7.76/7.39 MAYBE 7.76/7.39 Input TRS: 7.76/7.39 C symbols: d _+_ _*_ gcd 7.76/7.39 1: 1() -> s_(0()) 7.76/7.39 2: 2() -> s_(s_(0())) 7.76/7.39 3: 3() -> s_(s_(s_(0()))) 7.76/7.39 4: 4() -> s_(s_(s_(s_(0())))) 7.76/7.39 5: 5() -> s_(s_(s_(s_(s_(0()))))) 7.76/7.39 6: 6() -> s_(s_(s_(s_(s_(s_(0())))))) 7.76/7.39 7: 7() -> s_(s_(s_(s_(s_(s_(s_(0()))))))) 7.76/7.39 8: U101(tt(),M,N) -> U102(isNatKind(M),M,N) 7.76/7.39 9: U102(tt(),M,N) -> U103(isNat(N),M,N) 7.76/7.39 10: U103(tt(),M,N) -> U104(isNatKind(N),M,N) 7.76/7.39 11: U104(tt(),M,N) -> d(N,M) 7.76/7.39 12: U11(tt(),N) -> U12(isNatKind(N)) 7.76/7.39 13: U111(tt(),N) -> U112(isNatKind(N)) 7.76/7.39 14: U112(tt()) -> 0() 7.76/7.39 15: U12(tt()) -> 0() 7.76/7.39 16: U121(tt(),M',N') -> U122(isNatKind(M'),M',N') 7.76/7.39 17: U122(tt(),M',N') -> U123(isNzNat(N'),M',N') 7.76/7.39 18: U123(tt(),M',N') -> U124(isNatKind(N'),M',N') 7.76/7.39 19: U124(tt(),M',N') -> U125(equal(_>_(N',M'),true()),M',N') 7.76/7.39 20: U125(tt(),M',N') -> gcd(d(N',M'),M') 7.76/7.39 21: U131(tt(),N') -> U132(isNatKind(N'),N') 7.76/7.39 22: U132(tt(),N') -> N' 7.76/7.39 23: U141(tt(),V1,V2) -> U142(isNatKind(V1),V1,V2) 7.76/7.39 24: U142(tt(),V1,V2) -> U143(isNatKind(V2),V1,V2) 7.76/7.39 25: U143(tt(),V1,V2) -> U144(isNatKind(V2),V1,V2) 7.76/7.39 26: U144(tt(),V1,V2) -> U145(isNat(V1),V2) 7.76/7.39 27: U145(tt(),V2) -> U146(isNat(V2)) 7.76/7.39 28: U146(tt()) -> tt() 7.76/7.39 29: U151(tt(),V1,V2) -> U152(isNatKind(V1),V1,V2) 7.76/7.39 30: U152(tt(),V1,V2) -> U153(isNatKind(V2),V1,V2) 7.76/7.39 31: U153(tt(),V1,V2) -> U154(isNatKind(V2),V1,V2) 7.76/7.39 32: U154(tt(),V1,V2) -> U155(isNat(V1),V2) 7.76/7.39 33: U155(tt(),V2) -> U156(isNat(V2)) 7.76/7.39 34: U156(tt()) -> tt() 7.76/7.39 35: U161(tt(),V2) -> U162(isNatKind(V2)) 7.76/7.39 36: U162(tt()) -> tt() 7.76/7.39 37: U171(tt(),V2) -> U172(isNatKind(V2)) 7.76/7.39 38: U172(tt()) -> tt() 7.76/7.39 39: U181(tt(),V) -> U182(isNatKind(V),V) 7.76/7.39 40: U182(tt(),V) -> U183(isNzNat(V)) 7.76/7.39 41: U183(tt()) -> tt() 7.76/7.39 42: U191(tt(),V1,V2) -> U192(isNatKind(V1),V1,V2) 7.76/7.39 43: U192(tt(),V1,V2) -> U193(isNatKind(V2),V1,V2) 7.76/7.39 44: U193(tt(),V1,V2) -> U194(isNatKind(V2),V1,V2) 7.76/7.39 45: U194(tt(),V1,V2) -> U195(isNat(V1),V2) 7.76/7.39 46: U195(tt(),V2) -> U196(isNat(V2)) 7.76/7.39 47: U196(tt()) -> tt() 7.76/7.39 48: U201(tt(),V1,V2) -> U202(isNatKind(V1),V1,V2) 7.76/7.39 49: U202(tt(),V1,V2) -> U203(isNatKind(V2),V1,V2) 7.76/7.39 50: U203(tt(),V1,V2) -> U204(isNatKind(V2),V1,V2) 7.76/7.39 51: U204(tt(),V1,V2) -> U205(isNat(V1),V2) 7.76/7.39 52: U205(tt(),V2) -> U206(isNat(V2)) 7.76/7.39 53: U206(tt()) -> tt() 7.76/7.39 54: U21(tt(),M,N) -> U22(isNatKind(M),M,N) 7.76/7.39 55: U211(tt(),V1,V2) -> U212(isNatKind(V1),V1,V2) 7.76/7.39 56: U212(tt(),V1,V2) -> U213(isNatKind(V2),V1,V2) 7.76/7.39 57: U213(tt(),V1,V2) -> U214(isNatKind(V2),V1,V2) 7.76/7.39 58: U214(tt(),V1,V2) -> U215(isNat(V1),V2) 7.76/7.39 59: U215(tt(),V2) -> U216(isNat(V2)) 7.76/7.39 60: U216(tt()) -> tt() 7.76/7.39 61: U22(tt(),M,N) -> U23(isNat(N),M,N) 7.76/7.39 62: U221(tt(),V1,V2) -> U222(isNatKind(V1),V1,V2) 7.76/7.39 63: U222(tt(),V1,V2) -> U223(isNatKind(V2),V1,V2) 7.76/7.39 64: U223(tt(),V1,V2) -> U224(isNatKind(V2),V1,V2) 7.76/7.39 65: U224(tt(),V1,V2) -> U225(isNat(V1),V2) 7.76/7.39 66: U225(tt(),V2) -> U226(isNat(V2)) 7.76/7.39 67: U226(tt()) -> tt() 7.76/7.39 68: U23(tt(),M,N) -> U24(isNatKind(N),M,N) 7.76/7.39 69: U231(tt(),V1) -> U232(isNatKind(V1),V1) 7.76/7.39 70: U232(tt(),V1) -> U233(isNzNat(V1)) 7.76/7.39 71: U233(tt()) -> tt() 7.76/7.39 72: U24(tt(),M,N) -> s_(_+_(N,_+_(M,_*_(N,M)))) 7.76/7.39 73: U241(tt(),V1,V2) -> U242(isNatKind(V1),V1,V2) 7.76/7.39 74: U242(tt(),V1,V2) -> U243(isNatKind(V2),V1,V2) 7.76/7.39 75: U243(tt(),V1,V2) -> U244(isNatKind(V2),V1,V2) 7.76/7.39 76: U244(tt(),V1,V2) -> U245(isNat(V1),V2) 7.76/7.39 77: U245(tt(),V2) -> U246(isNzNat(V2)) 7.76/7.39 78: U246(tt()) -> tt() 7.76/7.39 79: U251(tt(),V2) -> U252(isNatKind(V2)) 7.76/7.39 80: U252(tt()) -> tt() 7.76/7.39 81: U261(tt(),V2) -> U262(isNatKind(V2)) 7.76/7.39 82: U262(tt()) -> tt() 7.76/7.39 83: U271(tt(),V2) -> U272(isNatKind(V2)) 7.76/7.39 84: U272(tt()) -> tt() 7.76/7.39 85: U281(tt(),V2) -> U282(isNatKind(V2)) 7.76/7.39 86: U282(tt()) -> tt() 7.76/7.39 87: U291(tt()) -> tt() 7.76/7.39 88: U301(tt(),V2) -> U302(isNatKind(V2)) 7.76/7.39 89: U302(tt()) -> tt() 7.76/7.39 90: U31(tt(),N) -> U32(isNatKind(N),N) 7.76/7.39 91: U311(tt()) -> tt() 7.76/7.39 92: U32(tt(),N) -> N 7.76/7.39 93: U321(tt(),V1,V2) -> U322(isNatKind(V1),V1,V2) 7.76/7.39 94: U322(tt(),V1,V2) -> U323(isNatKind(V2),V1,V2) 7.76/7.39 95: U323(tt(),V1,V2) -> U324(isNatKind(V2),V1,V2) 7.76/7.39 96: U324(tt(),V1,V2) -> U325(isNzNat(V1),V2) 7.76/7.39 97: U325(tt(),V2) -> U326(isNzNat(V2)) 7.76/7.39 98: U326(tt()) -> tt() 7.76/7.39 99: U331(tt(),V1,V2) -> U332(isNatKind(V1),V1,V2) 7.76/7.39 100: U332(tt(),V1,V2) -> U333(isNatKind(V2),V1,V2) 7.76/7.39 101: U333(tt(),V1,V2) -> U334(isNatKind(V2),V1,V2) 7.76/7.39 102: U334(tt(),V1,V2) -> U335(isNzNat(V1),V2) 7.76/7.39 103: U335(tt(),V2) -> U336(isNzNat(V2)) 7.76/7.39 104: U336(tt()) -> tt() 7.76/7.39 105: U341(tt(),V1) -> U342(isNatKind(V1),V1) 7.76/7.39 106: U342(tt(),V1) -> U343(isNat(V1)) 7.76/7.39 107: U343(tt()) -> tt() 7.76/7.39 108: U351(tt(),N) -> U352(isNatKind(N),N) 7.76/7.39 109: U352(tt(),N) -> N 7.76/7.39 110: U361(tt(),M') -> U362(isNatKind(M')) 7.76/7.39 111: U362(tt()) -> s_(0()) 7.76/7.39 112: U371(tt(),M',N) -> U372(isNatKind(M'),M',N) 7.76/7.39 113: U372(tt(),M',N) -> U373(isNat(N),M',N) 7.76/7.39 114: U373(tt(),M',N) -> U374(isNatKind(N),M',N) 7.76/7.39 115: U374(tt(),M',N) -> U375(equal(_>_(M',N),true())) 7.76/7.39 116: U375(tt()) -> 0() 7.76/7.39 117: U381(tt(),M',N) -> U382(isNatKind(M'),M',N) 7.76/7.39 118: U382(tt(),M',N) -> U383(isNat(N),M',N) 7.76/7.39 119: U383(tt(),M',N) -> U384(isNatKind(N),M',N) 7.76/7.39 120: U384(tt(),M',N) -> U385(equal(_>_(N,M'),true()),M',N) 7.76/7.39 121: U385(tt(),M',N) -> s_(quot(d(N,M'),M')) 7.76/7.39 122: U41(tt(),M,N) -> U42(isNatKind(M),M,N) 7.76/7.39 123: U42(tt(),M,N) -> U43(isNat(N),M,N) 7.76/7.39 124: U43(tt(),M,N) -> U44(isNatKind(N),M,N) 7.76/7.39 125: U44(tt(),M,N) -> s_(s_(_+_(N,M))) 7.76/7.39 126: U51(tt(),M,N) -> U52(isNatKind(M),M,N) 7.76/7.39 127: U52(tt(),M,N) -> U53(isNat(N),M,N) 7.76/7.39 128: U53(tt(),M,N) -> U54(isNatKind(N),M,N) 7.76/7.39 129: U54(tt(),M,N) -> _>_(M,N) 7.76/7.39 130: U61(tt(),M) -> U62(isNatKind(M)) 7.76/7.39 131: U62(tt()) -> false() 7.76/7.39 132: U71(tt(),N') -> U72(isNatKind(N')) 7.76/7.39 133: U72(tt()) -> true() 7.76/7.39 134: U81(tt(),M,N) -> U82(isNatKind(M),M,N) 7.76/7.39 135: U82(tt(),M,N) -> U83(isNat(N),M,N) 7.76/7.39 136: U83(tt(),M,N) -> U84(isNatKind(N),M,N) 7.76/7.39 137: U84(tt(),M,N) -> _>_(N,M) 7.76/7.39 138: U91(tt(),N) -> U92(isNatKind(N),N) 7.76/7.39 139: U92(tt(),N) -> N 7.76/7.39 140: _*_(N,0()) -> U11(isNat(N),N) 7.76/7.39 141: _*_(s_(N),s_(M)) -> U21(isNat(M),M,N) 7.76/7.39 142: _+_(N,0()) -> U31(isNat(N),N) 7.76/7.39 143: _+_(s_(N),s_(M)) -> U41(isNat(M),M,N) 7.76/7.39 144: _<_(N,M) -> U51(isNat(M),M,N) 7.76/7.39 145: _>_(0(),M) -> U61(isNat(M),M) 7.76/7.39 146: _>_(N',0()) -> U71(isNzNat(N'),N') 7.76/7.39 147: _>_(s_(N),s_(M)) -> U81(isNat(M),M,N) 7.76/7.39 148: d(0(),N) -> U91(isNat(N),N) 7.76/7.39 149: d(s_(N),s_(M)) -> U101(isNat(M),M,N) 7.76/7.39 150: equal(X,X) -> tt() 7.76/7.39 151: gcd(0(),N) -> U111(isNat(N),N) 7.76/7.39 152: gcd(N',M') -> U121(isNzNat(M'),M',N') 7.76/7.39 153: gcd(N',N') -> U131(isNzNat(N'),N') 7.76/7.39 154: isBoolean(false()) -> tt() 7.76/7.39 155: isBoolean(true()) -> tt() 7.76/7.39 156: isBoolean(_<_(V1,V2)) -> U141(isNatKind(V1),V1,V2) 7.76/7.39 157: isBoolean(_>_(V1,V2)) -> U151(isNatKind(V1),V1,V2) 7.76/7.39 158: isBooleanKind(false()) -> tt() 7.76/7.39 159: isBooleanKind(true()) -> tt() 7.76/7.39 160: isBooleanKind(_<_(V1,V2)) -> U161(isNatKind(V1),V2) 7.76/7.39 161: isBooleanKind(_>_(V1,V2)) -> U171(isNatKind(V1),V2) 7.76/7.39 162: isNat(0()) -> tt() 7.76/7.39 163: isNat(V) -> U181(isNatKind(V),V) 7.76/7.39 164: isNat(_*_(V1,V2)) -> U191(isNatKind(V1),V1,V2) 7.76/7.39 165: isNat(_+_(V1,V2)) -> U201(isNatKind(V1),V1,V2) 7.76/7.39 166: isNat(d(V1,V2)) -> U211(isNatKind(V1),V1,V2) 7.76/7.39 167: isNat(gcd(V1,V2)) -> U221(isNatKind(V1),V1,V2) 7.76/7.39 168: isNat(p_(V1)) -> U231(isNatKind(V1),V1) 7.76/7.39 169: isNat(quot(V1,V2)) -> U241(isNatKind(V1),V1,V2) 7.76/7.39 170: isNatKind(0()) -> tt() 7.76/7.39 171: isNatKind(1()) -> tt() 7.76/7.39 172: isNatKind(2()) -> tt() 7.76/7.39 173: isNatKind(3()) -> tt() 7.76/7.39 174: isNatKind(4()) -> tt() 7.76/7.39 175: isNatKind(5()) -> tt() 7.76/7.39 176: isNatKind(6()) -> tt() 7.76/7.39 177: isNatKind(7()) -> tt() 7.76/7.39 178: isNatKind(_*_(V1,V2)) -> U251(isNatKind(V1),V2) 7.76/7.39 179: isNatKind(_+_(V1,V2)) -> U261(isNatKind(V1),V2) 7.76/7.39 180: isNatKind(d(V1,V2)) -> U271(isNatKind(V1),V2) 7.76/7.39 181: isNatKind(gcd(V1,V2)) -> U281(isNatKind(V1),V2) 7.76/7.39 182: isNatKind(p_(V1)) -> U291(isNatKind(V1)) 7.76/7.39 183: isNatKind(quot(V1,V2)) -> U301(isNatKind(V1),V2) 7.76/7.39 184: isNatKind(s_(V1)) -> U311(isNatKind(V1)) 7.76/7.39 185: isNzNat(1()) -> tt() 7.76/7.39 186: isNzNat(2()) -> tt() 7.76/7.39 187: isNzNat(3()) -> tt() 7.76/7.39 188: isNzNat(4()) -> tt() 7.76/7.39 189: isNzNat(5()) -> tt() 7.76/7.39 190: isNzNat(6()) -> tt() 7.76/7.39 191: isNzNat(7()) -> tt() 7.76/7.39 192: isNzNat(_*_(V1,V2)) -> U321(isNatKind(V1),V1,V2) 7.76/7.39 193: isNzNat(gcd(V1,V2)) -> U331(isNatKind(V1),V1,V2) 7.76/7.39 194: isNzNat(s_(V1)) -> U341(isNatKind(V1),V1) 7.76/7.39 195: p_(s_(N)) -> U351(isNat(N),N) 7.76/7.39 196: quot(M',M') -> U361(isNzNat(M'),M') 7.76/7.39 197: quot(N,M') -> U371(isNzNat(M'),M',N) 7.76/7.39 198: quot(N,M') -> U381(isNzNat(M'),M',N) 7.76/7.39 Number of strict rules: 198 7.76/7.39 Direct POLO(bPol) ... failed. 7.76/7.39 Uncurrying ... failed. 7.76/7.39 Dependency Pairs: 7.76/7.39 #1: #U192(tt(),V1,V2) -> #U193(isNatKind(V2),V1,V2) 7.76/7.39 #2: #U192(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #3: #U151(tt(),V1,V2) -> #U152(isNatKind(V1),V1,V2) 7.76/7.39 #4: #U151(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #5: #U161(tt(),V2) -> #U162(isNatKind(V2)) 7.76/7.39 #6: #U161(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #7: #U271(tt(),V2) -> #U272(isNatKind(V2)) 7.76/7.39 #8: #U271(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #9: #U225(tt(),V2) -> #U226(isNat(V2)) 7.76/7.39 #10: #U225(tt(),V2) -> #isNat(V2) 7.76/7.39 #11: #U195(tt(),V2) -> #U196(isNat(V2)) 7.76/7.39 #12: #U195(tt(),V2) -> #isNat(V2) 7.76/7.39 #13: #U191(tt(),V1,V2) -> #U192(isNatKind(V1),V1,V2) 7.76/7.39 #14: #U191(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #15: #U374(tt(),M',N) -> #U375(equal(_>_(M',N),true())) 7.76/7.39 #16: #U374(tt(),M',N) -> #equal(_>_(M',N),true()) 7.76/7.39 #17: #U374(tt(),M',N) -> #_>_(M',N) 7.76/7.39 #18: #quot(N,M') -> #U381(isNzNat(M'),M',N) 7.76/7.39 #19: #quot(N,M') -> #isNzNat(M') 7.76/7.39 #20: #d(s_(N),s_(M)) -> #U101(isNat(M),M,N) 7.76/7.39 #21: #d(s_(N),s_(M)) -> #isNat(M) 7.76/7.39 #22: #U323(tt(),V1,V2) -> #U324(isNatKind(V2),V1,V2) 7.76/7.39 #23: #U323(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #24: #U171(tt(),V2) -> #U172(isNatKind(V2)) 7.76/7.39 #25: #U171(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #26: #U373(tt(),M',N) -> #U374(isNatKind(N),M',N) 7.76/7.39 #27: #U373(tt(),M',N) -> #isNatKind(N) 7.76/7.39 #28: #U331(tt(),V1,V2) -> #U332(isNatKind(V1),V1,V2) 7.76/7.39 #29: #U331(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #30: #isNat(V) -> #U181(isNatKind(V),V) 7.76/7.39 #31: #isNat(V) -> #isNatKind(V) 7.76/7.39 #32: #U325(tt(),V2) -> #U326(isNzNat(V2)) 7.76/7.39 #33: #U325(tt(),V2) -> #isNzNat(V2) 7.76/7.39 #34: #U241(tt(),V1,V2) -> #U242(isNatKind(V1),V1,V2) 7.76/7.39 #35: #U241(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #36: #_>_(s_(N),s_(M)) -> #U81(isNat(M),M,N) 7.76/7.39 #37: #_>_(s_(N),s_(M)) -> #isNat(M) 7.76/7.39 #38: #U201(tt(),V1,V2) -> #U202(isNatKind(V1),V1,V2) 7.76/7.39 #39: #U201(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #40: #U42(tt(),M,N) -> #U43(isNat(N),M,N) 7.76/7.39 #41: #U42(tt(),M,N) -> #isNat(N) 7.76/7.39 #42: #U243(tt(),V1,V2) -> #U244(isNatKind(V2),V1,V2) 7.76/7.39 #43: #U243(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #44: #isNatKind(_*_(V1,V2)) -> #U251(isNatKind(V1),V2) 7.76/7.39 #45: #isNatKind(_*_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #46: #U371(tt(),M',N) -> #U372(isNatKind(M'),M',N) 7.76/7.39 #47: #U371(tt(),M',N) -> #isNatKind(M') 7.76/7.39 #48: #U242(tt(),V1,V2) -> #U243(isNatKind(V2),V1,V2) 7.76/7.39 #49: #U242(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #50: #U214(tt(),V1,V2) -> #U215(isNat(V1),V2) 7.76/7.39 #51: #U214(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #52: #U91(tt(),N) -> #U92(isNatKind(N),N) 7.76/7.39 #53: #U91(tt(),N) -> #isNatKind(N) 7.76/7.39 #54: #U372(tt(),M',N) -> #U373(isNat(N),M',N) 7.76/7.39 #55: #U372(tt(),M',N) -> #isNat(N) 7.76/7.39 #56: #U22(tt(),M,N) -> #U23(isNat(N),M,N) 7.76/7.39 #57: #U22(tt(),M,N) -> #isNat(N) 7.76/7.39 #58: #gcd(0(),N) -> #U111(isNat(N),N) 7.76/7.39 #59: #gcd(0(),N) -> #isNat(N) 7.76/7.39 #60: #quot(M',M') -> #U361(isNzNat(M'),M') 7.76/7.39 #61: #quot(M',M') -> #isNzNat(M') 7.76/7.39 #62: #isNat(_+_(V1,V2)) -> #U201(isNatKind(V1),V1,V2) 7.76/7.39 #63: #isNat(_+_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #64: #U215(tt(),V2) -> #U216(isNat(V2)) 7.76/7.39 #65: #U215(tt(),V2) -> #isNat(V2) 7.76/7.39 #66: #isNzNat(gcd(V1,V2)) -> #U331(isNatKind(V1),V1,V2) 7.76/7.39 #67: #isNzNat(gcd(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #68: #U361(tt(),M') -> #U362(isNatKind(M')) 7.76/7.39 #69: #U361(tt(),M') -> #isNatKind(M') 7.76/7.39 #70: #U71(tt(),N') -> #U72(isNatKind(N')) 7.76/7.39 #71: #U71(tt(),N') -> #isNatKind(N') 7.76/7.39 #72: #U211(tt(),V1,V2) -> #U212(isNatKind(V1),V1,V2) 7.76/7.39 #73: #U211(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #74: #U182(tt(),V) -> #U183(isNzNat(V)) 7.76/7.39 #75: #U182(tt(),V) -> #isNzNat(V) 7.76/7.39 #76: #U31(tt(),N) -> #U32(isNatKind(N),N) 7.76/7.39 #77: #U31(tt(),N) -> #isNatKind(N) 7.76/7.39 #78: #_>_(N',0()) -> #U71(isNzNat(N'),N') 7.76/7.39 #79: #_>_(N',0()) -> #isNzNat(N') 7.76/7.39 #80: #U204(tt(),V1,V2) -> #U205(isNat(V1),V2) 7.76/7.39 #81: #U204(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #82: #U111(tt(),N) -> #U112(isNatKind(N)) 7.76/7.39 #83: #U111(tt(),N) -> #isNatKind(N) 7.76/7.39 #84: #U102(tt(),M,N) -> #U103(isNat(N),M,N) 7.76/7.39 #85: #U102(tt(),M,N) -> #isNat(N) 7.76/7.39 #86: #U104(tt(),M,N) -> #d(N,M) 7.76/7.39 #87: #isBoolean(_<_(V1,V2)) -> #U141(isNatKind(V1),V1,V2) 7.76/7.39 #88: #isBoolean(_<_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #89: #U213(tt(),V1,V2) -> #U214(isNatKind(V2),V1,V2) 7.76/7.39 #90: #U213(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #91: #quot(N,M') -> #U371(isNzNat(M'),M',N) 7.76/7.39 #92: #quot(N,M') -> #isNzNat(M') 7.76/7.39 #93: #U244(tt(),V1,V2) -> #U245(isNat(V1),V2) 7.76/7.39 #94: #U244(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #95: #isNat(gcd(V1,V2)) -> #U221(isNatKind(V1),V1,V2) 7.76/7.39 #96: #isNat(gcd(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #97: #U322(tt(),V1,V2) -> #U323(isNatKind(V2),V1,V2) 7.76/7.39 #98: #U322(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #99: #U142(tt(),V1,V2) -> #U143(isNatKind(V2),V1,V2) 7.76/7.39 #100: #U142(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #101: #U81(tt(),M,N) -> #U82(isNatKind(M),M,N) 7.76/7.39 #102: #U81(tt(),M,N) -> #isNatKind(M) 7.76/7.39 #103: #U232(tt(),V1) -> #U233(isNzNat(V1)) 7.76/7.39 #104: #U232(tt(),V1) -> #isNzNat(V1) 7.76/7.39 #105: #U141(tt(),V1,V2) -> #U142(isNatKind(V1),V1,V2) 7.76/7.39 #106: #U141(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #107: #U53(tt(),M,N) -> #U54(isNatKind(N),M,N) 7.76/7.39 #108: #U53(tt(),M,N) -> #isNatKind(N) 7.76/7.39 #109: #U261(tt(),V2) -> #U262(isNatKind(V2)) 7.76/7.39 #110: #U261(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #111: #U382(tt(),M',N) -> #U383(isNat(N),M',N) 7.76/7.39 #112: #U382(tt(),M',N) -> #isNat(N) 7.76/7.39 #113: #U194(tt(),V1,V2) -> #U195(isNat(V1),V2) 7.76/7.39 #114: #U194(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #115: #U324(tt(),V1,V2) -> #U325(isNzNat(V1),V2) 7.76/7.39 #116: #U324(tt(),V1,V2) -> #isNzNat(V1) 7.76/7.39 #117: #U231(tt(),V1) -> #U232(isNatKind(V1),V1) 7.76/7.39 #118: #U231(tt(),V1) -> #isNatKind(V1) 7.76/7.39 #119: #U333(tt(),V1,V2) -> #U334(isNatKind(V2),V1,V2) 7.76/7.39 #120: #U333(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #121: #U11(tt(),N) -> #U12(isNatKind(N)) 7.76/7.39 #122: #U11(tt(),N) -> #isNatKind(N) 7.76/7.39 #123: #U153(tt(),V1,V2) -> #U154(isNatKind(V2),V1,V2) 7.76/7.39 #124: #U153(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #125: #isNat(_*_(V1,V2)) -> #U191(isNatKind(V1),V1,V2) 7.76/7.39 #126: #isNat(_*_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #127: #U251(tt(),V2) -> #U252(isNatKind(V2)) 7.76/7.39 #128: #U251(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #129: #U212(tt(),V1,V2) -> #U213(isNatKind(V2),V1,V2) 7.76/7.39 #130: #U212(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #131: #U342(tt(),V1) -> #U343(isNat(V1)) 7.76/7.39 #132: #U342(tt(),V1) -> #isNat(V1) 7.76/7.39 #133: #U221(tt(),V1,V2) -> #U222(isNatKind(V1),V1,V2) 7.76/7.39 #134: #U221(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #135: #U152(tt(),V1,V2) -> #U153(isNatKind(V2),V1,V2) 7.76/7.39 #136: #U152(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #137: #U205(tt(),V2) -> #U206(isNat(V2)) 7.76/7.39 #138: #U205(tt(),V2) -> #isNat(V2) 7.76/7.39 #139: #U202(tt(),V1,V2) -> #U203(isNatKind(V2),V1,V2) 7.76/7.39 #140: #U202(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #141: #U143(tt(),V1,V2) -> #U144(isNatKind(V2),V1,V2) 7.76/7.39 #142: #U143(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #143: #U61(tt(),M) -> #U62(isNatKind(M)) 7.76/7.39 #144: #U61(tt(),M) -> #isNatKind(M) 7.76/7.39 #145: #isNat(d(V1,V2)) -> #U211(isNatKind(V1),V1,V2) 7.76/7.39 #146: #isNat(d(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #147: #U351(tt(),N) -> #U352(isNatKind(N),N) 7.76/7.39 #148: #U351(tt(),N) -> #isNatKind(N) 7.76/7.39 #149: #U54(tt(),M,N) -> #_>_(M,N) 7.76/7.39 #150: #U125(tt(),M',N') -> #gcd(d(N',M'),M') 7.76/7.39 #151: #U125(tt(),M',N') -> #d(N',M') 7.76/7.39 #152: #isNatKind(_+_(V1,V2)) -> #U261(isNatKind(V1),V2) 7.76/7.39 #153: #isNatKind(_+_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #154: #U51(tt(),M,N) -> #U52(isNatKind(M),M,N) 7.76/7.39 #155: #U51(tt(),M,N) -> #isNatKind(M) 7.76/7.39 #156: #U301(tt(),V2) -> #U302(isNatKind(V2)) 7.76/7.39 #157: #U301(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #158: #U181(tt(),V) -> #U182(isNatKind(V),V) 7.76/7.39 #159: #U181(tt(),V) -> #isNatKind(V) 7.76/7.39 #160: #gcd(N',N') -> #U131(isNzNat(N'),N') 7.76/7.39 #161: #gcd(N',N') -> #isNzNat(N') 7.76/7.39 #162: #U83(tt(),M,N) -> #U84(isNatKind(N),M,N) 7.76/7.39 #163: #U83(tt(),M,N) -> #isNatKind(N) 7.76/7.39 #164: #U103(tt(),M,N) -> #U104(isNatKind(N),M,N) 7.76/7.39 #165: #U103(tt(),M,N) -> #isNatKind(N) 7.76/7.39 #166: #U383(tt(),M',N) -> #U384(isNatKind(N),M',N) 7.76/7.39 #167: #U383(tt(),M',N) -> #isNatKind(N) 7.76/7.39 #168: #U321(tt(),V1,V2) -> #U322(isNatKind(V1),V1,V2) 7.76/7.39 #169: #U321(tt(),V1,V2) -> #isNatKind(V1) 7.76/7.39 #170: #U223(tt(),V1,V2) -> #U224(isNatKind(V2),V1,V2) 7.76/7.39 #171: #U223(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #172: #U155(tt(),V2) -> #U156(isNat(V2)) 7.76/7.39 #173: #U155(tt(),V2) -> #isNat(V2) 7.76/7.39 #174: #U24(tt(),M,N) -> #_+_(N,_+_(M,_*_(N,M))) 7.76/7.39 #175: #U24(tt(),M,N) -> #_+_(M,_*_(N,M)) 7.76/7.39 #176: #U24(tt(),M,N) -> #_*_(N,M) 7.76/7.39 #177: #isNatKind(s_(V1)) -> #U311(isNatKind(V1)) 7.76/7.39 #178: #isNatKind(s_(V1)) -> #isNatKind(V1) 7.76/7.39 #179: #U384(tt(),M',N) -> #U385(equal(_>_(N,M'),true()),M',N) 7.76/7.39 #180: #U384(tt(),M',N) -> #equal(_>_(N,M'),true()) 7.76/7.39 #181: #U384(tt(),M',N) -> #_>_(N,M') 7.76/7.39 #182: #U193(tt(),V1,V2) -> #U194(isNatKind(V2),V1,V2) 7.76/7.39 #183: #U193(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #184: #U224(tt(),V1,V2) -> #U225(isNat(V1),V2) 7.76/7.39 #185: #U224(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #186: #d(0(),N) -> #U91(isNat(N),N) 7.76/7.39 #187: #d(0(),N) -> #isNat(N) 7.76/7.39 #188: #U52(tt(),M,N) -> #U53(isNat(N),M,N) 7.76/7.39 #189: #U52(tt(),M,N) -> #isNat(N) 7.76/7.39 #190: #isNat(quot(V1,V2)) -> #U241(isNatKind(V1),V1,V2) 7.76/7.39 #191: #isNat(quot(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #192: #isNatKind(quot(V1,V2)) -> #U301(isNatKind(V1),V2) 7.76/7.39 #193: #isNatKind(quot(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #194: #isNzNat(s_(V1)) -> #U341(isNatKind(V1),V1) 7.76/7.39 #195: #isNzNat(s_(V1)) -> #isNatKind(V1) 7.76/7.39 #196: #isBoolean(_>_(V1,V2)) -> #U151(isNatKind(V1),V1,V2) 7.76/7.39 #197: #isBoolean(_>_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #198: #U145(tt(),V2) -> #U146(isNat(V2)) 7.76/7.39 #199: #U145(tt(),V2) -> #isNat(V2) 7.76/7.39 #200: #U84(tt(),M,N) -> #_>_(N,M) 7.76/7.39 #201: #_<_(N,M) -> #U51(isNat(M),M,N) 7.76/7.39 #202: #_<_(N,M) -> #isNat(M) 7.76/7.39 #203: #_+_(N,0()) -> #U31(isNat(N),N) 7.76/7.39 #204: #_+_(N,0()) -> #isNat(N) 7.76/7.39 #205: #isBooleanKind(_>_(V1,V2)) -> #U171(isNatKind(V1),V2) 7.76/7.39 #206: #isBooleanKind(_>_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #207: #U381(tt(),M',N) -> #U382(isNatKind(M'),M',N) 7.76/7.39 #208: #U381(tt(),M',N) -> #isNatKind(M') 7.76/7.39 #209: #U122(tt(),M',N') -> #U123(isNzNat(N'),M',N') 7.76/7.39 #210: #U122(tt(),M',N') -> #isNzNat(N') 7.76/7.39 #211: #U154(tt(),V1,V2) -> #U155(isNat(V1),V2) 7.76/7.39 #212: #U154(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #213: #U124(tt(),M',N') -> #U125(equal(_>_(N',M'),true()),M',N') 7.76/7.39 #214: #U124(tt(),M',N') -> #equal(_>_(N',M'),true()) 7.76/7.39 #215: #U124(tt(),M',N') -> #_>_(N',M') 7.76/7.39 #216: #_+_(s_(N),s_(M)) -> #U41(isNat(M),M,N) 7.76/7.39 #217: #_+_(s_(N),s_(M)) -> #isNat(M) 7.76/7.39 #218: #U44(tt(),M,N) -> #_+_(N,M) 7.76/7.39 #219: #isNzNat(_*_(V1,V2)) -> #U321(isNatKind(V1),V1,V2) 7.76/7.39 #220: #isNzNat(_*_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #221: #U222(tt(),V1,V2) -> #U223(isNatKind(V2),V1,V2) 7.76/7.39 #222: #U222(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #223: #U82(tt(),M,N) -> #U83(isNat(N),M,N) 7.76/7.39 #224: #U82(tt(),M,N) -> #isNat(N) 7.76/7.39 #225: #U341(tt(),V1) -> #U342(isNatKind(V1),V1) 7.76/7.39 #226: #U341(tt(),V1) -> #isNatKind(V1) 7.76/7.39 #227: #U144(tt(),V1,V2) -> #U145(isNat(V1),V2) 7.76/7.39 #228: #U144(tt(),V1,V2) -> #isNat(V1) 7.76/7.39 #229: #U332(tt(),V1,V2) -> #U333(isNatKind(V2),V1,V2) 7.76/7.39 #230: #U332(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #231: #U281(tt(),V2) -> #U282(isNatKind(V2)) 7.76/7.39 #232: #U281(tt(),V2) -> #isNatKind(V2) 7.76/7.39 #233: #isNatKind(gcd(V1,V2)) -> #U281(isNatKind(V1),V2) 7.76/7.39 #234: #isNatKind(gcd(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #235: #U41(tt(),M,N) -> #U42(isNatKind(M),M,N) 7.76/7.39 #236: #U41(tt(),M,N) -> #isNatKind(M) 7.76/7.39 #237: #U23(tt(),M,N) -> #U24(isNatKind(N),M,N) 7.76/7.39 #238: #U23(tt(),M,N) -> #isNatKind(N) 7.76/7.39 #239: #U131(tt(),N') -> #U132(isNatKind(N'),N') 7.76/7.39 #240: #U131(tt(),N') -> #isNatKind(N') 7.76/7.39 #241: #U121(tt(),M',N') -> #U122(isNatKind(M'),M',N') 7.76/7.39 #242: #U121(tt(),M',N') -> #isNatKind(M') 7.76/7.39 #243: #U245(tt(),V2) -> #U246(isNzNat(V2)) 7.76/7.39 #244: #U245(tt(),V2) -> #isNzNat(V2) 7.76/7.39 #245: #_*_(N,0()) -> #U11(isNat(N),N) 7.76/7.39 #246: #_*_(N,0()) -> #isNat(N) 7.76/7.39 #247: #U43(tt(),M,N) -> #U44(isNatKind(N),M,N) 7.76/7.39 #248: #U43(tt(),M,N) -> #isNatKind(N) 7.76/7.39 #249: #U21(tt(),M,N) -> #U22(isNatKind(M),M,N) 7.76/7.39 #250: #U21(tt(),M,N) -> #isNatKind(M) 7.76/7.39 #251: #p_(s_(N)) -> #U351(isNat(N),N) 7.76/7.39 #252: #p_(s_(N)) -> #isNat(N) 7.76/7.39 #253: #isBooleanKind(_<_(V1,V2)) -> #U161(isNatKind(V1),V2) 7.76/7.39 #254: #isBooleanKind(_<_(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #255: #U101(tt(),M,N) -> #U102(isNatKind(M),M,N) 7.76/7.39 #256: #U101(tt(),M,N) -> #isNatKind(M) 7.76/7.39 #257: #gcd(N',M') -> #U121(isNzNat(M'),M',N') 7.76/7.39 #258: #gcd(N',M') -> #isNzNat(M') 7.76/7.39 #259: #isNat(p_(V1)) -> #U231(isNatKind(V1),V1) 7.76/7.39 #260: #isNat(p_(V1)) -> #isNatKind(V1) 7.76/7.39 #261: #_*_(s_(N),s_(M)) -> #U21(isNat(M),M,N) 7.76/7.39 #262: #_*_(s_(N),s_(M)) -> #isNat(M) 7.76/7.39 #263: #U385(tt(),M',N) -> #quot(d(N,M'),M') 7.76/7.39 #264: #U385(tt(),M',N) -> #d(N,M') 7.76/7.39 #265: #isNatKind(d(V1,V2)) -> #U271(isNatKind(V1),V2) 7.76/7.39 #266: #isNatKind(d(V1,V2)) -> #isNatKind(V1) 7.76/7.39 #267: #_>_(0(),M) -> #U61(isNat(M),M) 7.76/7.39 #268: #_>_(0(),M) -> #isNat(M) 7.76/7.39 #269: #U334(tt(),V1,V2) -> #U335(isNzNat(V1),V2) 7.76/7.39 #270: #U334(tt(),V1,V2) -> #isNzNat(V1) 7.76/7.39 #271: #U335(tt(),V2) -> #U336(isNzNat(V2)) 7.76/7.39 #272: #U335(tt(),V2) -> #isNzNat(V2) 7.76/7.39 #273: #U203(tt(),V1,V2) -> #U204(isNatKind(V2),V1,V2) 7.76/7.39 #274: #U203(tt(),V1,V2) -> #isNatKind(V2) 7.76/7.39 #275: #U123(tt(),M',N') -> #U124(isNatKind(N'),M',N') 7.76/7.39 #276: #U123(tt(),M',N') -> #isNatKind(N') 7.76/7.39 #277: #isNatKind(p_(V1)) -> #U291(isNatKind(V1)) 7.76/7.39 #278: #isNatKind(p_(V1)) -> #isNatKind(V1) 7.76/7.39 Number of SCCs: 8, DPs: 107 7.76/7.39 SCC { #56 #176 #237 #249 #261 } 7.76/7.39 POLO(Sum)... succeeded. 7.76/7.39 7 w: 1 7.76/7.39 U291 w: 6 7.76/7.39 #U201 w: 0 7.76/7.39 U231 w: 6 7.76/7.39 U301 w: 6 7.76/7.39 U204 w: x1 7.76/7.39 #U72 w: 0 7.76/7.39 U123 w: 0 7.76/7.39 #U32 w: 0 7.76/7.39 #isNzNat w: 0 7.76/7.39 #U225 w: 0 7.76/7.39 isNatKind w: 6 7.76/7.39 U21 w: 0 7.76/7.39 #U146 w: 0 7.76/7.39 U261 w: 6 7.76/7.39 #U83 w: 0 7.76/7.39 1 w: 1 7.76/7.39 U333 w: 0 7.76/7.39 U193 w: x1 7.76/7.39 #U156 w: 0 7.76/7.39 U161 w: 0 7.76/7.39 U155 w: 0 7.76/7.39 U182 w: x1 7.76/7.39 U11 w: 0 7.76/7.39 #U144 w: 0 7.76/7.39 d w: 1 7.76/7.39 isBoolean w: 0 7.76/7.39 4 w: 1 7.76/7.39 #U272 w: 0 7.76/7.39 U243 w: x1 7.76/7.39 #U125 w: 0 7.76/7.39 #U324 w: 0 7.76/7.39 #isNat w: 0 7.76/7.39 #7 w: 0 7.76/7.39 U335 w: 6 7.76/7.39 #U384 w: 0 7.76/7.39 #U336 w: 0 7.76/7.39 U143 w: 0 7.76/7.39 #U246 w: 0 7.76/7.39 #U142 w: 0 7.76/7.39 U384 w: 0 7.76/7.39 U192 w: x1 7.76/7.39 U24 w: 0 7.76/7.39 #_+_ w: 0 7.76/7.39 5 w: 1 7.76/7.39 #U123 w: 0 7.76/7.39 #U24 w: x1 + x2 + x3 7.76/7.39 U142 w: 0 7.76/7.39 _*_ w: x1 + x2 + 1 7.76/7.39 _+_ w: 1 7.76/7.39 #U244 w: 0 7.76/7.39 #U152 w: 0 7.76/7.39 U242 w: x1 7.76/7.39 #U181 w: 0 7.76/7.39 U262 w: 6 7.76/7.39 #U195 w: 0 7.76/7.39 U244 w: x1 7.76/7.39 U272 w: x1 7.76/7.39 U42 w: 0 7.76/7.39 U91 w: 0 7.76/7.39 U221 w: 6 7.76/7.39 #U226 w: 0 7.76/7.39 gcd w: x1 + x2 + 5 7.76/7.39 #U101 w: 0 7.76/7.39 #equal w: 0 7.76/7.39 U325 w: 6 7.76/7.39 #U82 w: 0 7.76/7.39 3 w: 1 7.76/7.39 #U362 w: 0 7.76/7.39 U352 w: 0 7.76/7.39 #U183 w: 0 7.76/7.39 #U224 w: 0 7.76/7.39 #U104 w: 0 7.76/7.39 U71 w: 0 7.76/7.39 #U81 w: 0 7.76/7.39 #U322 w: 0 7.76/7.39 #U92 w: 0 7.76/7.39 #U323 w: 0 7.76/7.39 U131 w: 0 7.76/7.39 #U351 w: 0 7.76/7.39 #U222 w: 0 7.76/7.39 U206 w: x1 7.76/7.39 #U243 w: 0 7.76/7.39 #U212 w: 0 7.76/7.39 #U372 w: 0 7.76/7.39 #U334 w: 0 7.76/7.39 #U321 w: 0 7.76/7.39 U101 w: 0 7.76/7.39 #U231 w: 0 7.76/7.39 U361 w: 0 7.76/7.39 U383 w: 0 7.76/7.39 #_*_ w: x1 + x2 + 5 7.76/7.39 #U373 w: 0 7.76/7.39 U111 w: 0 7.76/7.39 U132 w: 0 7.76/7.39 U43 w: 0 7.76/7.39 #U342 w: 0 7.76/7.39 #6 w: 0 7.76/7.39 U152 w: 0 7.76/7.39 U381 w: 0 7.76/7.39 #U245 w: 0 7.76/7.39 U103 w: 0 7.76/7.39 false w: 0 7.76/7.39 #U155 w: 0 7.76/7.39 #U23 w: x1 + x2 + x3 + 1 7.76/7.39 #U53 w: 0 7.76/7.39 U281 w: x1 7.76/7.39 #U331 w: 0 7.76/7.39 #2 w: 0 7.76/7.39 U44 w: 0 7.76/7.39 #U43 w: 0 7.76/7.39 #U121 w: 0 7.76/7.39 #U381 w: 0 7.76/7.39 U84 w: 0 7.76/7.39 U341 w: 5 7.76/7.39 U23 w: 0 7.76/7.39 U342 w: 6 7.76/7.39 U371 w: 0 7.76/7.39 U172 w: 0 7.76/7.39 U144 w: 0 7.76/7.39 #U241 w: 0 7.76/7.39 U326 w: 6 7.76/7.39 #U131 w: 0 7.76/7.39 #U311 w: 0 7.76/7.39 U72 w: 0 7.76/7.39 #U143 w: 0 7.76/7.39 U124 w: 0 7.76/7.39 U241 w: x1 7.76/7.39 #p_ w: 0 7.76/7.39 #U271 w: 0 7.76/7.39 #U375 w: 0 7.76/7.39 #U52 w: 0 7.76/7.39 #U103 w: 0 7.76/7.39 U374 w: 0 7.76/7.39 #U223 w: 0 7.76/7.39 U12 w: 0 7.76/7.39 U271 w: x1 7.76/7.39 #U282 w: 0 7.76/7.39 _>_ w: 0 7.76/7.39 U213 w: x1 7.76/7.39 U214 w: x1 7.76/7.39 #isBoolean w: 0 7.76/7.39 #U202 w: 0 7.76/7.39 #U205 w: 0 7.76/7.39 true w: 0 7.76/7.39 U385 w: 0 7.76/7.39 U302 w: x1 7.76/7.39 U54 w: 0 7.76/7.39 U222 w: 6 7.76/7.39 U232 w: 6 7.76/7.39 #_<_ w: 0 7.76/7.39 U196 w: x1 7.76/7.39 U205 w: x1 7.76/7.39 #U252 w: 0 7.76/7.39 #U44 w: 0 7.76/7.39 U201 w: x1 7.76/7.39 #U54 w: 0 7.76/7.39 U104 w: 0 7.76/7.39 #4 w: 0 7.76/7.39 #U242 w: 0 7.76/7.39 #U213 w: 0 7.76/7.39 #U42 w: 0 7.76/7.39 #U141 w: 0 7.76/7.39 U252 w: x1 7.76/7.39 #U12 w: 0 7.76/7.39 U141 w: 0 7.76/7.39 #U171 w: 0 7.76/7.39 #U62 w: 0 7.76/7.39 U83 w: 0 7.76/7.39 s_ w: x1 + 3 7.76/7.39 #U301 w: 0 7.76/7.39 #U215 w: 0 7.76/7.39 0 w: 5 7.76/7.39 #U214 w: 0 7.76/7.39 U191 w: x1 7.76/7.39 U343 w: 0 7.76/7.39 quot w: 1 7.76/7.39 U332 w: x3 7.76/7.39 #U102 w: 0 7.76/7.39 U153 w: 0 7.76/7.39 #isBooleanKind w: 0 7.76/7.39 #U361 w: 0 7.76/7.39 isNzNat w: x1 + 1 7.76/7.39 U171 w: 0 7.76/7.39 U202 w: x1 7.76/7.39 #U211 w: 0 7.76/7.39 #U233 w: 0 7.76/7.39 U372 w: 0 7.76/7.39 U246 w: 6 7.76/7.39 U375 w: 0 7.76/7.39 #U385 w: 0 7.76/7.39 U62 w: 0 7.76/7.39 #U153 w: 0 7.76/7.39 U336 w: 6 7.76/7.39 #3 w: 0 7.76/7.39 #U182 w: 0 7.76/7.39 #d w: 0 7.76/7.39 U151 w: 0 7.76/7.39 U226 w: x1 7.76/7.39 U334 w: x2 + 6 7.76/7.39 isBooleanKind w: 0 7.76/7.39 #U341 w: 0 7.76/7.39 #U262 w: 0 7.76/7.39 #U192 w: 0 7.76/7.39 #U111 w: 0 7.76/7.39 #U326 w: 0 7.76/7.39 U32 w: 0 7.76/7.39 U195 w: x1 7.76/7.39 #U221 w: 0 7.76/7.39 #U154 w: 0 7.76/7.39 #U206 w: 0 7.76/7.39 #U371 w: 0 7.76/7.39 #U302 w: 0 7.76/7.39 #U232 w: 0 7.76/7.39 _<_ w: 0 7.76/7.39 #U251 w: 0 7.76/7.39 U154 w: 0 7.76/7.39 U211 w: x1 7.76/7.39 U223 w: 6 7.76/7.39 #U281 w: 0 7.76/7.39 #U145 w: 0 7.76/7.39 #U343 w: 0 7.76/7.39 U203 w: x1 7.76/7.39 p_ w: 1 7.76/7.39 isNat w: 6 7.76/7.39 #U352 w: 0 7.76/7.39 #U216 w: 0 7.76/7.39 U194 w: x1 7.76/7.39 U251 w: x1 7.76/7.39 #U291 w: 0 7.76/7.39 #U382 w: 0 7.76/7.39 #U124 w: 0 7.76/7.39 U216 w: x1 7.76/7.39 U52 w: 0 7.76/7.39 U156 w: 0 7.76/7.39 U382 w: 0 7.76/7.39 U61 w: 0 7.76/7.39 #U51 w: 0 7.76/7.39 #5 w: 0 7.76/7.39 #U11 w: 0 7.76/7.39 2 w: 1 7.76/7.39 U31 w: 0 7.76/7.39 U183 w: 6 7.76/7.39 U245 w: 6 7.76/7.39 U92 w: 0 7.76/7.39 U112 w: 0 7.76/7.39 #U193 w: 0 7.76/7.39 #U196 w: 0 7.76/7.39 U351 w: 0 7.76/7.39 #U335 w: 0 7.76/7.39 #U41 w: 0 7.76/7.39 U323 w: x1 7.76/7.39 #U325 w: 0 7.76/7.39 U102 w: 0 7.76/7.39 equal w: 0 7.76/7.39 #U191 w: 0 7.76/7.39 #U21 w: x2 + x3 + 9 7.76/7.39 6 w: 1 7.76/7.39 U146 w: 0 7.76/7.39 U373 w: 0 7.76/7.39 U81 w: 0 7.76/7.39 U82 w: 0 7.76/7.39 #U22 w: x1 + x2 + x3 + 2 7.76/7.39 #_>_ w: 0 7.76/7.39 #U112 w: 0 7.76/7.39 tt w: 6 7.76/7.39 #U374 w: 0 7.76/7.39 #quot w: 0 7.76/7.39 U125 w: 0 7.76/7.39 U362 w: 0 7.76/7.39 #U71 w: 0 7.76/7.39 #U84 w: 0 7.76/7.39 #U151 w: 0 7.76/7.39 U321 w: x1 7.76/7.39 #U162 w: 0 7.76/7.39 #1 w: 0 7.76/7.39 #U383 w: 0 7.76/7.39 U22 w: 0 7.76/7.39 U225 w: x1 7.76/7.39 U51 w: 0 7.76/7.39 #isNatKind w: 0 7.76/7.39 #U161 w: 0 7.76/7.39 U215 w: x1 7.76/7.39 #U172 w: 0 7.76/7.39 U311 w: x1 7.76/7.39 U162 w: 0 7.76/7.39 U322 w: x2 + x3 + 7 7.76/7.39 #U261 w: 0 7.76/7.39 #U203 w: 0 7.76/7.39 #U122 w: 0 7.76/7.39 U53 w: 0 7.76/7.39 U212 w: x1 7.76/7.39 U41 w: 0 7.76/7.39 #U31 w: 0 7.76/7.39 #U194 w: 0 7.76/7.39 #U332 w: 0 7.76/7.39 #U91 w: 0 7.76/7.39 U233 w: 6 7.76/7.39 U282 w: x1 7.76/7.39 U224 w: x1 7.76/7.39 #U132 w: 0 7.76/7.39 U121 w: 0 7.76/7.39 #U204 w: 0 7.76/7.39 #U61 w: 0 7.76/7.39 U181 w: x1 7.76/7.39 U145 w: 0 7.76/7.39 U324 w: 6 7.76/7.39 U331 w: x1 + x2 + x3 7.76/7.39 U122 w: 0 7.76/7.39 #U333 w: 0 7.76/7.39 #gcd w: 0 7.76/7.39 USABLE RULES: { 39..53 55..60 62..67 69..71 73..89 91 94..98 102..104 162..184 } 7.76/7.39 Removed DPs: #56 #176 #237 #249 #261 7.76/7.39 Number of SCCs: 7, DPs: 102 7.76/7.39 SCC { #40 #216 #218 #235 #247 } 7.76/7.39 POLO(Sum)... succeeded. 7.76/7.39 7 w: 1 7.76/7.39 U291 w: 3 7.76/7.39 #U201 w: 0 7.76/7.39 U231 w: 3 7.76/7.39 U301 w: 3 7.76/7.39 U204 w: x1 7.76/7.39 #U72 w: 0 7.76/7.39 U123 w: 0 7.76/7.39 #U32 w: 0 7.76/7.39 #isNzNat w: 0 7.76/7.39 #U225 w: 0 7.76/7.39 isNatKind w: 3 7.76/7.39 U21 w: 0 7.76/7.39 #U146 w: 0 7.76/7.39 U261 w: 3 7.76/7.39 #U83 w: 0 7.76/7.39 1 w: 1 7.76/7.39 U333 w: x1 7.76/7.39 U193 w: x1 7.76/7.39 #U156 w: 0 7.76/7.39 U161 w: 0 7.76/7.39 U155 w: 0 7.76/7.39 U182 w: x1 7.76/7.39 U11 w: 0 7.76/7.39 #U144 w: 0 7.76/7.39 d w: 1 7.76/7.39 isBoolean w: 0 7.76/7.39 4 w: 1 7.76/7.39 #U272 w: 0 7.76/7.39 U243 w: x1 7.76/7.39 #U125 w: 0 7.76/7.39 #U324 w: 0 7.76/7.39 #isNat w: 0 7.76/7.39 #7 w: 0 7.76/7.39 U335 w: 6 7.76/7.39 #U384 w: 0 7.76/7.39 #U336 w: 0 7.76/7.39 U143 w: 0 7.76/7.39 #U246 w: 0 7.76/7.39 #U142 w: 0 7.76/7.39 U384 w: 0 7.76/7.39 U192 w: x1 7.76/7.39 U24 w: 0 7.76/7.39 #_+_ w: x1 + x2 + 1 7.76/7.39 5 w: 1 7.76/7.39 #U123 w: 0 7.76/7.39 #U24 w: x1 7.76/7.39 U142 w: 0 7.76/7.39 _*_ w: x1 + x2 + 1 7.76/7.39 _+_ w: 1 7.76/7.39 #U244 w: 0 7.76/7.39 #U152 w: 0 7.76/7.39 U242 w: x1 7.76/7.39 #U181 w: 0 7.76/7.39 U262 w: 3 7.76/7.39 #U195 w: 0 7.76/7.39 U244 w: x1 7.76/7.39 U272 w: x1 7.76/7.39 U42 w: 0 7.76/7.39 U91 w: 0 7.76/7.39 U221 w: 3 7.76/7.39 #U226 w: 0 7.76/7.39 gcd w: x1 + x2 + 5 7.76/7.39 #U101 w: 0 7.76/7.39 #equal w: 0 7.76/7.39 U325 w: 3 7.76/7.39 #U82 w: 0 7.76/7.39 3 w: 1 7.76/7.39 #U362 w: 0 7.76/7.39 U352 w: 0 7.76/7.39 #U183 w: 0 7.76/7.39 #U224 w: 0 7.76/7.39 #U104 w: 0 7.76/7.39 U71 w: 0 7.76/7.39 #U81 w: 0 7.76/7.39 #U322 w: 0 7.76/7.39 #U92 w: 0 7.76/7.39 #U323 w: 0 7.76/7.39 U131 w: 0 7.76/7.39 #U351 w: 0 7.76/7.39 #U222 w: 0 7.76/7.39 U206 w: x1 7.76/7.39 #U243 w: 0 7.76/7.39 #U212 w: 0 7.76/7.39 #U372 w: 0 7.76/7.39 #U334 w: 0 7.76/7.39 #U321 w: 0 7.76/7.39 U101 w: 0 7.76/7.39 #U231 w: 0 7.76/7.39 U361 w: 0 7.76/7.39 U383 w: 0 7.76/7.39 #_*_ w: 5 7.76/7.39 #U373 w: 0 7.76/7.39 U111 w: 0 7.76/7.39 U132 w: 0 7.76/7.39 U43 w: 0 7.76/7.39 #U342 w: 0 7.76/7.39 #6 w: 0 7.76/7.39 U152 w: 0 7.76/7.39 U381 w: 0 7.76/7.39 #U245 w: 0 7.76/7.39 U103 w: 0 7.76/7.39 false w: 0 7.76/7.39 #U155 w: 0 7.76/7.39 #U23 w: x1 + 1 7.76/7.39 #U53 w: 0 7.76/7.39 U281 w: x1 7.76/7.39 #U331 w: 0 7.76/7.39 #2 w: 0 7.76/7.39 U44 w: 0 7.76/7.39 #U43 w: x1 + x2 + x3 + 1 7.76/7.39 #U121 w: 0 7.76/7.39 #U381 w: 0 7.76/7.39 U84 w: 0 7.76/7.39 U341 w: 5 7.76/7.39 U23 w: 0 7.76/7.39 U342 w: 6 7.76/7.39 U371 w: 0 7.76/7.39 U172 w: 0 7.76/7.39 U144 w: 0 7.76/7.39 #U241 w: 0 7.76/7.39 U326 w: 3 7.76/7.39 #U131 w: 0 7.76/7.39 #U311 w: 0 7.76/7.39 U72 w: 0 7.76/7.39 #U143 w: 0 7.76/7.39 U124 w: 0 7.76/7.39 U241 w: 3 7.76/7.39 #p_ w: 0 7.76/7.39 #U271 w: 0 7.76/7.39 #U375 w: 0 7.76/7.39 #U52 w: 0 7.76/7.39 #U103 w: 0 7.76/7.39 U374 w: 0 7.76/7.39 #U223 w: 0 7.76/7.39 U12 w: 0 7.76/7.39 U271 w: x1 7.76/7.39 #U282 w: 0 7.76/7.39 _>_ w: 0 7.76/7.39 U213 w: x1 7.76/7.39 U214 w: x1 7.76/7.39 #isBoolean w: 0 7.76/7.39 #U202 w: 0 7.76/7.39 #U205 w: 0 7.76/7.39 true w: 0 7.76/7.39 U385 w: 0 7.76/7.39 U302 w: 3 7.76/7.39 U54 w: 0 7.76/7.39 U222 w: x1 7.76/7.39 U232 w: 3 7.76/7.39 #_<_ w: 0 7.76/7.39 U196 w: x1 7.76/7.39 U205 w: x1 7.76/7.39 #U252 w: 0 7.76/7.39 #U44 w: x2 + x3 + 3 7.76/7.39 U201 w: x1 7.76/7.39 #U54 w: 0 7.76/7.39 U104 w: 0 7.76/7.39 #4 w: 0 7.76/7.39 #U242 w: 0 7.76/7.39 #U213 w: 0 7.76/7.39 #U42 w: x2 + x3 + 5 7.76/7.39 #U141 w: 0 7.76/7.39 U252 w: x1 7.76/7.39 #U12 w: 0 7.76/7.39 U141 w: 0 7.76/7.39 #U171 w: 0 7.76/7.39 #U62 w: 0 7.76/7.39 U83 w: 0 7.76/7.39 s_ w: x1 + 3 7.76/7.39 #U301 w: 0 7.76/7.39 #U215 w: 0 7.76/7.39 0 w: 5 7.76/7.39 #U214 w: 0 7.76/7.39 U191 w: x1 7.76/7.39 U343 w: 0 7.76/7.39 quot w: 1 7.76/7.39 U332 w: x3 + 3 7.76/7.39 #U102 w: 0 7.76/7.39 U153 w: 0 7.76/7.39 #isBooleanKind w: 0 7.76/7.39 #U361 w: 0 7.76/7.39 isNzNat w: x1 + 1 7.76/7.39 U171 w: 0 7.76/7.39 U202 w: x1 7.76/7.39 #U211 w: 0 7.76/7.39 #U233 w: 0 7.76/7.39 U372 w: 0 7.76/7.39 U246 w: 3 7.76/7.39 U375 w: 0 7.76/7.39 #U385 w: 0 7.76/7.39 U62 w: 0 7.76/7.39 #U153 w: 0 7.76/7.39 U336 w: 3 7.76/7.39 #3 w: 0 7.76/7.39 #U182 w: 0 7.76/7.39 #d w: 0 7.76/7.39 U151 w: 0 7.76/7.39 U226 w: x1 7.76/7.39 U334 w: x2 + 6 7.76/7.39 isBooleanKind w: 0 7.76/7.39 #U341 w: 0 7.76/7.39 #U262 w: 0 7.76/7.39 #U192 w: 0 7.76/7.39 #U111 w: 0 7.76/7.39 #U326 w: 0 7.76/7.39 U32 w: 0 7.76/7.39 U195 w: x1 7.76/7.39 #U221 w: 0 7.76/7.39 #U154 w: 0 7.76/7.39 #U206 w: 0 7.76/7.39 #U371 w: 0 7.76/7.39 #U302 w: 0 7.76/7.39 #U232 w: 0 7.76/7.39 _<_ w: 0 7.76/7.39 #U251 w: 0 7.76/7.39 U154 w: 0 7.76/7.39 U211 w: x1 7.76/7.39 U223 w: 3 7.76/7.39 #U281 w: 0 7.76/7.39 #U145 w: 0 7.76/7.39 #U343 w: 0 7.76/7.39 U203 w: x1 7.76/7.39 p_ w: 1 7.76/7.39 isNat w: 3 7.76/7.39 #U352 w: 0 7.76/7.39 #U216 w: 0 7.76/7.39 U194 w: x1 7.76/7.39 U251 w: x1 7.76/7.39 #U291 w: 0 7.76/7.39 #U382 w: 0 7.76/7.39 #U124 w: 0 7.76/7.39 U216 w: x1 7.76/7.39 U52 w: 0 7.76/7.39 U156 w: 0 7.76/7.39 U382 w: 0 7.76/7.39 U61 w: 0 7.76/7.39 #U51 w: 0 7.76/7.39 #5 w: 0 7.76/7.39 #U11 w: 0 7.76/7.39 2 w: 1 7.76/7.39 U31 w: 0 7.76/7.39 U183 w: 3 7.76/7.39 U245 w: 3 7.76/7.39 U92 w: 0 7.76/7.39 U112 w: 0 7.76/7.39 #U193 w: 0 7.76/7.39 #U196 w: 0 7.76/7.39 U351 w: 0 7.76/7.39 #U335 w: 0 7.76/7.39 #U41 w: x2 + x3 + 6 7.76/7.39 U323 w: 6 7.76/7.39 #U325 w: 0 7.76/7.39 U102 w: 0 7.76/7.39 equal w: 0 7.76/7.39 #U191 w: 0 7.76/7.39 #U21 w: 9 7.76/7.39 6 w: 1 7.76/7.39 U146 w: 0 7.76/7.39 U373 w: 0 7.76/7.39 U81 w: 0 7.76/7.39 U82 w: 0 7.76/7.39 #U22 w: x1 + 2 7.76/7.39 #_>_ w: 0 7.76/7.39 #U112 w: 0 7.76/7.39 tt w: 3 7.76/7.39 #U374 w: 0 7.76/7.39 #quot w: 0 7.76/7.39 U125 w: 0 7.76/7.39 U362 w: 0 7.76/7.39 #U71 w: 0 7.76/7.39 #U84 w: 0 7.76/7.39 #U151 w: 0 7.76/7.39 U321 w: x1 7.76/7.39 #U162 w: 0 7.76/7.39 #1 w: 0 7.76/7.39 #U383 w: 0 7.76/7.39 U22 w: 0 7.76/7.39 U225 w: x1 7.76/7.39 U51 w: 0 7.76/7.39 #isNatKind w: 0 7.76/7.39 #U161 w: 0 7.76/7.39 U215 w: x1 7.76/7.39 #U172 w: 0 7.76/7.39 U311 w: x1 7.76/7.39 U162 w: 0 7.76/7.39 U322 w: x2 + x3 + 7 7.76/7.39 #U261 w: 0 7.76/7.39 #U203 w: 0 7.76/7.39 #U122 w: 0 7.76/7.39 U53 w: 0 7.76/7.39 U212 w: x1 7.76/7.39 U41 w: 0 7.76/7.39 #U31 w: 0 7.76/7.39 #U194 w: 0 7.76/7.39 #U332 w: 0 7.76/7.39 #U91 w: 0 7.76/7.39 U233 w: 3 7.76/7.39 U282 w: 3 7.76/7.39 U224 w: x1 7.76/7.39 #U132 w: 0 7.76/7.39 U121 w: 0 7.76/7.39 #U204 w: 0 7.76/7.39 #U61 w: 0 7.76/7.39 U181 w: 3 7.76/7.39 U145 w: 0 7.76/7.39 U324 w: 3 7.76/7.39 U331 w: x1 + x2 + x3 7.76/7.39 U122 w: 0 7.76/7.39 #U333 w: 0 7.76/7.39 #gcd w: 0 7.76/7.39 USABLE RULES: { 39..53 55..60 62..67 69..71 73..89 91 94..98 102..104 162..184 } 7.76/7.39 Removed DPs: #40 #216 #218 #235 #247 7.76/7.39 Number of SCCs: 6, DPs: 97 7.76/7.39 SCC { #36 #101 #162 #200 #223 } 7.76/7.39 POLO(Sum)... succeeded. 7.76/7.39 7 w: 1 7.76/7.39 U291 w: 0 7.76/7.39 #U201 w: 0 7.76/7.39 U231 w: 5 7.76/7.39 U301 w: 4 7.76/7.39 U204 w: x3 + 2 7.76/7.39 #U72 w: 0 7.76/7.39 U123 w: 0 7.76/7.39 #U32 w: 0 7.76/7.39 #isNzNat w: 0 7.76/7.39 #U225 w: 0 7.76/7.39 isNatKind w: x1 + 2 7.76/7.39 U21 w: 0 7.76/7.39 #U146 w: 0 7.76/7.39 U261 w: 3 7.76/7.39 #U83 w: x2 + 3 7.76/7.39 1 w: 1 7.76/7.39 U333 w: x1 7.76/7.39 U193 w: x1 + x2 7.76/7.39 #U156 w: 0 7.76/7.39 U161 w: 0 7.76/7.39 U155 w: 0 7.76/7.39 U182 w: 5 7.76/7.39 U11 w: 0 7.76/7.39 #U144 w: 0 7.76/7.39 d w: 1 7.76/7.39 isBoolean w: 0 7.76/7.39 4 w: 1 7.76/7.39 #U272 w: 0 7.76/7.39 U243 w: x1 + x2 + 15 7.76/7.39 #U125 w: 0 7.76/7.39 #U324 w: 0 7.76/7.39 #isNat w: 0 7.76/7.39 #7 w: 0 7.76/7.39 U335 w: 8 7.76/7.39 #U384 w: 0 7.76/7.39 #U336 w: 0 7.76/7.39 U143 w: 0 7.76/7.39 #U246 w: 0 7.76/7.39 #U142 w: 0 7.76/7.39 U384 w: 0 7.76/7.39 U192 w: x1 + 4 7.76/7.39 U24 w: 0 7.76/7.39 #_+_ w: 1 7.76/7.39 5 w: 1 7.76/7.39 #U123 w: 0 7.76/7.39 #U24 w: 0 7.76/7.39 U142 w: 0 7.76/7.39 _*_ w: 1 7.76/7.39 _+_ w: 1 7.76/7.39 #U244 w: 0 7.76/7.39 #U152 w: 0 7.76/7.39 U242 w: x1 + x2 + 9 7.76/7.39 #U181 w: 0 7.76/7.39 U262 w: x1 + 3 7.76/7.39 #U195 w: 0 7.76/7.39 U244 w: x1 + 21 7.76/7.39 U272 w: 5 7.76/7.39 U42 w: 0 7.76/7.39 U91 w: 0 7.76/7.39 U221 w: x3 7.76/7.39 #U226 w: 0 7.76/7.39 gcd w: 1 7.76/7.39 #U101 w: 0 7.76/7.39 #equal w: 0 7.76/7.39 U325 w: 7 7.76/7.39 #U82 w: x2 + 4 7.76/7.39 3 w: 1 7.76/7.39 #U362 w: 0 7.76/7.39 U352 w: 0 7.76/7.39 #U183 w: 0 7.76/7.39 #U224 w: 0 7.76/7.39 #U104 w: 0 7.76/7.39 U71 w: 0 7.76/7.39 #U81 w: x2 + 5 7.76/7.39 #U322 w: 0 7.76/7.39 #U92 w: 0 7.76/7.39 #U323 w: 0 7.76/7.39 U131 w: 0 7.76/7.39 #U351 w: 0 7.76/7.39 #U222 w: 0 7.76/7.39 U206 w: 4 7.76/7.39 #U243 w: 0 7.76/7.39 #U212 w: 0 7.76/7.39 #U372 w: 0 7.76/7.39 #U334 w: 0 7.76/7.39 #U321 w: 0 7.76/7.39 U101 w: 0 7.76/7.39 #U231 w: 0 7.76/7.39 U361 w: 0 7.76/7.39 U383 w: 0 7.76/7.39 #_*_ w: 5 7.76/7.39 #U373 w: 0 7.76/7.39 U111 w: 0 7.76/7.39 U132 w: 0 7.76/7.39 U43 w: 0 7.76/7.39 #U342 w: 0 7.76/7.39 #6 w: 0 7.76/7.39 U152 w: 0 7.76/7.39 U381 w: 0 7.76/7.39 #U245 w: 0 7.76/7.39 U103 w: 0 7.76/7.39 false w: 0 7.76/7.39 #U155 w: 0 7.76/7.39 #U23 w: 1 7.76/7.39 #U53 w: 0 7.76/7.39 U281 w: x2 + 4 7.76/7.39 #U331 w: 0 7.76/7.39 #2 w: 0 7.76/7.39 U44 w: 0 7.76/7.39 #U43 w: 0 7.76/7.39 #U121 w: 0 7.76/7.39 #U381 w: 0 7.76/7.39 U84 w: 0 7.76/7.39 U341 w: x1 + 6 7.76/7.39 U23 w: 0 7.76/7.39 U342 w: x1 + 12 7.76/7.39 U371 w: 0 7.76/7.39 U172 w: 0 7.76/7.39 U144 w: 0 7.76/7.39 #U241 w: 0 7.76/7.39 U326 w: 7 7.76/7.39 #U131 w: 0 7.76/7.39 #U311 w: 0 7.76/7.39 U72 w: 0 7.76/7.39 #U143 w: 0 7.76/7.39 U124 w: 0 7.76/7.39 U241 w: x1 + x2 + x3 + 3 7.76/7.39 #p_ w: 0 7.76/7.39 #U271 w: 0 7.76/7.39 #U375 w: 0 7.76/7.39 #U52 w: 0 7.76/7.39 #U103 w: 0 7.76/7.39 U374 w: 0 7.76/7.39 #U223 w: 0 7.76/7.40 U12 w: 0 7.76/7.40 U271 w: x2 + 4 7.76/7.40 #U282 w: 0 7.76/7.40 _>_ w: 0 7.76/7.40 U213 w: x1 + x2 + 1 7.76/7.40 U214 w: x1 + x2 7.76/7.40 #isBoolean w: 0 7.76/7.40 #U202 w: 0 7.76/7.40 #U205 w: 0 7.76/7.40 true w: 0 7.76/7.40 U385 w: 0 7.76/7.40 U302 w: 5 7.76/7.40 U54 w: 0 7.76/7.40 U222 w: x2 + x3 + 1 7.76/7.40 U232 w: 7 7.76/7.40 #_<_ w: 0 7.76/7.40 U196 w: 0 7.76/7.40 U205 w: 3 7.76/7.40 #U252 w: 0 7.76/7.40 #U44 w: 2 7.76/7.40 U201 w: x1 7.76/7.40 #U54 w: 0 7.76/7.40 U104 w: 0 7.76/7.40 #4 w: 0 7.76/7.40 #U242 w: 0 7.76/7.40 #U213 w: 0 7.76/7.40 #U42 w: 4 7.76/7.40 #U141 w: 0 7.76/7.40 U252 w: 5 7.76/7.40 #U12 w: 0 7.76/7.40 U141 w: 0 7.76/7.40 #U171 w: 0 7.76/7.40 #U62 w: 0 7.76/7.40 U83 w: 0 7.76/7.40 s_ w: x1 + 5 7.76/7.40 #U301 w: 0 7.76/7.40 #U215 w: 0 7.76/7.40 0 w: 4 7.76/7.40 #U214 w: 0 7.76/7.40 U191 w: x1 + x3 7.76/7.40 U343 w: 0 7.76/7.40 quot w: x1 + x2 + 1 7.76/7.40 U332 w: x3 + 2 7.76/7.40 #U102 w: 0 7.76/7.40 U153 w: 0 7.76/7.40 #isBooleanKind w: 0 7.76/7.40 #U361 w: 0 7.76/7.40 isNzNat w: x1 + 1 7.76/7.40 U171 w: 0 7.76/7.40 U202 w: x2 + x3 7.76/7.40 #U211 w: 0 7.76/7.40 #U233 w: 0 7.76/7.40 U372 w: 0 7.76/7.40 U246 w: 6 7.76/7.40 U375 w: 0 7.76/7.40 #U385 w: 0 7.76/7.40 U62 w: 0 7.76/7.40 #U153 w: 0 7.76/7.40 U336 w: 7 7.76/7.40 #3 w: 0 7.76/7.40 #U182 w: 0 7.76/7.40 #d w: 0 7.76/7.40 U151 w: 0 7.76/7.40 U226 w: 6 7.76/7.40 U334 w: x2 + 8 7.76/7.40 isBooleanKind w: 0 7.76/7.40 #U341 w: 0 7.76/7.40 #U262 w: 0 7.76/7.40 #U192 w: 0 7.76/7.40 #U111 w: 0 7.76/7.40 #U326 w: 0 7.76/7.40 U32 w: 0 7.76/7.40 U195 w: x2 + 12 7.76/7.40 #U221 w: 0 7.76/7.40 #U154 w: 0 7.76/7.40 #U206 w: 0 7.76/7.40 #U371 w: 0 7.76/7.40 #U302 w: 0 7.76/7.40 #U232 w: 0 7.76/7.40 _<_ w: 0 7.76/7.40 #U251 w: 0 7.76/7.40 U154 w: 0 7.76/7.40 U211 w: x1 + x2 + x3 7.76/7.40 U223 w: x1 + x2 + x3 7.76/7.40 #U281 w: 0 7.76/7.40 #U145 w: 0 7.76/7.40 #U343 w: 0 7.76/7.40 U203 w: 1 7.76/7.40 p_ w: x1 + 1 7.76/7.40 isNat w: x1 + 3 7.76/7.40 #U352 w: 0 7.76/7.40 #U216 w: 0 7.76/7.40 U194 w: x1 + 5 7.76/7.40 U251 w: x2 + 4 7.76/7.40 #U291 w: 0 7.76/7.40 #U382 w: 0 7.76/7.40 #U124 w: 0 7.76/7.40 U216 w: 0 7.76/7.40 U52 w: 0 7.76/7.40 U156 w: 0 7.76/7.40 U382 w: 0 7.76/7.40 U61 w: 0 7.76/7.40 #U51 w: 0 7.76/7.40 #5 w: 0 7.76/7.40 #U11 w: 0 7.76/7.40 2 w: 1 7.76/7.40 U31 w: 0 7.76/7.40 U183 w: 6 7.76/7.40 U245 w: x2 + 5 7.76/7.40 U92 w: 0 7.76/7.40 U112 w: 0 7.76/7.40 #U193 w: 0 7.76/7.40 #U196 w: 0 7.76/7.40 U351 w: 0 7.76/7.40 #U335 w: 0 7.76/7.40 #U41 w: 5 7.76/7.40 U323 w: 13 7.76/7.40 #U325 w: 0 7.76/7.40 U102 w: 0 7.76/7.40 equal w: 0 7.76/7.40 #U191 w: 0 7.76/7.40 #U21 w: 9 7.76/7.40 6 w: 5 7.76/7.40 U146 w: 0 7.76/7.40 U373 w: 0 7.76/7.40 U81 w: 0 7.76/7.40 U82 w: 0 7.76/7.40 #U22 w: 2 7.76/7.40 #_>_ w: x2 + 1 7.76/7.40 #U112 w: 0 7.76/7.40 tt w: 7 7.76/7.40 #U374 w: 0 7.76/7.40 #quot w: 0 7.76/7.40 U125 w: 0 7.76/7.40 U362 w: 0 7.76/7.40 #U71 w: 0 7.76/7.40 #U84 w: x2 + 2 7.76/7.40 #U151 w: 0 7.76/7.40 U321 w: 3 7.76/7.40 #U162 w: 0 7.76/7.40 #1 w: 0 7.76/7.40 #U383 w: 0 7.76/7.40 U22 w: 0 7.76/7.40 U225 w: x2 + 5 7.76/7.40 U51 w: 0 7.76/7.40 #isNatKind w: 0 7.76/7.40 #U161 w: 0 7.76/7.40 U215 w: x1 + 4 7.76/7.40 #U172 w: 0 7.76/7.40 U311 w: x1 + 6 7.76/7.40 U162 w: 0 7.76/7.40 U322 w: x1 + x2 + x3 + 7 7.76/7.40 #U261 w: 0 7.76/7.40 #U203 w: 0 7.76/7.40 #U122 w: 0 7.76/7.40 U53 w: 0 7.76/7.40 U212 w: x1 + x2 7.76/7.40 U41 w: 0 7.76/7.40 #U31 w: 0 7.76/7.40 #U194 w: 0 7.76/7.40 #U332 w: 0 7.76/7.40 #U91 w: 0 7.76/7.40 U233 w: 7 7.76/7.40 U282 w: 5 7.76/7.40 U224 w: x2 + 4 7.76/7.40 #U132 w: 0 7.76/7.40 U121 w: 0 7.76/7.40 #U204 w: 0 7.76/7.40 #U61 w: 0 7.76/7.40 U181 w: x2 + 4 7.76/7.40 U145 w: 0 7.76/7.40 U324 w: x1 7.76/7.40 U331 w: x1 + x2 + x3 7.76/7.40 U122 w: 0 7.76/7.40 #U333 w: 0 7.76/7.40 #gcd w: 0 7.76/7.40 USABLE RULES: { 70 71 96..98 102..104 } 7.76/7.40 Removed DPs: #36 #101 #162 #200 #223 7.76/7.40 Number of SCCs: 5, DPs: 92 7.76/7.40 SCC { #20 #84 #86 #164 #255 } 7.76/7.40 POLO(Sum)... succeeded. 7.76/7.40 7 w: 1 7.76/7.40 U291 w: 0 7.76/7.40 #U201 w: 0 7.76/7.40 U231 w: 5 7.76/7.40 U301 w: 4 7.76/7.40 U204 w: x3 + 2 7.76/7.40 #U72 w: 0 7.76/7.40 U123 w: 0 7.76/7.40 #U32 w: 0 7.76/7.40 #isNzNat w: 0 7.76/7.40 #U225 w: 0 7.76/7.40 isNatKind w: x1 + 2 7.76/7.40 U21 w: 0 7.76/7.40 #U146 w: 0 7.76/7.40 U261 w: 3 7.76/7.40 #U83 w: 3 7.76/7.40 1 w: 1 7.76/7.40 U333 w: x1 7.76/7.40 U193 w: x1 + x2 7.76/7.40 #U156 w: 0 7.76/7.40 U161 w: 0 7.76/7.40 U155 w: 0 7.76/7.40 U182 w: 5 7.76/7.40 U11 w: 0 7.76/7.40 #U144 w: 0 7.76/7.40 d w: 1 7.76/7.40 isBoolean w: 0 7.76/7.40 4 w: 1 7.76/7.40 #U272 w: 0 7.76/7.40 U243 w: x1 + x2 + 15 7.76/7.40 #U125 w: 0 7.76/7.40 #U324 w: 0 7.76/7.40 #isNat w: 0 7.76/7.40 #7 w: 0 7.76/7.40 U335 w: 8 7.76/7.40 #U384 w: 0 7.76/7.40 #U336 w: 0 7.76/7.40 U143 w: 0 7.76/7.40 #U246 w: 0 7.76/7.40 #U142 w: 0 7.76/7.40 U384 w: 0 7.76/7.40 U192 w: x1 + 4 7.76/7.40 U24 w: 0 7.76/7.40 #_+_ w: 1 7.76/7.40 5 w: 1 7.76/7.40 #U123 w: 0 7.76/7.40 #U24 w: 0 7.76/7.40 U142 w: 0 7.76/7.40 _*_ w: 1 7.76/7.40 _+_ w: 1 7.76/7.40 #U244 w: 0 7.76/7.40 #U152 w: 0 7.76/7.40 U242 w: x1 + x2 + 9 7.76/7.40 #U181 w: 0 7.76/7.40 U262 w: x1 + 3 7.76/7.40 #U195 w: 0 7.76/7.40 U244 w: x1 + 21 7.76/7.40 U272 w: 5 7.76/7.40 U42 w: 0 7.76/7.40 U91 w: 0 7.76/7.40 U221 w: x3 7.76/7.40 #U226 w: 0 7.76/7.40 gcd w: 1 7.76/7.40 #U101 w: x2 + x3 + 11 7.76/7.40 #equal w: 0 7.76/7.40 U325 w: 7 7.76/7.40 #U82 w: 4 7.76/7.40 3 w: 1 7.76/7.40 #U362 w: 0 7.76/7.40 U352 w: 0 7.76/7.40 #U183 w: 0 7.76/7.40 #U224 w: 0 7.76/7.40 #U104 w: x2 + x3 + 2 7.76/7.40 U71 w: 0 7.76/7.40 #U81 w: 5 7.76/7.40 #U322 w: 0 7.76/7.40 #U92 w: 0 7.76/7.40 #U323 w: 0 7.76/7.40 U131 w: 0 7.76/7.40 #U351 w: 0 7.76/7.40 #U222 w: 0 7.76/7.40 U206 w: 4 7.76/7.40 #U243 w: 0 7.76/7.40 #U212 w: 0 7.76/7.40 #U372 w: 0 7.76/7.40 #U334 w: 0 7.76/7.40 #U321 w: 0 7.76/7.40 U101 w: 0 7.76/7.40 #U231 w: 0 7.76/7.40 U361 w: 0 7.76/7.40 U383 w: 0 7.76/7.40 #_*_ w: 5 7.76/7.40 #U373 w: 0 7.76/7.40 U111 w: 0 7.76/7.40 U132 w: 0 7.76/7.40 U43 w: 0 7.76/7.40 #U342 w: 0 7.76/7.40 #6 w: 0 7.76/7.40 U152 w: 0 7.76/7.40 U381 w: 0 7.76/7.40 #U245 w: 0 7.76/7.40 U103 w: 0 7.76/7.40 false w: 0 7.76/7.40 #U155 w: 0 7.76/7.40 #U23 w: 1 7.76/7.40 #U53 w: 0 7.76/7.40 U281 w: x2 + 4 7.76/7.40 #U331 w: 0 7.76/7.40 #2 w: 0 7.76/7.40 U44 w: 0 7.76/7.40 #U43 w: 0 7.76/7.40 #U121 w: 0 7.76/7.40 #U381 w: 0 7.76/7.40 U84 w: 0 7.76/7.40 U341 w: x1 + 6 7.76/7.40 U23 w: 0 7.76/7.40 U342 w: x1 + 12 7.76/7.40 U371 w: 0 7.76/7.40 U172 w: 0 7.76/7.40 U144 w: 0 7.76/7.40 #U241 w: 0 7.76/7.40 U326 w: 7 7.76/7.40 #U131 w: 0 7.76/7.40 #U311 w: 0 7.76/7.40 U72 w: 0 7.76/7.40 #U143 w: 0 7.76/7.40 U124 w: 0 7.76/7.40 U241 w: x1 + x2 + x3 + 3 7.76/7.40 #p_ w: 0 7.76/7.40 #U271 w: 0 7.76/7.40 #U375 w: 0 7.76/7.40 #U52 w: 0 7.76/7.40 #U103 w: x2 + x3 + 8 7.76/7.40 U374 w: 0 7.76/7.40 #U223 w: 0 7.76/7.40 U12 w: 0 7.76/7.40 U271 w: x2 + 4 7.76/7.40 #U282 w: 0 7.76/7.40 _>_ w: 0 7.76/7.40 U213 w: x1 + x2 + 1 7.76/7.40 U214 w: x1 + x2 7.76/7.40 #isBoolean w: 0 7.76/7.40 #U202 w: 0 7.76/7.40 #U205 w: 0 7.76/7.40 true w: 0 7.76/7.40 U385 w: 0 7.76/7.40 U302 w: 5 7.76/7.40 U54 w: 0 7.76/7.40 U222 w: x2 + x3 + 1 7.76/7.40 U232 w: 7 7.76/7.40 #_<_ w: 0 7.76/7.40 U196 w: 0 7.76/7.40 U205 w: 3 7.76/7.40 #U252 w: 0 7.76/7.40 #U44 w: 2 7.76/7.40 U201 w: x1 7.76/7.40 #U54 w: 0 7.76/7.40 U104 w: 0 7.76/7.40 #4 w: 0 7.76/7.40 #U242 w: 0 7.76/7.40 #U213 w: 0 7.76/7.40 #U42 w: 4 7.76/7.40 #U141 w: 0 7.76/7.40 U252 w: 5 7.76/7.40 #U12 w: 0 7.76/7.40 U141 w: 0 7.76/7.40 #U171 w: 0 7.76/7.40 #U62 w: 0 7.76/7.40 U83 w: 0 7.76/7.40 s_ w: x1 + 6 7.76/7.40 #U301 w: 0 7.76/7.40 #U215 w: 0 7.76/7.40 0 w: 4 7.76/7.40 #U214 w: 0 7.76/7.40 U191 w: x1 + x3 7.76/7.40 U343 w: 0 7.76/7.40 quot w: x1 + x2 + 1 7.76/7.40 U332 w: x3 + 2 7.76/7.40 #U102 w: x2 + x3 + 9 7.76/7.40 U153 w: 0 7.76/7.40 #isBooleanKind w: 0 7.76/7.40 #U361 w: 0 7.76/7.40 isNzNat w: x1 + 1 7.76/7.40 U171 w: 0 7.76/7.40 U202 w: x2 + x3 7.76/7.40 #U211 w: 0 7.76/7.40 #U233 w: 0 7.76/7.40 U372 w: 0 7.76/7.40 U246 w: 6 7.76/7.40 U375 w: 0 7.76/7.40 #U385 w: 0 7.76/7.40 U62 w: 0 7.76/7.40 #U153 w: 0 7.76/7.40 U336 w: 7 7.76/7.40 #3 w: 0 7.76/7.40 #U182 w: 0 7.76/7.40 #d w: x1 + x2 7.76/7.40 U151 w: 0 7.76/7.40 U226 w: 6 7.76/7.40 U334 w: x2 + 8 7.76/7.40 isBooleanKind w: 0 7.76/7.40 #U341 w: 0 7.76/7.40 #U262 w: 0 7.76/7.40 #U192 w: 0 7.76/7.40 #U111 w: 0 7.76/7.40 #U326 w: 0 7.76/7.40 U32 w: 0 7.76/7.40 U195 w: x2 + 12 7.76/7.40 #U221 w: 0 7.76/7.40 #U154 w: 0 7.76/7.40 #U206 w: 0 7.76/7.40 #U371 w: 0 7.76/7.40 #U302 w: 0 7.76/7.40 #U232 w: 0 7.76/7.40 _<_ w: 0 7.76/7.40 #U251 w: 0 7.76/7.40 U154 w: 0 7.76/7.40 U211 w: x1 + x2 + x3 7.76/7.40 U223 w: x1 + x2 + x3 7.76/7.40 #U281 w: 0 7.76/7.40 #U145 w: 0 7.76/7.40 #U343 w: 0 7.76/7.40 U203 w: 1 7.76/7.40 p_ w: x1 + 1 7.76/7.40 isNat w: x1 + 3 7.76/7.40 #U352 w: 0 7.76/7.40 #U216 w: 0 7.76/7.40 U194 w: x1 + 5 7.76/7.40 U251 w: x2 + 4 7.76/7.40 #U291 w: 0 7.76/7.40 #U382 w: 0 7.76/7.40 #U124 w: 0 7.76/7.40 U216 w: 0 7.76/7.40 U52 w: 0 7.76/7.40 U156 w: 0 7.76/7.40 U382 w: 0 7.76/7.40 U61 w: 0 7.76/7.40 #U51 w: 0 7.76/7.40 #5 w: 0 7.76/7.40 #U11 w: 0 7.76/7.40 2 w: 1 7.76/7.40 U31 w: 0 7.76/7.40 U183 w: 6 7.76/7.40 U245 w: x2 + 5 7.76/7.40 U92 w: 0 7.76/7.40 U112 w: 0 7.76/7.40 #U193 w: 0 7.76/7.40 #U196 w: 0 7.76/7.40 U351 w: 0 7.76/7.40 #U335 w: 0 7.76/7.40 #U41 w: 5 7.76/7.40 U323 w: 13 7.76/7.40 #U325 w: 0 7.76/7.40 U102 w: 0 7.76/7.40 equal w: 0 7.76/7.40 #U191 w: 0 7.76/7.40 #U21 w: 9 7.76/7.40 6 w: 5 7.76/7.40 U146 w: 0 7.76/7.40 U373 w: 0 7.76/7.40 U81 w: 0 7.76/7.40 U82 w: 0 7.76/7.40 #U22 w: 2 7.76/7.40 #_>_ w: 1 7.76/7.40 #U112 w: 0 7.76/7.40 tt w: 7 7.76/7.40 #U374 w: 0 7.76/7.40 #quot w: 0 7.76/7.40 U125 w: 0 7.76/7.40 U362 w: 0 7.76/7.40 #U71 w: 0 7.76/7.40 #U84 w: 2 7.76/7.40 #U151 w: 0 7.76/7.40 U321 w: 3 7.76/7.40 #U162 w: 0 7.76/7.40 #1 w: 0 7.76/7.40 #U383 w: 0 7.76/7.40 U22 w: 0 7.76/7.40 U225 w: x2 + 5 7.76/7.40 U51 w: 0 7.76/7.40 #isNatKind w: 0 7.76/7.40 #U161 w: 0 7.76/7.40 U215 w: x1 + 4 7.76/7.40 #U172 w: 0 7.76/7.40 U311 w: x1 + 7 7.76/7.40 U162 w: 0 7.76/7.40 U322 w: x1 + x2 + x3 + 7 7.76/7.40 #U261 w: 0 7.76/7.40 #U203 w: 0 7.76/7.40 #U122 w: 0 7.76/7.40 U53 w: 0 7.76/7.40 U212 w: x1 + x2 7.76/7.40 U41 w: 0 7.76/7.40 #U31 w: 0 7.76/7.40 #U194 w: 0 7.76/7.40 #U332 w: 0 7.76/7.40 #U91 w: 0 7.76/7.40 U233 w: 7 7.76/7.40 U282 w: 5 7.76/7.40 U224 w: x2 + 4 7.76/7.40 #U132 w: 0 7.76/7.40 U121 w: 0 7.76/7.40 #U204 w: 0 7.76/7.40 #U61 w: 0 7.76/7.40 U181 w: x2 + 4 7.76/7.40 U145 w: 0 7.76/7.40 U324 w: x1 7.76/7.40 U331 w: x1 + x2 + x3 7.76/7.40 U122 w: 0 7.76/7.40 #U333 w: 0 7.76/7.40 #gcd w: 0 7.76/7.40 USABLE RULES: { 70 71 96..98 102..104 } 7.76/7.40 Removed DPs: #20 #84 #86 #164 #255 7.76/7.40 Number of SCCs: 4, DPs: 87 7.76/7.40 SCC { #150 #209 #213 #241 #257 #275 } 7.76/7.40 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 7.76/7.40 Finding a loop... failed. 7.76/7.40 EOF