NO
Input TRS:
AC symbols: _or_ _xor_ _and_
      1: U11(tt(),U',U) -> U12(equal(_isNotEqualTo_(U,U'),true()))
      2: U12(tt()) -> false()
      3: U21(tt(),B,U') -> U22(equal(_isNotEqualTo_(B,true()),true()),U')
      4: U22(tt(),U') -> U'
      5: _and_(A,A) -> A
      6: _and_(A,_xor_(B,C)) -> _xor_(_and_(A,B),_and_(A,C))
      7: _and_(false(),A) -> false()
      8: _and_(true(),A) -> A
      9: _implies_(A,B) -> not_(_xor_(A,_and_(A,B)))
      10: _isEqualTo_(U,U') -> U11(tt(),U',U)
      11: _isEqualTo_(U,U) -> true()
      12: _isNotEqualTo_(U,U') -> if_then_else_fi(_isEqualTo_(U,U'),false(),true())
      13: _isNotEqualTo_(U,U) -> false()
      14: _or_(A,B) -> _xor_(_and_(A,B),_xor_(A,B))
      15: _xor_(A,A) -> false()
      16: _xor_(false(),A) -> A
      17: and(tt(),X) -> X
      18: equal(X,X) -> tt()
      19: if_then_else_fi(B,U,U') -> U21(tt(),B,U')
      20: if_then_else_fi(true(),U,U') -> U
      21: not_(A) -> _xor_(A,true())
      22: not_(false()) -> true()
      23: not_(true()) -> false()
Number of strict rules: 23
Direct POLO(bPol) ... failed.
Uncurrying U11 U21
AC symbols: _or_ _xor_ _and_
      1: U11^1_tt(U',U) -> U12(equal(_isNotEqualTo_(U,U'),true()))
      2: U12(tt()) -> false()
      3: U21^1_tt(B,U') -> U22(equal(_isNotEqualTo_(B,true()),true()),U')
      4: U22(tt(),U') -> U'
      5: _and_(A,A) -> A
      6: _and_(A,_xor_(B,C)) -> _xor_(_and_(A,B),_and_(A,C))
      7: _and_(false(),A) -> false()
      8: _and_(true(),A) -> A
      9: _implies_(A,B) -> not_(_xor_(A,_and_(A,B)))
      10: _isEqualTo_(U,U') -> U11^1_tt(U',U)
      11: _isEqualTo_(U,U) -> true()
      12: _isNotEqualTo_(U,U') -> if_then_else_fi(_isEqualTo_(U,U'),false(),true())
      13: _isNotEqualTo_(U,U) -> false()
      14: _or_(A,B) -> _xor_(_and_(A,B),_xor_(A,B))
      15: _xor_(A,A) -> false()
      16: _xor_(false(),A) -> A
      17: and(tt(),X) -> X
      18: equal(X,X) -> tt()
      19: if_then_else_fi(B,U,U') -> U21^1_tt(B,U')
      20: if_then_else_fi(true(),U,U') -> U
      21: not_(A) -> _xor_(A,true())
      22: not_(false()) -> true()
      23: not_(true()) -> false()
      24: U21(tt(),_2,_3) ->= U21^1_tt(_2,_3)
      25: U11(tt(),_2,_3) ->= U11^1_tt(_2,_3)
Number of strict rules: 23
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #_and_(A,_xor_(B,C)) -> #_xor_(_and_(A,B),_and_(A,C))
     #2: #_and_(A,_xor_(B,C)) -> #_and_(A,B)
     #3: #_and_(A,_xor_(B,C)) -> #_and_(A,C)
     #4: #_implies_(A,B) -> #not_(_xor_(A,_and_(A,B)))
     #5: #_implies_(A,B) -> #_xor_(A,_and_(A,B))
     #6: #_implies_(A,B) -> #_and_(A,B)
     #7: #U21(tt(),_2,_3) ->? #U21^1_tt(_2,_3)
     #8: #_isNotEqualTo_(U,U') -> #if_then_else_fi(_isEqualTo_(U,U'),false(),true())
     #9: #_isNotEqualTo_(U,U') -> #_isEqualTo_(U,U')
     #10: #_or_(A,B) -> #_xor_(_and_(A,B),_xor_(A,B))
     #11: #_or_(A,B) -> #_and_(A,B)
     #12: #_or_(A,B) -> #_xor_(A,B)
     #13: #U11(tt(),_2,_3) ->? #U11^1_tt(_2,_3)
     #14: #_isEqualTo_(U,U') -> #U11^1_tt(U',U)
     #15: #_and_(x,_and_(y,z)) ->= #_and_(_and_(x,y),z)
     #16: #_and_(x,_and_(y,z)) ->= #_and_(x,y)
     #17: #_xor_(x,_xor_(y,z)) ->= #_xor_(_xor_(x,y),z)
     #18: #_xor_(x,_xor_(y,z)) ->= #_xor_(x,y)
     #19: #if_then_else_fi(B,U,U') -> #U21^1_tt(B,U')
     #20: #_or_(x,_or_(y,z)) ->= #_or_(_or_(x,y),z)
     #21: #_or_(x,_or_(y,z)) ->= #_or_(x,y)
     #22: #not_(A) -> #_xor_(A,true())
     #23: #U21^1_tt(B,U') -> #U22(equal(_isNotEqualTo_(B,true()),true()),U')
     #24: #U21^1_tt(B,U') -> #equal(_isNotEqualTo_(B,true()),true())
     #25: #U21^1_tt(B,U') -> #_isNotEqualTo_(B,true())
     #26: #U11^1_tt(U',U) -> #U12(equal(_isNotEqualTo_(U,U'),true()))
     #27: #U11^1_tt(U',U) -> #equal(_isNotEqualTo_(U,U'),true())
     #28: #U11^1_tt(U',U) -> #_isNotEqualTo_(U,U')
Number of SCCs: 4, DPs: 14
  SCC { #20 #21 }
only weak rules.
Number of SCCs: 3, DPs: 12
  SCC { #17 #18 }
only weak rules.
Number of SCCs: 2, DPs: 10
  SCC { #2 #3 #15 #16 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      U21	s: [3,2,1]	p: 0
      _and_	s: {1,2}	p: 2
      U11	s: [3,2,1]	p: 0
      #_isNotEqualTo_	s: [1,2]	p: 0
      not_	s: []	p: 0
      #_and_	s: {1,2}	p: 2
      #equal	s: [1,2]	p: 0
      and	s: [1,2]	p: 0
      _or_	s: {}	p: 0
      false	s: []	p: 0
      U12	s: []	p: 0
      true	s: []	p: 0
      _implies_	s: [1,2]	p: 0
      #_implies_	s: [1,2]	p: 0
      #U12	s: []	p: 0
      _isNotEqualTo_	s: [1,2]	p: 0
      #_xor_	s: {}	p: 1
      _xor_	s: {1,2}	p: 1
      U21^1_tt	s: [1,2]	p: 0
      #U21^1_tt	s: [1,2]	p: 0
      U11^1_tt	s: [1,2]	p: 0
      #if_then_else_fi	s: [3,2,1]	p: 0
      #not_	s: []	p: 0
      #U11	s: [3,2,1]	p: 0
      #_isEqualTo_	s: [1,2]	p: 0
      equal	s: [1,2]	p: 0
      #U21	s: [3,2,1]	p: 0
      #U22	s: [1,2]	p: 0
      tt	s: []	p: 0
      #_or_	s: {}	p: 0
      U22	s: [1,2]	p: 0
      _isEqualTo_	s: [1,2]	p: 0
      #and	s: [1,2]	p: 0
      if_then_else_fi	s: [3,2,1]	p: 0
      #U11^1_tt	s: [1,2]	p: 0
    USABLE RULES: { 5..8 15 16 27 28 }
    Removed DPs: #2 #3 #16
Number of SCCs: 2, DPs: 7
  SCC { #15 }
only weak rules.
Number of SCCs: 1, DPs: 6
  SCC { #8 #9 #14 #19 #25 #28 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #U21^1_tt(U_{1},U')	-#25->
  #_isNotEqualTo_(U_{1},true())	--->*
  #_isNotEqualTo_(U_{1},true())	-#8->
  #if_then_else_fi(_isEqualTo_(U_{1},true()),false(),true())	--->*
  #if_then_else_fi(_isEqualTo_(U_{1},true()),false(),true())	-#19->
  #U21^1_tt(_isEqualTo_(U_{1},true()),true())	--->*
  #U21^1_tt(_isEqualTo_(U_{1},true()),true())
  Looping with: [ U_{1} := _isEqualTo_(U_{1},true()); U' := true(); ]