1.33/1.48 MAYBE 1.33/1.48 Input TRS: 1.33/1.48 C symbols: d _+_ _*_ gcd 1.33/1.48 1: 1() -> s_(0()) 1.33/1.48 2: 2() -> s_(s_(0())) 1.33/1.48 3: 3() -> s_(s_(s_(0()))) 1.33/1.48 4: 4() -> s_(s_(s_(s_(0())))) 1.33/1.48 5: 5() -> s_(s_(s_(s_(s_(0()))))) 1.33/1.48 6: 6() -> s_(s_(s_(s_(s_(s_(0())))))) 1.33/1.48 7: 7() -> s_(s_(s_(s_(s_(s_(s_(0()))))))) 1.33/1.48 8: U101(tt(),M,N) -> d(N,M) 1.33/1.48 9: U11(tt()) -> 0() 1.33/1.48 10: U111(tt()) -> 0() 1.33/1.48 11: U121(tt(),M',N') -> U122(equal(_>_(N',M'),true()),M',N') 1.33/1.48 12: U122(tt(),M',N') -> gcd(d(N',M'),M') 1.33/1.48 13: U131(tt(),N') -> N' 1.33/1.48 14: U141(tt(),V1,V2) -> U142(isNat(V1),V2) 1.33/1.48 15: U142(tt(),V2) -> U143(isNat(V2)) 1.33/1.48 16: U143(tt()) -> tt() 1.33/1.48 17: U151(tt(),V1,V2) -> U152(isNat(V1),V2) 1.33/1.48 18: U152(tt(),V2) -> U153(isNat(V2)) 1.33/1.48 19: U153(tt()) -> tt() 1.33/1.48 20: U161(tt(),V) -> U162(isNzNat(V)) 1.33/1.48 21: U162(tt()) -> tt() 1.33/1.48 22: U171(tt(),V1,V2) -> U172(isNat(V1),V2) 1.33/1.48 23: U172(tt(),V2) -> U173(isNat(V2)) 1.33/1.48 24: U173(tt()) -> tt() 1.33/1.48 25: U181(tt(),V1,V2) -> U182(isNat(V1),V2) 1.33/1.48 26: U182(tt(),V2) -> U183(isNat(V2)) 1.33/1.48 27: U183(tt()) -> tt() 1.33/1.48 28: U191(tt(),V1,V2) -> U192(isNat(V1),V2) 1.33/1.48 29: U192(tt(),V2) -> U193(isNat(V2)) 1.33/1.48 30: U193(tt()) -> tt() 1.33/1.48 31: U201(tt(),V1,V2) -> U202(isNat(V1),V2) 1.33/1.48 32: U202(tt(),V2) -> U203(isNat(V2)) 1.33/1.48 33: U203(tt()) -> tt() 1.33/1.48 34: U21(tt(),M,N) -> s_(_+_(N,_+_(M,_*_(N,M)))) 1.33/1.48 35: U211(tt(),V1) -> U212(isNzNat(V1)) 1.33/1.48 36: U212(tt()) -> tt() 1.33/1.48 37: U221(tt(),V1,V2) -> U222(isNat(V1),V2) 1.33/1.48 38: U222(tt(),V2) -> U223(isNzNat(V2)) 1.33/1.48 39: U223(tt()) -> tt() 1.33/1.48 40: U231(tt(),V1,V2) -> U232(isNzNat(V1),V2) 1.33/1.48 41: U232(tt(),V2) -> U233(isNzNat(V2)) 1.33/1.48 42: U233(tt()) -> tt() 1.33/1.48 43: U241(tt(),V1,V2) -> U242(isNzNat(V1),V2) 1.33/1.48 44: U242(tt(),V2) -> U243(isNzNat(V2)) 1.33/1.48 45: U243(tt()) -> tt() 1.33/1.48 46: U251(tt(),V1) -> U252(isNat(V1)) 1.33/1.48 47: U252(tt()) -> tt() 1.33/1.48 48: U261(tt(),N) -> N 1.33/1.48 49: U271(tt()) -> s_(0()) 1.33/1.48 50: U281(tt(),M',N) -> U282(equal(_>_(M',N),true())) 1.33/1.48 51: U282(tt()) -> 0() 1.33/1.48 52: U291(tt(),M',N) -> U292(equal(_>_(N,M'),true()),M',N) 1.33/1.48 53: U292(tt(),M',N) -> s_(quot(d(N,M'),M')) 1.33/1.48 54: U31(tt(),N) -> N 1.33/1.48 55: U41(tt(),M,N) -> s_(s_(_+_(N,M))) 1.33/1.48 56: U51(tt(),M,N) -> _>_(M,N) 1.33/1.48 57: U61(tt()) -> false() 1.33/1.48 58: U71(tt()) -> true() 1.33/1.48 59: U81(tt(),M,N) -> _>_(N,M) 1.33/1.48 60: U91(tt(),N) -> N 1.33/1.48 61: _*_(N,0()) -> U11(and(isNat(N),isNatKind(N))) 1.33/1.48 62: _*_(s_(N),s_(M)) -> U21(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 63: _+_(N,0()) -> U31(and(isNat(N),isNatKind(N)),N) 1.33/1.48 64: _+_(s_(N),s_(M)) -> U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 65: _<_(N,M) -> U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 66: _>_(0(),M) -> U61(and(isNat(M),isNatKind(M))) 1.33/1.48 67: _>_(N',0()) -> U71(and(isNzNat(N'),isNatKind(N'))) 1.33/1.48 68: _>_(s_(N),s_(M)) -> U81(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 69: and(tt(),X) -> X 1.33/1.48 70: d(0(),N) -> U91(and(isNat(N),isNatKind(N)),N) 1.33/1.48 71: d(s_(N),s_(M)) -> U101(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 72: equal(X,X) -> tt() 1.33/1.48 73: gcd(0(),N) -> U111(and(isNat(N),isNatKind(N))) 1.33/1.48 74: gcd(N',M') -> U121(and(and(isNzNat(M'),isNatKind(M')),and(isNzNat(N'),isNatKind(N'))),M',N') 1.33/1.48 75: gcd(N',N') -> U131(and(isNzNat(N'),isNatKind(N')),N') 1.33/1.48 76: isBoolean(false()) -> tt() 1.33/1.48 77: isBoolean(true()) -> tt() 1.33/1.48 78: isBoolean(_<_(V1,V2)) -> U141(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 79: isBoolean(_>_(V1,V2)) -> U151(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 80: isBooleanKind(false()) -> tt() 1.33/1.48 81: isBooleanKind(true()) -> tt() 1.33/1.48 82: isBooleanKind(_<_(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 83: isBooleanKind(_>_(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 84: isNat(0()) -> tt() 1.33/1.48 85: isNat(V) -> U161(isNatKind(V),V) 1.33/1.48 86: isNat(_*_(V1,V2)) -> U171(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 87: isNat(_+_(V1,V2)) -> U181(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 88: isNat(d(V1,V2)) -> U191(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 89: isNat(gcd(V1,V2)) -> U201(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 90: isNat(p_(V1)) -> U211(isNatKind(V1),V1) 1.33/1.48 91: isNat(quot(V1,V2)) -> U221(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 92: isNatKind(0()) -> tt() 1.33/1.48 93: isNatKind(1()) -> tt() 1.33/1.48 94: isNatKind(2()) -> tt() 1.33/1.48 95: isNatKind(3()) -> tt() 1.33/1.48 96: isNatKind(4()) -> tt() 1.33/1.48 97: isNatKind(5()) -> tt() 1.33/1.48 98: isNatKind(6()) -> tt() 1.33/1.48 99: isNatKind(7()) -> tt() 1.33/1.48 100: isNatKind(_*_(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 101: isNatKind(_+_(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 102: isNatKind(d(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 103: isNatKind(gcd(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 104: isNatKind(p_(V1)) -> isNatKind(V1) 1.33/1.48 105: isNatKind(quot(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 106: isNatKind(s_(V1)) -> isNatKind(V1) 1.33/1.48 107: isNzNat(1()) -> tt() 1.33/1.48 108: isNzNat(2()) -> tt() 1.33/1.48 109: isNzNat(3()) -> tt() 1.33/1.48 110: isNzNat(4()) -> tt() 1.33/1.48 111: isNzNat(5()) -> tt() 1.33/1.48 112: isNzNat(6()) -> tt() 1.33/1.48 113: isNzNat(7()) -> tt() 1.33/1.48 114: isNzNat(_*_(V1,V2)) -> U231(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 115: isNzNat(gcd(V1,V2)) -> U241(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 116: isNzNat(s_(V1)) -> U251(isNatKind(V1),V1) 1.33/1.48 117: p_(s_(N)) -> U261(and(isNat(N),isNatKind(N)),N) 1.33/1.48 118: quot(M',M') -> U271(and(isNzNat(M'),isNatKind(M'))) 1.33/1.48 119: quot(N,M') -> U281(and(and(isNzNat(M'),isNatKind(M')),and(isNat(N),isNatKind(N))),M',N) 1.33/1.48 120: quot(N,M') -> U291(and(and(isNzNat(M'),isNatKind(M')),and(isNat(N),isNatKind(N))),M',N) 1.33/1.48 Number of strict rules: 120 1.33/1.48 Direct POLO(bPol) ... failed. 1.33/1.48 Uncurrying ... failed. 1.33/1.48 Dependency Pairs: 1.33/1.48 #1: #isNat(_*_(V1,V2)) -> #U171(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #2: #isNat(_*_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #3: #isNat(_*_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #4: #isNat(_*_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #5: #U241(tt(),V1,V2) -> #U242(isNzNat(V1),V2) 1.33/1.48 #6: #U241(tt(),V1,V2) -> #isNzNat(V1) 1.33/1.48 #7: #U192(tt(),V2) -> #U193(isNat(V2)) 1.33/1.48 #8: #U192(tt(),V2) -> #isNat(V2) 1.33/1.48 #9: #U211(tt(),V1) -> #U212(isNzNat(V1)) 1.33/1.48 #10: #U211(tt(),V1) -> #isNzNat(V1) 1.33/1.48 #11: #isBooleanKind(_>_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #12: #isBooleanKind(_>_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #13: #isBooleanKind(_>_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #14: #_>_(0(),M) -> #U61(and(isNat(M),isNatKind(M))) 1.33/1.48 #15: #_>_(0(),M) -> #and(isNat(M),isNatKind(M)) 1.33/1.48 #16: #_>_(0(),M) -> #isNat(M) 1.33/1.48 #17: #_>_(0(),M) -> #isNatKind(M) 1.33/1.48 #18: #U251(tt(),V1) -> #U252(isNat(V1)) 1.33/1.48 #19: #U251(tt(),V1) -> #isNat(V1) 1.33/1.48 #20: #isNzNat(gcd(V1,V2)) -> #U241(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #21: #isNzNat(gcd(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #22: #isNzNat(gcd(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #23: #isNzNat(gcd(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #24: #U232(tt(),V2) -> #U233(isNzNat(V2)) 1.33/1.48 #25: #U232(tt(),V2) -> #isNzNat(V2) 1.33/1.48 #26: #U221(tt(),V1,V2) -> #U222(isNat(V1),V2) 1.33/1.48 #27: #U221(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #28: #isNzNat(_*_(V1,V2)) -> #U231(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #29: #isNzNat(_*_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #30: #isNzNat(_*_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #31: #isNzNat(_*_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #32: #isNat(quot(V1,V2)) -> #U221(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #33: #isNat(quot(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #34: #isNat(quot(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #35: #isNat(quot(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #36: #gcd(0(),N) -> #U111(and(isNat(N),isNatKind(N))) 1.33/1.48 #37: #gcd(0(),N) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #38: #gcd(0(),N) -> #isNat(N) 1.33/1.48 #39: #gcd(0(),N) -> #isNatKind(N) 1.33/1.48 #40: #U292(tt(),M',N) -> #quot(d(N,M'),M') 1.33/1.48 #41: #U292(tt(),M',N) -> #d(N,M') 1.33/1.48 #42: #d(s_(N),s_(M)) -> #U101(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 #43: #d(s_(N),s_(M)) -> #and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))) 1.33/1.48 #44: #d(s_(N),s_(M)) -> #and(isNat(M),isNatKind(M)) 1.33/1.48 #45: #d(s_(N),s_(M)) -> #isNat(M) 1.33/1.48 #46: #d(s_(N),s_(M)) -> #isNatKind(M) 1.33/1.48 #47: #d(s_(N),s_(M)) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #48: #d(s_(N),s_(M)) -> #isNat(N) 1.33/1.48 #49: #d(s_(N),s_(M)) -> #isNatKind(N) 1.33/1.48 #50: #gcd(N',N') -> #U131(and(isNzNat(N'),isNatKind(N')),N') 1.33/1.48 #51: #gcd(N',N') -> #and(isNzNat(N'),isNatKind(N')) 1.33/1.48 #52: #gcd(N',N') -> #isNzNat(N') 1.33/1.48 #53: #gcd(N',N') -> #isNatKind(N') 1.33/1.48 #54: #gcd(N',M') -> #U121(and(and(isNzNat(M'),isNatKind(M')),and(isNzNat(N'),isNatKind(N'))),M',N') 1.33/1.48 #55: #gcd(N',M') -> #and(and(isNzNat(M'),isNatKind(M')),and(isNzNat(N'),isNatKind(N'))) 1.33/1.48 #56: #gcd(N',M') -> #and(isNzNat(M'),isNatKind(M')) 1.33/1.48 #57: #gcd(N',M') -> #isNzNat(M') 1.33/1.48 #58: #gcd(N',M') -> #isNatKind(M') 1.33/1.48 #59: #gcd(N',M') -> #and(isNzNat(N'),isNatKind(N')) 1.33/1.48 #60: #gcd(N',M') -> #isNzNat(N') 1.33/1.48 #61: #gcd(N',M') -> #isNatKind(N') 1.33/1.48 #62: #_*_(N,0()) -> #U11(and(isNat(N),isNatKind(N))) 1.33/1.48 #63: #_*_(N,0()) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #64: #_*_(N,0()) -> #isNat(N) 1.33/1.48 #65: #_*_(N,0()) -> #isNatKind(N) 1.33/1.48 #66: #U222(tt(),V2) -> #U223(isNzNat(V2)) 1.33/1.48 #67: #U222(tt(),V2) -> #isNzNat(V2) 1.33/1.48 #68: #isNzNat(s_(V1)) -> #U251(isNatKind(V1),V1) 1.33/1.48 #69: #isNzNat(s_(V1)) -> #isNatKind(V1) 1.33/1.48 #70: #U81(tt(),M,N) -> #_>_(N,M) 1.33/1.48 #71: #U41(tt(),M,N) -> #_+_(N,M) 1.33/1.48 #72: #_>_(N',0()) -> #U71(and(isNzNat(N'),isNatKind(N'))) 1.33/1.48 #73: #_>_(N',0()) -> #and(isNzNat(N'),isNatKind(N')) 1.33/1.48 #74: #_>_(N',0()) -> #isNzNat(N') 1.33/1.48 #75: #_>_(N',0()) -> #isNatKind(N') 1.33/1.48 #76: #U231(tt(),V1,V2) -> #U232(isNzNat(V1),V2) 1.33/1.48 #77: #U231(tt(),V1,V2) -> #isNzNat(V1) 1.33/1.48 #78: #isNat(p_(V1)) -> #U211(isNatKind(V1),V1) 1.33/1.48 #79: #isNat(p_(V1)) -> #isNatKind(V1) 1.33/1.48 #80: #U121(tt(),M',N') -> #U122(equal(_>_(N',M'),true()),M',N') 1.33/1.48 #81: #U121(tt(),M',N') -> #equal(_>_(N',M'),true()) 1.33/1.48 #82: #U121(tt(),M',N') -> #_>_(N',M') 1.33/1.48 #83: #d(0(),N) -> #U91(and(isNat(N),isNatKind(N)),N) 1.33/1.48 #84: #d(0(),N) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #85: #d(0(),N) -> #isNat(N) 1.33/1.48 #86: #d(0(),N) -> #isNatKind(N) 1.33/1.48 #87: #U172(tt(),V2) -> #U173(isNat(V2)) 1.33/1.48 #88: #U172(tt(),V2) -> #isNat(V2) 1.33/1.48 #89: #quot(M',M') -> #U271(and(isNzNat(M'),isNatKind(M'))) 1.33/1.48 #90: #quot(M',M') -> #and(isNzNat(M'),isNatKind(M')) 1.33/1.48 #91: #quot(M',M') -> #isNzNat(M') 1.33/1.48 #92: #quot(M',M') -> #isNatKind(M') 1.33/1.48 #93: #isBoolean(_<_(V1,V2)) -> #U141(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #94: #isBoolean(_<_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #95: #isBoolean(_<_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #96: #isBoolean(_<_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #97: #isNatKind(_+_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #98: #isNatKind(_+_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #99: #isNatKind(_+_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #100: #U122(tt(),M',N') -> #gcd(d(N',M'),M') 1.33/1.48 #101: #U122(tt(),M',N') -> #d(N',M') 1.33/1.48 #102: #U201(tt(),V1,V2) -> #U202(isNat(V1),V2) 1.33/1.48 #103: #U201(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #104: #isBoolean(_>_(V1,V2)) -> #U151(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #105: #isBoolean(_>_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #106: #isBoolean(_>_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #107: #isBoolean(_>_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #108: #U51(tt(),M,N) -> #_>_(M,N) 1.33/1.48 #109: #isNat(gcd(V1,V2)) -> #U201(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #110: #isNat(gcd(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #111: #isNat(gcd(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #112: #isNat(gcd(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #113: #isBooleanKind(_<_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #114: #isBooleanKind(_<_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #115: #isBooleanKind(_<_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #116: #U141(tt(),V1,V2) -> #U142(isNat(V1),V2) 1.33/1.48 #117: #U141(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #118: #isNatKind(s_(V1)) -> #isNatKind(V1) 1.33/1.48 #119: #_*_(s_(N),s_(M)) -> #U21(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 #120: #_*_(s_(N),s_(M)) -> #and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))) 1.33/1.48 #121: #_*_(s_(N),s_(M)) -> #and(isNat(M),isNatKind(M)) 1.33/1.48 #122: #_*_(s_(N),s_(M)) -> #isNat(M) 1.33/1.48 #123: #_*_(s_(N),s_(M)) -> #isNatKind(M) 1.33/1.48 #124: #_*_(s_(N),s_(M)) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #125: #_*_(s_(N),s_(M)) -> #isNat(N) 1.33/1.48 #126: #_*_(s_(N),s_(M)) -> #isNatKind(N) 1.33/1.48 #127: #U291(tt(),M',N) -> #U292(equal(_>_(N,M'),true()),M',N) 1.33/1.48 #128: #U291(tt(),M',N) -> #equal(_>_(N,M'),true()) 1.33/1.48 #129: #U291(tt(),M',N) -> #_>_(N,M') 1.33/1.48 #130: #U181(tt(),V1,V2) -> #U182(isNat(V1),V2) 1.33/1.48 #131: #U181(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #132: #U161(tt(),V) -> #U162(isNzNat(V)) 1.33/1.48 #133: #U161(tt(),V) -> #isNzNat(V) 1.33/1.48 #134: #isNat(d(V1,V2)) -> #U191(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #135: #isNat(d(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #136: #isNat(d(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #137: #isNat(d(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #138: #quot(N,M') -> #U281(and(and(isNzNat(M'),isNatKind(M')),and(isNat(N),isNatKind(N))),M',N) 1.33/1.48 #139: #quot(N,M') -> #and(and(isNzNat(M'),isNatKind(M')),and(isNat(N),isNatKind(N))) 1.33/1.48 #140: #quot(N,M') -> #and(isNzNat(M'),isNatKind(M')) 1.33/1.48 #141: #quot(N,M') -> #isNzNat(M') 1.33/1.48 #142: #quot(N,M') -> #isNatKind(M') 1.33/1.48 #143: #quot(N,M') -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #144: #quot(N,M') -> #isNat(N) 1.33/1.48 #145: #quot(N,M') -> #isNatKind(N) 1.33/1.48 #146: #_+_(s_(N),s_(M)) -> #U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 #147: #_+_(s_(N),s_(M)) -> #and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))) 1.33/1.48 #148: #_+_(s_(N),s_(M)) -> #and(isNat(M),isNatKind(M)) 1.33/1.48 #149: #_+_(s_(N),s_(M)) -> #isNat(M) 1.33/1.48 #150: #_+_(s_(N),s_(M)) -> #isNatKind(M) 1.33/1.48 #151: #_+_(s_(N),s_(M)) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #152: #_+_(s_(N),s_(M)) -> #isNat(N) 1.33/1.48 #153: #_+_(s_(N),s_(M)) -> #isNatKind(N) 1.33/1.48 #154: #quot(N,M') -> #U291(and(and(isNzNat(M'),isNatKind(M')),and(isNat(N),isNatKind(N))),M',N) 1.33/1.48 #155: #quot(N,M') -> #and(and(isNzNat(M'),isNatKind(M')),and(isNat(N),isNatKind(N))) 1.33/1.48 #156: #quot(N,M') -> #and(isNzNat(M'),isNatKind(M')) 1.33/1.48 #157: #quot(N,M') -> #isNzNat(M') 1.33/1.48 #158: #quot(N,M') -> #isNatKind(M') 1.33/1.48 #159: #quot(N,M') -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #160: #quot(N,M') -> #isNat(N) 1.33/1.48 #161: #quot(N,M') -> #isNatKind(N) 1.33/1.48 #162: #U242(tt(),V2) -> #U243(isNzNat(V2)) 1.33/1.48 #163: #U242(tt(),V2) -> #isNzNat(V2) 1.33/1.48 #164: #_<_(N,M) -> #U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 #165: #_<_(N,M) -> #and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))) 1.33/1.48 #166: #_<_(N,M) -> #and(isNat(M),isNatKind(M)) 1.33/1.48 #167: #_<_(N,M) -> #isNat(M) 1.33/1.48 #168: #_<_(N,M) -> #isNatKind(M) 1.33/1.48 #169: #_<_(N,M) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #170: #_<_(N,M) -> #isNat(N) 1.33/1.48 #171: #_<_(N,M) -> #isNatKind(N) 1.33/1.48 #172: #U191(tt(),V1,V2) -> #U192(isNat(V1),V2) 1.33/1.48 #173: #U191(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #174: #U171(tt(),V1,V2) -> #U172(isNat(V1),V2) 1.33/1.48 #175: #U171(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #176: #U21(tt(),M,N) -> #_+_(N,_+_(M,_*_(N,M))) 1.33/1.48 #177: #U21(tt(),M,N) -> #_+_(M,_*_(N,M)) 1.33/1.48 #178: #U21(tt(),M,N) -> #_*_(N,M) 1.33/1.48 #179: #isNat(_+_(V1,V2)) -> #U181(and(isNatKind(V1),isNatKind(V2)),V1,V2) 1.33/1.48 #180: #isNat(_+_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #181: #isNat(_+_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #182: #isNat(_+_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #183: #p_(s_(N)) -> #U261(and(isNat(N),isNatKind(N)),N) 1.33/1.48 #184: #p_(s_(N)) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #185: #p_(s_(N)) -> #isNat(N) 1.33/1.48 #186: #p_(s_(N)) -> #isNatKind(N) 1.33/1.48 #187: #U151(tt(),V1,V2) -> #U152(isNat(V1),V2) 1.33/1.48 #188: #U151(tt(),V1,V2) -> #isNat(V1) 1.33/1.48 #189: #U202(tt(),V2) -> #U203(isNat(V2)) 1.33/1.48 #190: #U202(tt(),V2) -> #isNat(V2) 1.33/1.48 #191: #_+_(N,0()) -> #U31(and(isNat(N),isNatKind(N)),N) 1.33/1.48 #192: #_+_(N,0()) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #193: #_+_(N,0()) -> #isNat(N) 1.33/1.48 #194: #_+_(N,0()) -> #isNatKind(N) 1.33/1.48 #195: #isNatKind(quot(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #196: #isNatKind(quot(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #197: #isNatKind(quot(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #198: #U182(tt(),V2) -> #U183(isNat(V2)) 1.33/1.48 #199: #U182(tt(),V2) -> #isNat(V2) 1.33/1.48 #200: #isNatKind(_*_(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #201: #isNatKind(_*_(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #202: #isNatKind(_*_(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #203: #isNat(V) -> #U161(isNatKind(V),V) 1.33/1.48 #204: #isNat(V) -> #isNatKind(V) 1.33/1.48 #205: #_>_(s_(N),s_(M)) -> #U81(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) 1.33/1.48 #206: #_>_(s_(N),s_(M)) -> #and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))) 1.33/1.48 #207: #_>_(s_(N),s_(M)) -> #and(isNat(M),isNatKind(M)) 1.33/1.48 #208: #_>_(s_(N),s_(M)) -> #isNat(M) 1.33/1.48 #209: #_>_(s_(N),s_(M)) -> #isNatKind(M) 1.33/1.48 #210: #_>_(s_(N),s_(M)) -> #and(isNat(N),isNatKind(N)) 1.33/1.48 #211: #_>_(s_(N),s_(M)) -> #isNat(N) 1.33/1.48 #212: #_>_(s_(N),s_(M)) -> #isNatKind(N) 1.33/1.48 #213: #U101(tt(),M,N) -> #d(N,M) 1.33/1.48 #214: #U142(tt(),V2) -> #U143(isNat(V2)) 1.33/1.48 #215: #U142(tt(),V2) -> #isNat(V2) 1.33/1.48 #216: #isNatKind(d(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #217: #isNatKind(d(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #218: #isNatKind(d(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #219: #isNatKind(gcd(V1,V2)) -> #and(isNatKind(V1),isNatKind(V2)) 1.33/1.48 #220: #isNatKind(gcd(V1,V2)) -> #isNatKind(V1) 1.33/1.48 #221: #isNatKind(gcd(V1,V2)) -> #isNatKind(V2) 1.33/1.48 #222: #isNatKind(p_(V1)) -> #isNatKind(V1) 1.33/1.48 #223: #U281(tt(),M',N) -> #U282(equal(_>_(M',N),true())) 1.33/1.48 #224: #U281(tt(),M',N) -> #equal(_>_(M',N),true()) 1.33/1.48 #225: #U281(tt(),M',N) -> #_>_(M',N) 1.33/1.48 #226: #U152(tt(),V2) -> #U153(isNat(V2)) 1.33/1.48 #227: #U152(tt(),V2) -> #isNat(V2) 1.33/1.48 Number of SCCs: 8, DPs: 60 1.33/1.48 SCC { #70 #205 } 1.33/1.48 POLO(Sum)... succeeded. 1.33/1.48 7 w: 1 1.33/1.48 U291 w: 0 1.33/1.48 #U201 w: 0 1.33/1.48 U231 w: x1 1.33/1.48 #isNzNat w: 0 1.33/1.48 isNatKind w: x1 + 1 1.33/1.48 U21 w: 0 1.33/1.48 U261 w: 0 1.33/1.48 1 w: 1 1.33/1.48 U193 w: 0 1.33/1.48 U161 w: x1 1.33/1.48 U182 w: x2 + 1 1.33/1.48 U11 w: 0 1.33/1.48 d w: 1 1.33/1.48 isBoolean w: 0 1.33/1.48 4 w: 1 1.33/1.48 U243 w: x1 1.33/1.48 #isNat w: 0 1.33/1.48 #7 w: 0 1.33/1.48 U143 w: 0 1.33/1.48 #U142 w: 0 1.33/1.48 U192 w: 0 1.33/1.48 #_+_ w: 0 1.33/1.48 5 w: 1 1.33/1.48 U142 w: 0 1.33/1.48 _*_ w: x1 + x2 + 3 1.33/1.48 _+_ w: 1 1.33/1.48 #U152 w: 0 1.33/1.48 U242 w: x1 + x2 1.33/1.48 #U181 w: 0 1.33/1.48 U91 w: 0 1.33/1.48 U221 w: x1 + x2 1.33/1.48 gcd w: 2 1.33/1.48 #U101 w: 0 1.33/1.48 #equal w: 0 1.33/1.48 3 w: 1 1.33/1.48 #U183 w: 0 1.33/1.48 U71 w: 0 1.33/1.48 #U81 w: x2 + x3 + 1 1.33/1.48 and w: x1 + x2 + 1 1.33/1.48 U131 w: 0 1.33/1.48 #U222 w: 0 1.33/1.48 #U243 w: 0 1.33/1.48 #U212 w: 0 1.33/1.48 U101 w: 0 1.33/1.48 #U231 w: 0 1.33/1.48 #_*_ w: 0 1.33/1.48 U111 w: 0 1.33/1.48 #6 w: 0 1.33/1.48 U152 w: 0 1.33/1.48 false w: 0 1.33/1.48 U281 w: 0 1.33/1.48 #2 w: 0 1.33/1.48 #U121 w: 0 1.33/1.48 U292 w: 0 1.33/1.48 U172 w: x2 + 4 1.33/1.48 #U241 w: 0 1.33/1.48 #U131 w: 0 1.33/1.48 #U143 w: 0 1.33/1.48 U241 w: x1 + x2 + x3 + 3 1.33/1.48 #p_ w: 0 1.33/1.48 #U271 w: 0 1.33/1.48 #U173 w: 0 1.33/1.48 #U223 w: 0 1.33/1.48 U271 w: 0 1.33/1.48 #U282 w: 0 1.33/1.48 _>_ w: 0 1.33/1.48 #isBoolean w: 0 1.33/1.48 #U202 w: 0 1.33/1.48 true w: 0 1.33/1.48 U222 w: 0 1.33/1.48 U232 w: x1 + x2 1.33/1.48 #_<_ w: 0 1.33/1.48 #U252 w: 0 1.33/1.48 U201 w: x2 + 3 1.33/1.48 #4 w: 0 1.33/1.48 #U242 w: 0 1.33/1.48 #U141 w: 0 1.33/1.48 U252 w: 3 1.33/1.48 U141 w: 0 1.33/1.48 #U171 w: 0 1.33/1.48 s_ w: x1 + 1 1.33/1.48 U173 w: 5 1.33/1.48 0 w: 1 1.33/1.48 U191 w: x2 + x3 + 2 1.33/1.48 quot w: x1 + 3 1.33/1.48 U153 w: 0 1.33/1.48 #isBooleanKind w: 0 1.33/1.48 isNzNat w: x1 + 1 1.33/1.48 U171 w: x1 1.33/1.48 U202 w: x2 + 4 1.33/1.48 #U211 w: 0 1.33/1.48 #U233 w: 0 1.33/1.48 #U153 w: 0 1.33/1.48 #3 w: 0 1.33/1.48 #U182 w: 0 1.33/1.48 #d w: 0 1.33/1.48 U151 w: 0 1.33/1.48 #U292 w: 0 1.33/1.48 isBooleanKind w: 0 1.33/1.48 #U111 w: 0 1.33/1.48 #U192 w: 0 1.33/1.48 #U221 w: 0 1.33/1.48 #U232 w: 0 1.33/1.48 _<_ w: 0 1.33/1.48 #U251 w: 0 1.33/1.48 U211 w: x1 + x2 + 1 1.33/1.48 U223 w: 0 1.33/1.48 #U281 w: 0 1.33/1.48 U203 w: 3 1.33/1.48 p_ w: x1 + 1 1.33/1.48 isNat w: x1 1.33/1.48 U251 w: x1 1.33/1.48 #U291 w: 0 1.33/1.48 U61 w: 0 1.33/1.48 #U51 w: 0 1.33/1.48 #5 w: 0 1.33/1.48 #U11 w: 0 1.33/1.48 2 w: 1 1.33/1.48 U31 w: 0 1.33/1.48 U183 w: x1 + 2 1.33/1.48 #U193 w: 0 1.33/1.48 #U41 w: 0 1.33/1.48 equal w: 0 1.33/1.48 #U191 w: 0 1.33/1.48 #U21 w: 0 1.33/1.48 6 w: 1 1.33/1.48 U81 w: 0 1.33/1.48 #_>_ w: x1 + x2 1.33/1.48 tt w: 3 1.33/1.48 #quot w: 0 1.33/1.48 #U71 w: 0 1.33/1.48 #U151 w: 0 1.33/1.48 #U162 w: 0 1.33/1.48 #1 w: 0 1.33/1.48 U51 w: 0 1.33/1.48 #isNatKind w: 0 1.33/1.48 #U161 w: 0 1.33/1.48 #U172 w: 0 1.33/1.48 U162 w: 0 1.33/1.48 #U261 w: 0 1.33/1.48 #U203 w: 0 1.33/1.48 #U122 w: 0 1.33/1.48 U212 w: 4 1.33/1.48 U41 w: 0 1.33/1.48 #U31 w: 0 1.33/1.48 #and w: 0 1.33/1.48 #U91 w: 0 1.33/1.48 U233 w: 0 1.33/1.48 U282 w: 0 1.33/1.48 U121 w: 0 1.33/1.48 #U61 w: 0 1.33/1.48 U181 w: 0 1.33/1.48 U122 w: 0 1.33/1.48 #gcd w: 0 1.33/1.48 USABLE RULES: { 32 33 36 47 } 1.33/1.48 Removed DPs: #70 #205 1.33/1.48 Number of SCCs: 7, DPs: 58 1.33/1.48 SCC { #119 #178 } 1.33/1.48 POLO(Sum)... succeeded. 1.33/1.48 7 w: 1 1.33/1.48 U291 w: 0 1.33/1.48 #U201 w: 0 1.33/1.48 U231 w: x1 1.33/1.48 #isNzNat w: 0 1.33/1.48 isNatKind w: x1 + 1 1.33/1.48 U21 w: 0 1.33/1.48 U261 w: 0 1.33/1.48 1 w: 1 1.33/1.48 U193 w: 0 1.33/1.48 U161 w: x1 1.33/1.48 U182 w: x2 + 1 1.33/1.48 U11 w: 0 1.33/1.48 d w: 1 1.33/1.48 isBoolean w: 0 1.33/1.48 4 w: 1 1.33/1.48 U243 w: x1 1.33/1.48 #isNat w: 0 1.33/1.48 #7 w: 0 1.33/1.48 U143 w: 0 1.33/1.48 #U142 w: 0 1.33/1.48 U192 w: 0 1.33/1.48 #_+_ w: 0 1.33/1.48 5 w: 1 1.33/1.48 U142 w: 0 1.33/1.48 _*_ w: x1 + x2 + 3 1.33/1.48 _+_ w: 1 1.33/1.48 #U152 w: 0 1.33/1.48 U242 w: x1 + x2 1.33/1.48 #U181 w: 0 1.33/1.48 U91 w: 0 1.33/1.48 U221 w: x1 + x2 1.33/1.48 gcd w: 2 1.33/1.48 #U101 w: 0 1.33/1.48 #equal w: 0 1.33/1.48 3 w: 1 1.33/1.48 #U183 w: 0 1.33/1.48 U71 w: 0 1.33/1.48 #U81 w: 1 1.33/1.48 and w: x1 + x2 + 1 1.33/1.48 U131 w: 0 1.33/1.48 #U222 w: 0 1.33/1.48 #U243 w: 0 1.33/1.48 #U212 w: 0 1.33/1.48 U101 w: 0 1.33/1.48 #U231 w: 0 1.33/1.48 #_*_ w: x1 + x2 1.33/1.48 U111 w: 0 1.33/1.48 #6 w: 0 1.33/1.48 U152 w: 0 1.33/1.48 false w: 0 1.33/1.48 U281 w: 0 1.33/1.48 #2 w: 0 1.33/1.48 #U121 w: 0 1.33/1.48 U292 w: 0 1.33/1.48 U172 w: x2 + 4 1.33/1.48 #U241 w: 0 1.33/1.48 #U131 w: 0 1.33/1.48 #U143 w: 0 1.33/1.48 U241 w: x1 + x2 + x3 + 3 1.33/1.48 #p_ w: 0 1.33/1.48 #U271 w: 0 1.33/1.48 #U173 w: 0 1.33/1.48 #U223 w: 0 1.33/1.48 U271 w: 0 1.33/1.48 #U282 w: 0 1.33/1.48 _>_ w: 0 1.33/1.48 #isBoolean w: 0 1.33/1.48 #U202 w: 0 1.33/1.48 true w: 0 1.33/1.48 U222 w: 0 1.33/1.48 U232 w: x1 + x2 1.33/1.48 #_<_ w: 0 1.33/1.48 #U252 w: 0 1.33/1.48 U201 w: x2 + 3 1.33/1.48 #4 w: 0 1.33/1.48 #U242 w: 0 1.33/1.48 #U141 w: 0 1.33/1.48 U252 w: 3 1.33/1.48 U141 w: 0 1.33/1.48 #U171 w: 0 1.33/1.48 s_ w: x1 + 1 1.33/1.48 U173 w: 5 1.33/1.48 0 w: 1 1.33/1.48 U191 w: x2 + x3 + 2 1.33/1.48 quot w: x1 + 3 1.33/1.48 U153 w: 0 1.33/1.48 #isBooleanKind w: 0 1.33/1.48 isNzNat w: x1 + 1 1.33/1.48 U171 w: x1 1.33/1.48 U202 w: x2 + 4 1.33/1.48 #U211 w: 0 1.33/1.48 #U233 w: 0 1.33/1.48 #U153 w: 0 1.33/1.48 #3 w: 0 1.33/1.48 #U182 w: 0 1.33/1.48 #d w: 0 1.33/1.48 U151 w: 0 1.33/1.48 #U292 w: 0 1.33/1.48 isBooleanKind w: 0 1.33/1.48 #U111 w: 0 1.33/1.48 #U192 w: 0 1.33/1.48 #U221 w: 0 1.33/1.48 #U232 w: 0 1.33/1.48 _<_ w: 0 1.33/1.48 #U251 w: 0 1.33/1.48 U211 w: x1 + x2 + 1 1.33/1.48 U223 w: 0 1.33/1.48 #U281 w: 0 1.33/1.48 U203 w: 3 1.33/1.48 p_ w: x1 + 1 1.33/1.48 isNat w: x1 1.33/1.48 U251 w: x1 1.33/1.48 #U291 w: 0 1.33/1.48 U61 w: 0 1.33/1.48 #U51 w: 0 1.33/1.48 #5 w: 0 1.33/1.48 #U11 w: 0 1.33/1.48 2 w: 1 1.33/1.48 U31 w: 0 1.33/1.48 U183 w: x1 + 2 1.33/1.48 #U193 w: 0 1.33/1.48 #U41 w: 0 1.33/1.48 equal w: 0 1.33/1.48 #U191 w: 0 1.33/1.48 #U21 w: x2 + x3 + 1 1.33/1.48 6 w: 1 1.33/1.48 U81 w: 0 1.33/1.48 #_>_ w: 0 1.33/1.48 tt w: 3 1.33/1.48 #quot w: 0 1.33/1.48 #U71 w: 0 1.33/1.48 #U151 w: 0 1.33/1.48 #U162 w: 0 1.33/1.48 #1 w: 0 1.33/1.48 U51 w: 0 1.33/1.48 #isNatKind w: 0 1.33/1.48 #U161 w: 0 1.33/1.48 #U172 w: 0 1.33/1.48 U162 w: 0 1.33/1.48 #U261 w: 0 1.33/1.48 #U203 w: 0 1.33/1.48 #U122 w: 0 1.33/1.48 U212 w: 4 1.33/1.48 U41 w: 0 1.33/1.48 #U31 w: 0 1.33/1.48 #and w: 0 1.33/1.48 #U91 w: 0 1.33/1.48 U233 w: 0 1.33/1.48 U282 w: 0 1.33/1.48 U121 w: 0 1.33/1.48 #U61 w: 0 1.33/1.48 U181 w: 0 1.33/1.48 U122 w: 0 1.33/1.48 #gcd w: 0 1.33/1.48 USABLE RULES: { 32 33 36 47 } 1.33/1.48 Removed DPs: #119 #178 1.33/1.48 Number of SCCs: 6, DPs: 56 1.33/1.48 SCC { #42 #213 } 1.33/1.48 POLO(Sum)... succeeded. 1.33/1.48 7 w: 1 1.33/1.48 U291 w: 0 1.33/1.48 #U201 w: 0 1.33/1.48 U231 w: x1 1.33/1.48 #isNzNat w: 0 1.33/1.48 isNatKind w: x1 + 1 1.33/1.48 U21 w: 0 1.33/1.48 U261 w: 0 1.33/1.48 1 w: 1 1.33/1.48 U193 w: 0 1.33/1.48 U161 w: x1 1.33/1.48 U182 w: x2 + 1 1.33/1.48 U11 w: 0 1.33/1.48 d w: 1 1.33/1.48 isBoolean w: 0 1.33/1.48 4 w: 1 1.33/1.48 U243 w: x1 1.33/1.48 #isNat w: 0 1.33/1.48 #7 w: 0 1.33/1.48 U143 w: 0 1.33/1.48 #U142 w: 0 1.33/1.48 U192 w: 0 1.33/1.48 #_+_ w: 0 1.33/1.48 5 w: 1 1.33/1.48 U142 w: 0 1.33/1.48 _*_ w: x1 + x2 + 3 1.33/1.48 _+_ w: 1 1.33/1.48 #U152 w: 0 1.33/1.48 U242 w: x1 + x2 1.33/1.48 #U181 w: 0 1.33/1.48 U91 w: 0 1.33/1.48 U221 w: x1 + x2 1.33/1.48 gcd w: 2 1.33/1.48 #U101 w: x2 + x3 + 1 1.33/1.48 #equal w: 0 1.33/1.48 3 w: 1 1.33/1.48 #U183 w: 0 1.33/1.48 U71 w: 0 1.33/1.48 #U81 w: 1 1.33/1.48 and w: x1 + x2 + 1 1.33/1.48 U131 w: 0 1.33/1.48 #U222 w: 0 1.33/1.48 #U243 w: 0 1.33/1.48 #U212 w: 0 1.33/1.48 U101 w: 0 1.33/1.48 #U231 w: 0 1.33/1.48 #_*_ w: 0 1.33/1.48 U111 w: 0 1.33/1.48 #6 w: 0 1.33/1.48 U152 w: 0 1.33/1.48 false w: 0 1.33/1.48 U281 w: 0 1.33/1.48 #2 w: 0 1.33/1.48 #U121 w: 0 1.33/1.48 U292 w: 0 1.33/1.48 U172 w: x2 + 4 1.33/1.48 #U241 w: 0 1.33/1.48 #U131 w: 0 1.33/1.48 #U143 w: 0 1.33/1.48 U241 w: x1 + x2 + x3 + 3 1.33/1.48 #p_ w: 0 1.33/1.48 #U271 w: 0 1.33/1.48 #U173 w: 0 1.33/1.48 #U223 w: 0 1.33/1.48 U271 w: 0 1.33/1.48 #U282 w: 0 1.33/1.48 _>_ w: 0 1.33/1.48 #isBoolean w: 0 1.33/1.48 #U202 w: 0 1.33/1.48 true w: 0 1.33/1.48 U222 w: 0 1.33/1.48 U232 w: x1 + x2 1.33/1.48 #_<_ w: 0 1.33/1.48 #U252 w: 0 1.33/1.48 U201 w: x2 + 3 1.33/1.48 #4 w: 0 1.33/1.48 #U242 w: 0 1.33/1.48 #U141 w: 0 1.33/1.48 U252 w: 3 1.33/1.48 U141 w: 0 1.33/1.48 #U171 w: 0 1.33/1.48 s_ w: x1 + 1 1.33/1.48 U173 w: 5 1.33/1.48 0 w: 1 1.33/1.48 U191 w: x2 + x3 + 2 1.33/1.48 quot w: x1 + 3 1.33/1.48 U153 w: 0 1.33/1.48 #isBooleanKind w: 0 1.33/1.48 isNzNat w: x1 + 1 1.33/1.48 U171 w: x1 1.33/1.48 U202 w: x2 + 4 1.33/1.48 #U211 w: 0 1.33/1.48 #U233 w: 0 1.33/1.48 #U153 w: 0 1.33/1.48 #3 w: 0 1.33/1.48 #U182 w: 0 1.33/1.48 #d w: x1 + x2 1.33/1.48 U151 w: 0 1.33/1.48 #U292 w: 0 1.33/1.48 isBooleanKind w: 0 1.33/1.48 #U111 w: 0 1.33/1.48 #U192 w: 0 1.33/1.48 #U221 w: 0 1.33/1.48 #U232 w: 0 1.33/1.48 _<_ w: 0 1.33/1.48 #U251 w: 0 1.33/1.48 U211 w: x1 + x2 + 1 1.33/1.48 U223 w: 0 1.33/1.48 #U281 w: 0 1.33/1.48 U203 w: 3 1.33/1.48 p_ w: x1 + 1 1.33/1.48 isNat w: x1 1.33/1.48 U251 w: x1 1.33/1.48 #U291 w: 0 1.33/1.48 U61 w: 0 1.33/1.48 #U51 w: 0 1.33/1.48 #5 w: 0 1.33/1.48 #U11 w: 0 1.33/1.48 2 w: 1 1.33/1.48 U31 w: 0 1.33/1.48 U183 w: x1 + 2 1.33/1.48 #U193 w: 0 1.33/1.48 #U41 w: 0 1.33/1.48 equal w: 0 1.33/1.48 #U191 w: 0 1.33/1.48 #U21 w: 1 1.33/1.48 6 w: 1 1.33/1.48 U81 w: 0 1.33/1.48 #_>_ w: 0 1.33/1.48 tt w: 3 1.33/1.48 #quot w: 0 1.33/1.48 #U71 w: 0 1.33/1.48 #U151 w: 0 1.33/1.48 #U162 w: 0 1.33/1.48 #1 w: 0 1.33/1.48 U51 w: 0 1.33/1.48 #isNatKind w: 0 1.33/1.48 #U161 w: 0 1.33/1.48 #U172 w: 0 1.33/1.48 U162 w: 0 1.33/1.48 #U261 w: 0 1.33/1.48 #U203 w: 0 1.33/1.48 #U122 w: 0 1.33/1.48 U212 w: 4 1.33/1.48 U41 w: 0 1.33/1.48 #U31 w: 0 1.33/1.48 #and w: 0 1.33/1.48 #U91 w: 0 1.33/1.48 U233 w: 0 1.33/1.48 U282 w: 0 1.33/1.48 U121 w: 0 1.33/1.48 #U61 w: 0 1.33/1.48 U181 w: 0 1.33/1.48 U122 w: 0 1.33/1.48 #gcd w: 0 1.33/1.48 USABLE RULES: { 32 33 36 47 } 1.33/1.48 Removed DPs: #42 #213 1.33/1.48 Number of SCCs: 5, DPs: 54 1.33/1.48 SCC { #71 #146 } 1.33/1.48 POLO(Sum)... succeeded. 1.33/1.48 7 w: 1 1.33/1.48 U291 w: 0 1.33/1.48 #U201 w: 0 1.33/1.48 U231 w: x1 1.33/1.48 #isNzNat w: 0 1.33/1.48 isNatKind w: x1 + 1 1.33/1.48 U21 w: 0 1.33/1.48 U261 w: 0 1.33/1.48 1 w: 1 1.33/1.48 U193 w: 0 1.33/1.48 U161 w: x1 1.33/1.48 U182 w: x2 + 1 1.33/1.48 U11 w: 0 1.33/1.48 d w: 1 1.33/1.48 isBoolean w: 0 1.33/1.48 4 w: 1 1.33/1.48 U243 w: x1 1.33/1.48 #isNat w: 0 1.33/1.48 #7 w: 0 1.33/1.48 U143 w: 0 1.33/1.48 #U142 w: 0 1.33/1.48 U192 w: 0 1.33/1.48 #_+_ w: x1 + x2 1.33/1.48 5 w: 1 1.33/1.48 U142 w: 0 1.33/1.48 _*_ w: x1 + x2 + 3 1.33/1.48 _+_ w: 1 1.33/1.48 #U152 w: 0 1.33/1.48 U242 w: x1 + x2 1.33/1.48 #U181 w: 0 1.33/1.48 U91 w: 0 1.33/1.48 U221 w: x1 + x2 1.33/1.48 gcd w: 2 1.33/1.48 #U101 w: 1 1.33/1.48 #equal w: 0 1.33/1.48 3 w: 1 1.33/1.48 #U183 w: 0 1.33/1.48 U71 w: 0 1.33/1.48 #U81 w: 1 1.33/1.48 and w: x1 + x2 + 1 1.33/1.48 U131 w: 0 1.33/1.48 #U222 w: 0 1.33/1.48 #U243 w: 0 1.33/1.48 #U212 w: 0 1.33/1.49 U101 w: 0 1.33/1.49 #U231 w: 0 1.33/1.49 #_*_ w: 0 1.33/1.49 U111 w: 0 1.33/1.49 #6 w: 0 1.33/1.49 U152 w: 0 1.33/1.49 false w: 0 1.33/1.49 U281 w: 0 1.33/1.49 #2 w: 0 1.33/1.49 #U121 w: 0 1.33/1.49 U292 w: 0 1.33/1.49 U172 w: x2 + 4 1.33/1.49 #U241 w: 0 1.33/1.49 #U131 w: 0 1.33/1.49 #U143 w: 0 1.33/1.49 U241 w: x1 + x2 + x3 + 3 1.33/1.49 #p_ w: 0 1.33/1.49 #U271 w: 0 1.33/1.49 #U173 w: 0 1.33/1.49 #U223 w: 0 1.33/1.49 U271 w: 0 1.33/1.49 #U282 w: 0 1.33/1.49 _>_ w: 0 1.33/1.49 #isBoolean w: 0 1.33/1.49 #U202 w: 0 1.33/1.49 true w: 0 1.33/1.49 U222 w: 0 1.33/1.49 U232 w: x1 + x2 1.33/1.49 #_<_ w: 0 1.33/1.49 #U252 w: 0 1.33/1.49 U201 w: x2 + 3 1.33/1.49 #4 w: 0 1.33/1.49 #U242 w: 0 1.33/1.49 #U141 w: 0 1.33/1.49 U252 w: 3 1.33/1.49 U141 w: 0 1.33/1.49 #U171 w: 0 1.33/1.49 s_ w: x1 + 1 1.33/1.49 U173 w: 5 1.33/1.49 0 w: 1 1.33/1.49 U191 w: x2 + x3 + 2 1.33/1.49 quot w: x1 + 3 1.33/1.49 U153 w: 0 1.33/1.49 #isBooleanKind w: 0 1.33/1.49 isNzNat w: x1 + 1 1.33/1.49 U171 w: x1 1.33/1.49 U202 w: x2 + 4 1.33/1.49 #U211 w: 0 1.33/1.49 #U233 w: 0 1.33/1.49 #U153 w: 0 1.33/1.49 #3 w: 0 1.33/1.49 #U182 w: 0 1.33/1.49 #d w: 0 1.33/1.49 U151 w: 0 1.33/1.49 #U292 w: 0 1.33/1.49 isBooleanKind w: 0 1.33/1.49 #U111 w: 0 1.33/1.49 #U192 w: 0 1.33/1.49 #U221 w: 0 1.33/1.49 #U232 w: 0 1.33/1.49 _<_ w: 0 1.33/1.49 #U251 w: 0 1.33/1.49 U211 w: x1 + x2 + 1 1.33/1.49 U223 w: 0 1.33/1.49 #U281 w: 0 1.33/1.49 U203 w: 3 1.33/1.49 p_ w: x1 + 1 1.33/1.49 isNat w: x1 1.33/1.49 U251 w: x1 1.33/1.49 #U291 w: 0 1.33/1.49 U61 w: 0 1.33/1.49 #U51 w: 0 1.33/1.49 #5 w: 0 1.33/1.49 #U11 w: 0 1.33/1.49 2 w: 1 1.33/1.49 U31 w: 0 1.33/1.49 U183 w: x1 + 2 1.33/1.49 #U193 w: 0 1.33/1.49 #U41 w: x2 + x3 + 1 1.33/1.49 equal w: 0 1.33/1.49 #U191 w: 0 1.33/1.49 #U21 w: 1 1.33/1.49 6 w: 1 1.33/1.49 U81 w: 0 1.33/1.49 #_>_ w: 0 1.33/1.49 tt w: 3 1.33/1.49 #quot w: 0 1.33/1.49 #U71 w: 0 1.33/1.49 #U151 w: 0 1.33/1.49 #U162 w: 0 1.33/1.49 #1 w: 0 1.33/1.49 U51 w: 0 1.33/1.49 #isNatKind w: 0 1.33/1.49 #U161 w: 0 1.33/1.49 #U172 w: 0 1.33/1.49 U162 w: 0 1.33/1.49 #U261 w: 0 1.33/1.49 #U203 w: 0 1.33/1.49 #U122 w: 0 1.33/1.49 U212 w: 4 1.33/1.49 U41 w: 0 1.33/1.49 #U31 w: 0 1.33/1.49 #and w: 0 1.33/1.49 #U91 w: 0 1.33/1.49 U233 w: 0 1.33/1.49 U282 w: 0 1.33/1.49 U121 w: 0 1.33/1.49 #U61 w: 0 1.33/1.49 U181 w: 0 1.33/1.49 U122 w: 0 1.33/1.49 #gcd w: 0 1.33/1.49 USABLE RULES: { 32 33 36 47 } 1.33/1.49 Removed DPs: #71 #146 1.33/1.49 Number of SCCs: 4, DPs: 52 1.33/1.49 SCC { #54 #80 #100 } 1.33/1.49 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 1.33/1.49 Finding a loop... failed. 1.33/1.49 EOF