/1.16	29: _xor_(false(),A) -> U121(isBool(A),A)
1.12/1.16	30: and^1_tt(X) -> X
1.12/1.16	31: equal(X,X) -> tt()
1.12/1.16	32: if_then_else_fi(B,U,U') -> U131(and(isBool(B),and^1_isS(U',isS(U))),B,U')
1.12/1.16	33: if_then_else_fi(true(),U,U') -> U141(and^1_isS(U',isS(U)),U)
1.12/1.16	34: isBool(false()) -> tt()
1.12/1.16	35: isBool(true()) -> tt()
1.12/1.16	36: isBool(_and_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	37: isBool(_implies_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	38: isBool(_isEqualTo_(V1,V2)) -> and^1_isUniversal(V1,isUniversal(V2))
1.12/1.16	39: isBool(_isNotEqualTo_(V1,V2)) -> and^1_isUniversal(V1,isUniversal(V2))
1.12/1.16	40: isBool(_or_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	41: isBool(_xor_(V1,V2)) -> and(isBool(V1),isBool(V2))
1.12/1.16	42: isBool(not_(V1)) -> isBool(V1)
1.12/1.16	43: not_(A) -> U151(isBool(A),A)
1.12/1.16	44: not_(false()) -> true()
1.12/1.16	45: not_(true()) -> false()
1.12/1.16	46: U91(tt()) ->= U91^1_tt()
1.12/1.16	47: U91(isS(_1)) ->= U91^1_isS(_1)
1.12/1.16	48: U71(tt()) ->= U71^1_tt()
1.12/1.16	49: U71(isS(_1)) ->= U71^1_isS(_1)
1.12/1.16	50: and(tt(),_1) ->= and^1_tt(_1)
1.12/1.16	51: and(isUniversal(_1),_2) ->= and^1_isUniversal(_1,_2)
1.12/1.16	52: and(isS(_1),_2) ->= and^1_isS(_1,_2)
1.12/1.16	Number of strict rules: 45
1.12/1.16	Direct POLO(bPol) ... failed.
1.12/1.16	Dependency Pairs:
1.12/1.16	   #1: #not_(A) -> #U151(isBool(A),A)
1.12/1.16	   #2: #not_(A) -> #isBool(A)
1.12/1.16	   #3: #_xor_(false(),A) -> #U121(isBool(A),A)
1.12/1.16	   #4: #_xor_(false(),A) -> #isBool(A)
1.12/1.16	   #5: #U91(tt()) ->? #U91^1_tt()
1.12/1.16	   #6: #isBool(not_(V1)) -> #isBool(V1)
1.12/1.16	   #7: #isBool(_xor_(V1,V2)) -> #and(isBool(V1),isBool(V2))
1.12/1.16	   #8: #isBool(_xor_(V1,V2)) -> #isBool(V1)
1.12/1.16	   #9: #isBool(_xor_(V1,V2)) -> #isBool(V2)
1.12/1.16	   #10: #isBool(_implies_(V1,V2)) -> #and(isBool(V1),isBool(V2))
1.12/1.16	   #11: #isBool(_implies_(V1,V2)) -> #isBool(V1)
1.12/1.16	   #12: #isBool(_implies_(V1,V2)) -> #isBool(V2)
1.12/1.16	   #13: #_or_(x,_or_(y,z)) ->= #_or_(_or_(x,y),z)
1.12/1.16	   #14: #_or_(x,_or_(y,z)) ->= #_or_(x,y)
1.12/1.16	   #15: #U71(tt()) ->? #U71^1_tt()
1.12/1.16	   #16: #_and_(x,_and_(y,z)) ->= #_and_(_and_(x,y),z)
1.12/1.16	   #17: #_and_(x,_and_(y,z)) ->= #_and_(x,y)
1.12/1.16	   #18: #isBool(_or_(V1,V2)) -> #and(isBool(V1),isBool(V2))
1.12/1.16	   #19: #isBool(_or_(V1,V2)) -> #isBool(V1)
1.12/1.16	   #20: #isBool(_or_(V1,V2)) -> #isBool(V2)
1.12/1.16	   #21: #U61(tt(),U',U) -> #U62(equal(_isNotEqualTo_(U,U'),true()))
1.12/1.16	   #22: #U61(tt(),U',U) -> #equal(_isNotEqualTo_(U,U'),true())
1.12/1.16	   #23: #U61(tt(),U',U) -> #_isNotEqualTo_(U,U')
1.12/1.16	   #24: #U21(tt(),A,B,C) -> #_xor_(_and_(A,B),_and_(A,C))
1.12/1.16	   #25: #U21(tt(),A,B,C) -> #_and_(A,B)
1.12/1.16	   #26: #U21(tt(),A,B,C) -> #_and_(A,C)
1.12/1.16	   #27: #_isEqualTo_(U,U') -> #U61(and^1_isS(U',isS(U)),U',U)
1.12/1.16	   #28: #U51(tt(),A,B) -> #not_(_xor_(A,_and_(A,B)))
1.12/1.16	   #29: #U51(tt(),A,B) -> #_xor_(A,_and_(A,B))
1.12/1.16	   #30: #U51(tt(),A,B) -> #_and_(A,B)
1.12/1.16	   #31: #_isNotEqualTo_(U,U') -> #U81(and^1_isS(U',isS(U)),U',U)
1.12/1.16	   #32: #_and_(false(),A) -> #U31(isBool(A))
1.12/1.16	   #33: #_and_(false(),A) -> #isBool(A)
1.12/1.16	   #34: #if_then_else_fi(true(),U,U') -> #U141(and^1_isS(U',isS(U)),U)
1.12/1.16	   #35: #U131(tt(),B,U') -> #U132(equal(_isNotEqualTo_(B,true()),true()),U')
1.12/1.16	   #36: #U131(tt(),B,U') -> #equal(_isNotEqualTo_(B,true()),true())
1.12/1.16	   #37: #U131(tt(),B,U') -> #_isNotEqualTo_(B,true())
1.12/1.16	   #38: #_xor_(A,A) -> #U111(isBool(A))
1.12/1.16	   #39: #_xor_(A,A) -> #isBool(A)
1.12/1.16	   #40: #_implies_(A,B) -> #U51(and(isBool(A),isBool(B)),A,B)
1.12/1.16	   #41: #_implies_(A,B) -> #and(isBool(A),isBool(B))
1.12/1.16	   #42: #_implies_(A,B) -> #isBool(A)
1.12/1.16	   #43: #_implies_(A,B) -> #isBool(B)
1.12/1.16	   #44: #_or_(A,B) -> #U101(and(isBool(A),isBool(B)),A,B)
1.12/1.16	   #45: #_or_(A,B) -> #and(isBool(A),isBool(B))
1.12/1.16	   #46: #_or_(A,B) -> #isBool(A)
1.12/1.16	   #47: #_or_(A,B) -> #isBool(B)
1.12/1.16	   #48: #_and_(A,_xor_(B,C)) -> #U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C)
1.12/1.16	   #49: #_and_(A,_xor_(B,C)) -> #and(isBool(A),and(isBool(B),isBool(C)))
1.12/1.16	   #50: #_and_(A,_xor_(B,C)) -> #isBool(A)
1.12/1.16	   #51: #_and_(A,_xor_(B,C)) -> #and(isBool(B),isBool(C))
1.12/1.16	   #52: #_and_(A,_xor_(B,C)) -> #isBool(B)
1.12/1.16	   #53: #_and_(A,_xor_(B,C)) -> #isBool(C)
1.12/1.16	   #54: #if_then_else_fi(B,U,U') -> #U131(and(isBool(B),and^1_isS(U',isS(U))),B,U')
1.12/1.16	   #55: #if_then_else_fi(B,U,U') -> #and(isBool(B),and^1_isS(U',isS(U)))
1.12/1.16	   #56: #if_then_else_fi(B,U,U') -> #isBool(B)
1.12/1.16	   #57: #isBool(_and_(V1,V2)) -> #and(isBool(V1),isBool(V2))
1.12/1.16	   #58: #isBool(_and_(V1,V2)) -> #isBool(V1)
1.12/1.16	   #59: #isBool(_and_(V1,V2)) -> #isBool(V2)
1.12/1.16	   #60: #_and_(true(),A) -> #U41(isBool(A),A)
1.12/1.16	   #61: #_and_(true(),A) -> #isBool(A)
1.12/1.16	   #62: #U81(tt(),U',U) -> #if_then_else_fi(_isEqualTo_(U,U'),false(),true())
1.12/1.16	   #63: #U81(tt(),U',U) -> #_isEqualTo_(U,U')
1.12/1.16	   #64: #U101(tt(),A,B) -> #_xor_(_and_(A,B),_xor_(A,B))
1.12/1.16	   #65: #U101(tt(),A,B) -> #_and_(A,B)
1.12/1.16	   #66: #U101(tt(),A,B) -> #_xor_(A,B)
1.12/1.16	   #67: #_xor_(x,_xor_(y,z)) ->= #_xor_(_xor_(x,y),z)
1.12/1.16	   #68: #_xor_(x,_xor_(y,z)) ->= #_xor_(x,y)
1.12/1.16	   #69: #U151(tt(),A) -> #_xor_(A,true())
1.12/1.16	   #70: #and(tt(),_1) ->? #and^1_tt(_1)
1.12/1.16	   #71: #_and_(A,A) -> #U11(isBool(A),A)
1.12/1.16	   #72: #_and_(A,A) -> #isBool(A)
1.12/1.16	Number of SCCs: 4, DPs: 18
1.12/1.16	  SCC { #13 #14 }
1.12/1.16	only weak rules.
1.12/1.16	Number of SCCs: 3, DPs: 16
1.12/1.16	  SCC { #67 #68 }
1.12/1.16	only weak rules.
1.12/1.16	Number of SCCs: 2, DPs: 14
1.12/1.16	  SCC { #16 #17 #25 #26 #48 }
1.12/1.16	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
1.12/1.16	Finding a loop...  failed.
1.12/1.16	EOF