MAYBE Input TRS: 1: U101(tt(),V2) -> U102(isLNat(activate(V2))) 2: U102(tt()) -> tt() 3: U11(tt(),N,XS) -> U12(isLNat(activate(XS)),activate(N),activate(XS)) 4: U111(tt()) -> tt() 5: U12(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS))) 6: U121(tt()) -> tt() 7: U131(tt(),V2) -> U132(isLNat(activate(V2))) 8: U132(tt()) -> tt() 9: U141(tt(),V2) -> U142(isLNat(activate(V2))) 10: U142(tt()) -> tt() 11: U151(tt(),V2) -> U152(isLNat(activate(V2))) 12: U152(tt()) -> tt() 13: U161(tt(),N) -> cons(activate(N),n__natsFrom(s(activate(N)))) 14: U171(tt(),N,XS) -> U172(isLNat(activate(XS)),activate(N),activate(XS)) 15: U172(tt(),N,XS) -> head(afterNth(activate(N),activate(XS))) 16: U181(tt(),Y) -> U182(isLNat(activate(Y)),activate(Y)) 17: U182(tt(),Y) -> activate(Y) 18: U191(tt(),XS) -> pair(nil(),activate(XS)) 19: U201(tt(),N,X,XS) -> U202(isNatural(activate(X)),activate(N),activate(X),activate(XS)) 20: U202(tt(),N,X,XS) -> U203(isLNat(activate(XS)),activate(N),activate(X),activate(XS)) 21: U203(tt(),N,X,XS) -> U204(splitAt(activate(N),activate(XS)),activate(X)) 22: U204(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS) 23: U21(tt(),X,Y) -> U22(isLNat(activate(Y)),activate(X)) 24: U211(tt(),XS) -> U212(isLNat(activate(XS)),activate(XS)) 25: U212(tt(),XS) -> activate(XS) 26: U22(tt(),X) -> activate(X) 27: U221(tt(),N,XS) -> U222(isLNat(activate(XS)),activate(N),activate(XS)) 28: U222(tt(),N,XS) -> fst(splitAt(activate(N),activate(XS))) 29: U31(tt(),N,XS) -> U32(isLNat(activate(XS)),activate(N)) 30: U32(tt(),N) -> activate(N) 31: U41(tt(),V2) -> U42(isLNat(activate(V2))) 32: U42(tt()) -> tt() 33: U51(tt(),V2) -> U52(isLNat(activate(V2))) 34: U52(tt()) -> tt() 35: U61(tt()) -> tt() 36: U71(tt()) -> tt() 37: U81(tt()) -> tt() 38: U91(tt()) -> tt() 39: afterNth(N,XS) -> U11(isNatural(N),N,XS) 40: fst(pair(X,Y)) -> U21(isLNat(X),X,Y) 41: head(cons(N,XS)) -> U31(isNatural(N),N,activate(XS)) 42: isLNat(n__nil()) -> tt() 43: isLNat(n__afterNth(V1,V2)) -> U41(isNatural(activate(V1)),activate(V2)) 44: isLNat(n__cons(V1,V2)) -> U51(isNatural(activate(V1)),activate(V2)) 45: isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1))) 46: isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1))) 47: isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1))) 48: isLNat(n__tail(V1)) -> U91(isLNat(activate(V1))) 49: isLNat(n__take(V1,V2)) -> U101(isNatural(activate(V1)),activate(V2)) 50: isNatural(n__0()) -> tt() 51: isNatural(n__head(V1)) -> U111(isLNat(activate(V1))) 52: isNatural(n__s(V1)) -> U121(isNatural(activate(V1))) 53: isNatural(n__sel(V1,V2)) -> U131(isNatural(activate(V1)),activate(V2)) 54: isPLNat(n__pair(V1,V2)) -> U141(isLNat(activate(V1)),activate(V2)) 55: isPLNat(n__splitAt(V1,V2)) -> U151(isNatural(activate(V1)),activate(V2)) 56: natsFrom(N) -> U161(isNatural(N),N) 57: sel(N,XS) -> U171(isNatural(N),N,XS) 58: snd(pair(X,Y)) -> U181(isLNat(X),Y) 59: splitAt(0(),XS) -> U191(isLNat(XS),XS) 60: splitAt(s(N),cons(X,XS)) -> U201(isNatural(N),N,X,activate(XS)) 61: tail(cons(N,XS)) -> U211(isNatural(N),activate(XS)) 62: take(N,XS) -> U221(isNatural(N),N,XS) 63: natsFrom(X) -> n__natsFrom(X) 64: nil() -> n__nil() 65: afterNth(X1,X2) -> n__afterNth(X1,X2) 66: cons(X1,X2) -> n__cons(X1,X2) 67: fst(X) -> n__fst(X) 68: snd(X) -> n__snd(X) 69: tail(X) -> n__tail(X) 70: take(X1,X2) -> n__take(X1,X2) 71: 0() -> n__0() 72: head(X) -> n__head(X) 73: s(X) -> n__s(X) 74: sel(X1,X2) -> n__sel(X1,X2) 75: pair(X1,X2) -> n__pair(X1,X2) 76: splitAt(X1,X2) -> n__splitAt(X1,X2) 77: activate(n__natsFrom(X)) -> natsFrom(X) 78: activate(n__nil()) -> nil() 79: activate(n__afterNth(X1,X2)) -> afterNth(X1,X2) 80: activate(n__cons(X1,X2)) -> cons(X1,X2) 81: activate(n__fst(X)) -> fst(X) 82: activate(n__snd(X)) -> snd(X) 83: activate(n__tail(X)) -> tail(X) 84: activate(n__take(X1,X2)) -> take(X1,X2) 85: activate(n__0()) -> 0() 86: activate(n__head(X)) -> head(X) 87: activate(n__s(X)) -> s(X) 88: activate(n__sel(X1,X2)) -> sel(X1,X2) 89: activate(n__pair(X1,X2)) -> pair(X1,X2) 90: activate(n__splitAt(X1,X2)) -> splitAt(X1,X2) 91: activate(X) -> X Number of strict rules: 91 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #activate(n__head(X)) -> #head(X) #2: #isLNat(n__afterNth(V1,V2)) -> #U41(isNatural(activate(V1)),activate(V2)) #3: #isLNat(n__afterNth(V1,V2)) -> #isNatural(activate(V1)) #4: #isLNat(n__afterNth(V1,V2)) -> #activate(V1) #5: #isLNat(n__afterNth(V1,V2)) -> #activate(V2) #6: #U31(tt(),N,XS) -> #U32(isLNat(activate(XS)),activate(N)) #7: #U31(tt(),N,XS) -> #isLNat(activate(XS)) #8: #U31(tt(),N,XS) -> #activate(XS) #9: #U31(tt(),N,XS) -> #activate(N) #10: #activate(n__tail(X)) -> #tail(X) #11: #isLNat(n__natsFrom(V1)) -> #U71(isNatural(activate(V1))) #12: #isLNat(n__natsFrom(V1)) -> #isNatural(activate(V1)) #13: #isLNat(n__natsFrom(V1)) -> #activate(V1) #14: #head(cons(N,XS)) -> #U31(isNatural(N),N,activate(XS)) #15: #head(cons(N,XS)) -> #isNatural(N) #16: #head(cons(N,XS)) -> #activate(XS) #17: #isLNat(n__snd(V1)) -> #U81(isPLNat(activate(V1))) #18: #isLNat(n__snd(V1)) -> #isPLNat(activate(V1)) #19: #isLNat(n__snd(V1)) -> #activate(V1) #20: #isNatural(n__sel(V1,V2)) -> #U131(isNatural(activate(V1)),activate(V2)) #21: #isNatural(n__sel(V1,V2)) -> #isNatural(activate(V1)) #22: #isNatural(n__sel(V1,V2)) -> #activate(V1) #23: #isNatural(n__sel(V1,V2)) -> #activate(V2) #24: #isLNat(n__tail(V1)) -> #U91(isLNat(activate(V1))) #25: #isLNat(n__tail(V1)) -> #isLNat(activate(V1)) #26: #isLNat(n__tail(V1)) -> #activate(V1) #27: #snd(pair(X,Y)) -> #U181(isLNat(X),Y) #28: #snd(pair(X,Y)) -> #isLNat(X) #29: #tail(cons(N,XS)) -> #U211(isNatural(N),activate(XS)) #30: #tail(cons(N,XS)) -> #isNatural(N) #31: #tail(cons(N,XS)) -> #activate(XS) #32: #splitAt(0(),XS) -> #U191(isLNat(XS),XS) #33: #splitAt(0(),XS) -> #isLNat(XS) #34: #isPLNat(n__splitAt(V1,V2)) -> #U151(isNatural(activate(V1)),activate(V2)) #35: #isPLNat(n__splitAt(V1,V2)) -> #isNatural(activate(V1)) #36: #isPLNat(n__splitAt(V1,V2)) -> #activate(V1) #37: #isPLNat(n__splitAt(V1,V2)) -> #activate(V2) #38: #fst(pair(X,Y)) -> #U21(isLNat(X),X,Y) #39: #fst(pair(X,Y)) -> #isLNat(X) #40: #activate(n__splitAt(X1,X2)) -> #splitAt(X1,X2) #41: #isNatural(n__head(V1)) -> #U111(isLNat(activate(V1))) #42: #isNatural(n__head(V1)) -> #isLNat(activate(V1)) #43: #isNatural(n__head(V1)) -> #activate(V1) #44: #U161(tt(),N) -> #cons(activate(N),n__natsFrom(s(activate(N)))) #45: #U161(tt(),N) -> #activate(N) #46: #U161(tt(),N) -> #s(activate(N)) #47: #U161(tt(),N) -> #activate(N) #48: #U141(tt(),V2) -> #U142(isLNat(activate(V2))) #49: #U141(tt(),V2) -> #isLNat(activate(V2)) #50: #U141(tt(),V2) -> #activate(V2) #51: #U151(tt(),V2) -> #U152(isLNat(activate(V2))) #52: #U151(tt(),V2) -> #isLNat(activate(V2)) #53: #U151(tt(),V2) -> #activate(V2) #54: #sel(N,XS) -> #U171(isNatural(N),N,XS) #55: #sel(N,XS) -> #isNatural(N) #56: #U211(tt(),XS) -> #U212(isLNat(activate(XS)),activate(XS)) #57: #U211(tt(),XS) -> #isLNat(activate(XS)) #58: #U211(tt(),XS) -> #activate(XS) #59: #U211(tt(),XS) -> #activate(XS) #60: #U21(tt(),X,Y) -> #U22(isLNat(activate(Y)),activate(X)) #61: #U21(tt(),X,Y) -> #isLNat(activate(Y)) #62: #U21(tt(),X,Y) -> #activate(Y) #63: #U21(tt(),X,Y) -> #activate(X) #64: #activate(n__fst(X)) -> #fst(X) #65: #activate(n__nil()) -> #nil() #66: #isLNat(n__fst(V1)) -> #U61(isPLNat(activate(V1))) #67: #isLNat(n__fst(V1)) -> #isPLNat(activate(V1)) #68: #isLNat(n__fst(V1)) -> #activate(V1) #69: #U41(tt(),V2) -> #U42(isLNat(activate(V2))) #70: #U41(tt(),V2) -> #isLNat(activate(V2)) #71: #U41(tt(),V2) -> #activate(V2) #72: #activate(n__afterNth(X1,X2)) -> #afterNth(X1,X2) #73: #natsFrom(N) -> #U161(isNatural(N),N) #74: #natsFrom(N) -> #isNatural(N) #75: #activate(n__pair(X1,X2)) -> #pair(X1,X2) #76: #activate(n__snd(X)) -> #snd(X) #77: #U171(tt(),N,XS) -> #U172(isLNat(activate(XS)),activate(N),activate(XS)) #78: #U171(tt(),N,XS) -> #isLNat(activate(XS)) #79: #U171(tt(),N,XS) -> #activate(XS) #80: #U171(tt(),N,XS) -> #activate(N) #81: #U171(tt(),N,XS) -> #activate(XS) #82: #take(N,XS) -> #U221(isNatural(N),N,XS) #83: #take(N,XS) -> #isNatural(N) #84: #U32(tt(),N) -> #activate(N) #85: #isNatural(n__s(V1)) -> #U121(isNatural(activate(V1))) #86: #isNatural(n__s(V1)) -> #isNatural(activate(V1)) #87: #isNatural(n__s(V1)) -> #activate(V1) #88: #isLNat(n__take(V1,V2)) -> #U101(isNatural(activate(V1)),activate(V2)) #89: #isLNat(n__take(V1,V2)) -> #isNatural(activate(V1)) #90: #isLNat(n__take(V1,V2)) -> #activate(V1) #91: #isLNat(n__take(V1,V2)) -> #activate(V2) #92: #U212(tt(),XS) -> #activate(XS) #93: #U202(tt(),N,X,XS) -> #U203(isLNat(activate(XS)),activate(N),activate(X),activate(XS)) #94: #U202(tt(),N,X,XS) -> #isLNat(activate(XS)) #95: #U202(tt(),N,X,XS) -> #activate(XS) #96: #U202(tt(),N,X,XS) -> #activate(N) #97: #U202(tt(),N,X,XS) -> #activate(X) #98: #U202(tt(),N,X,XS) -> #activate(XS) #99: #activate(n__sel(X1,X2)) -> #sel(X1,X2) #100: #U131(tt(),V2) -> #U132(isLNat(activate(V2))) #101: #U131(tt(),V2) -> #isLNat(activate(V2)) #102: #U131(tt(),V2) -> #activate(V2) #103: #afterNth(N,XS) -> #U11(isNatural(N),N,XS) #104: #afterNth(N,XS) -> #isNatural(N) #105: #U51(tt(),V2) -> #U52(isLNat(activate(V2))) #106: #U51(tt(),V2) -> #isLNat(activate(V2)) #107: #U51(tt(),V2) -> #activate(V2) #108: #U12(tt(),N,XS) -> #snd(splitAt(activate(N),activate(XS))) #109: #U12(tt(),N,XS) -> #splitAt(activate(N),activate(XS)) #110: #U12(tt(),N,XS) -> #activate(N) #111: #U12(tt(),N,XS) -> #activate(XS) #112: #isLNat(n__cons(V1,V2)) -> #U51(isNatural(activate(V1)),activate(V2)) #113: #isLNat(n__cons(V1,V2)) -> #isNatural(activate(V1)) #114: #isLNat(n__cons(V1,V2)) -> #activate(V1) #115: #isLNat(n__cons(V1,V2)) -> #activate(V2) #116: #U222(tt(),N,XS) -> #fst(splitAt(activate(N),activate(XS))) #117: #U222(tt(),N,XS) -> #splitAt(activate(N),activate(XS)) #118: #U222(tt(),N,XS) -> #activate(N) #119: #U222(tt(),N,XS) -> #activate(XS) #120: #U204(pair(YS,ZS),X) -> #pair(cons(activate(X),YS),ZS) #121: #U204(pair(YS,ZS),X) -> #cons(activate(X),YS) #122: #U204(pair(YS,ZS),X) -> #activate(X) #123: #activate(n__take(X1,X2)) -> #take(X1,X2) #124: #activate(n__s(X)) -> #s(X) #125: #U221(tt(),N,XS) -> #U222(isLNat(activate(XS)),activate(N),activate(XS)) #126: #U221(tt(),N,XS) -> #isLNat(activate(XS)) #127: #U221(tt(),N,XS) -> #activate(XS) #128: #U221(tt(),N,XS) -> #activate(N) #129: #U221(tt(),N,XS) -> #activate(XS) #130: #splitAt(s(N),cons(X,XS)) -> #U201(isNatural(N),N,X,activate(XS)) #131: #splitAt(s(N),cons(X,XS)) -> #isNatural(N) #132: #splitAt(s(N),cons(X,XS)) -> #activate(XS) #133: #U182(tt(),Y) -> #activate(Y) #134: #U201(tt(),N,X,XS) -> #U202(isNatural(activate(X)),activate(N),activate(X),activate(XS)) #135: #U201(tt(),N,X,XS) -> #isNatural(activate(X)) #136: #U201(tt(),N,X,XS) -> #activate(X) #137: #U201(tt(),N,X,XS) -> #activate(N) #138: #U201(tt(),N,X,XS) -> #activate(X) #139: #U201(tt(),N,X,XS) -> #activate(XS) #140: #U22(tt(),X) -> #activate(X) #141: #activate(n__0()) -> #0() #142: #U203(tt(),N,X,XS) -> #U204(splitAt(activate(N),activate(XS)),activate(X)) #143: #U203(tt(),N,X,XS) -> #splitAt(activate(N),activate(XS)) #144: #U203(tt(),N,X,XS) -> #activate(N) #145: #U203(tt(),N,X,XS) -> #activate(XS) #146: #U203(tt(),N,X,XS) -> #activate(X) #147: #U181(tt(),Y) -> #U182(isLNat(activate(Y)),activate(Y)) #148: #U181(tt(),Y) -> #isLNat(activate(Y)) #149: #U181(tt(),Y) -> #activate(Y) #150: #U181(tt(),Y) -> #activate(Y) #151: #U11(tt(),N,XS) -> #U12(isLNat(activate(XS)),activate(N),activate(XS)) #152: #U11(tt(),N,XS) -> #isLNat(activate(XS)) #153: #U11(tt(),N,XS) -> #activate(XS) #154: #U11(tt(),N,XS) -> #activate(N) #155: #U11(tt(),N,XS) -> #activate(XS) #156: #activate(n__natsFrom(X)) -> #natsFrom(X) #157: #U101(tt(),V2) -> #U102(isLNat(activate(V2))) #158: #U101(tt(),V2) -> #isLNat(activate(V2)) #159: #U101(tt(),V2) -> #activate(V2) #160: #isPLNat(n__pair(V1,V2)) -> #U141(isLNat(activate(V1)),activate(V2)) #161: #isPLNat(n__pair(V1,V2)) -> #isLNat(activate(V1)) #162: #isPLNat(n__pair(V1,V2)) -> #activate(V1) #163: #isPLNat(n__pair(V1,V2)) -> #activate(V2) #164: #U172(tt(),N,XS) -> #head(afterNth(activate(N),activate(XS))) #165: #U172(tt(),N,XS) -> #afterNth(activate(N),activate(XS)) #166: #U172(tt(),N,XS) -> #activate(N) #167: #U172(tt(),N,XS) -> #activate(XS) #168: #activate(n__cons(X1,X2)) -> #cons(X1,X2) #169: #U191(tt(),XS) -> #pair(nil(),activate(XS)) #170: #U191(tt(),XS) -> #nil() #171: #U191(tt(),XS) -> #activate(XS) Number of SCCs: 1, DPs: 148 SCC { #1..10 #12..16 #18..23 #25..40 #42 #43 #45 #47 #49 #50 #52..64 #67 #68 #70..74 #76..84 #86..99 #101..104 #106..119 #122 #123 #125..140 #142..156 #158..167 #171 } POLO(Sum)... POLO(max)... succeeded. #U201 w: max(x1 + 27, x2 + 30, x3 + 32, x4 + 28) U204 w: max(x1, x2 + 17) #0 w: 0 #U32 w: max(x2 + 8) U21 w: max(x1 + 9, x2 + 14, x3 + 1) U161 w: max(x2 + 4) U182 w: max(x2 + 9) U11 w: max(x1 + 26, x2 + 29, x3 + 31) #cons w: 0 s w: x1 n__pair w: max(x1 + 13, x2 + 8) #U142 w: 0 #take w: max(x1 + 34330, x2 + 34330) U142 w: 4 #U152 w: 0 #U181 w: max(x1 + 11, x2 + 10) isPLNat w: x1 + 1 U42 w: x1 U91 w: x1 U221 w: max(x1, x2 + 7597, x3 + 7598) #U101 w: max(x1 + 32418, x2 + 11470) activate w: x1 take w: max(x1 + 34325, x2 + 34324) U71 w: 4 #U81 w: 0 U131 w: max(x1) #U222 w: max(x1 + 34327, x2 + 1799, x3 + 1401) #U212 w: max(x1 + 6, x2 + 9) U101 w: max(x2 + 34325) pair w: max(x1 + 13, x2 + 8) fst w: x1 + 1 U111 w: 4 U132 w: 4 #activate w: x1 + 7 U152 w: 4 natsFrom w: x1 + 4 #head w: x1 + 11 #U121 w: 0 U172 w: max(x2 + 34, x3 + 36) splitAt w: max(x1 + 27, x2 + 22) #U131 w: max(x2 + 34) #fst w: x1 + 4 n__nil w: 7 #U52 w: 0 U12 w: max(x2 + 29, x3 + 31) #U202 w: max(x1 + 28, x2 + 30, x3 + 32, x4 + 28) n__natsFrom w: x1 + 4 isNatural w: 4 U222 w: max(x1 + 7597, x2 + 3774, x3 + 23) n__snd w: x1 + 1 U201 w: max(x2 + 27, x3 + 20, x4 + 22) n__s w: x1 n__splitAt w: max(x1 + 27, x2 + 22) #U42 w: 0 #U141 w: max(x1 + 20, x2 + 16) #U12 w: max(x1 + 32, x2 + 31, x3 + 31) U141 w: max(x1 + 9, x2 + 4) #U171 w: max(x1 + 40, x2 + 46, x3 + 48) tail w: x1 + 4 0 w: 1 U191 w: max(x2 + 21) n__take w: max(x1 + 34325, x2 + 34324) #sel w: max(x1 + 47, x2 + 49) #U102 w: 0 U171 w: max(x2 + 34, x3 + 42) #isLNat w: x1 + 9 U202 w: max(x1, x2 + 27, x3 + 17, x4 + 22) sel w: max(x1 + 44, x2 + 43) #s w: 0 afterNth w: max(x1 + 29, x2 + 31) n__cons w: max(x1 + 4, x2) #U211 w: max(x1 + 10, x2 + 10) #isPLNat w: x1 + 9 nil w: 7 isLNat w: x1 + 1 n__sel w: max(x1 + 44, x2 + 43) #tail w: x1 + 10 #U182 w: max(x2 + 8) #splitAt w: max(x1 + 30, x2 + 28) U151 w: max(x1 + 22) #nil w: 0 n__tail w: x1 + 4 #afterNth w: max(x1 + 35, x2 + 35) #U111 w: 0 U32 w: max(x2 + 4) #U221 w: max(x1 + 34325, x2 + 1800, x3 + 34329) n__0 w: 1 n__afterNth w: max(x1 + 29, x2 + 31) U211 w: max(x1 + 1, x2 + 4) U203 w: max(x1 + 17, x2 + 27, x3 + 17, x4 + 22) U52 w: x1 U61 w: x1 #U51 w: max(x1 + 9, x2 + 9) n__fst w: x1 + 1 #U11 w: max(x1 + 28, x2 + 34, x3 + 34) U31 w: max(x2 + 9) head w: x1 + 5 #snd w: x1 + 3 #U41 w: max(x1 + 6, x2 + 32) cons w: max(x1 + 4, x2) #natsFrom w: x1 + 9 U102 w: x1 snd w: x1 + 1 #U191 w: max(x2 + 24) #U21 w: max(x2 + 11, x3 + 11) U81 w: x1 #U22 w: max(x1 + 4, x2 + 9) tt w: 4 #U71 w: 0 #U151 w: max(x2 + 13) #isNatural w: x1 + 8 #pair w: 0 U22 w: max(x1, x2 + 14) n__head w: x1 + 5 U51 w: max(x2 + 1) #U161 w: max(x1 + 4, x2 + 8) #U172 w: max(x1 + 44, x2 + 43, x3 + 43) #U203 w: max(x1 + 27, x2 + 30, x3 + 32, x4 + 28) U212 w: max(x2 + 3) U41 w: max(x2 + 32) #U31 w: max(x1 + 6, x2 + 10, x3 + 10) #U91 w: 0 #U132 w: 0 U121 w: 4 #U61 w: 0 #U204 w: max(x1, x2 + 26) U181 w: max(x1 + 12, x2 + 9) USABLE RULES: { 1..91 } Removed DPs: #1..10 #12..16 #18..23 #25..28 #30..40 #42 #43 #45 #47 #49 #50 #52..64 #67 #68 #70..74 #76..84 #87..92 #94..99 #101..104 #107..111 #113..119 #122 #123 #125..129 #131..133 #135..140 #142 #144..156 #158..167 #171 Number of SCCs: 3, DPs: 7 SCC { #86 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #U201 s: [3,1] p: 0 w: max(x1 + 1, x3 + 1) U204 s: [] p: 6 w: max(x1, x2 + 111961) #0 s: [] p: 0 w: 0 #U32 s: [2,1] p: 0 w: x1 + x2 + 1 U21 s: [] p: 3 w: max(x2 + 55981) U161 s: [2] p: 5 w: max(x2 + 55979) U182 s: [2] p: 6 w: max(x2) U11 s: [] p: 8 w: max(x1 + 111968, x3 + 167946) #cons s: [] p: 0 w: max(x2 + 1) s s: [1] p: 0 w: x1 n__pair s: [] p: 4 w: max(x1 + 55981, x2 + 55980) #U142 s: [] p: 0 w: 1 #take s: [1] p: 0 w: x1 + 1 U142 s: [] p: 12 w: 1 #U152 s: [] p: 0 w: 1 #U181 s: 1 isPLNat s: [] p: 1 w: 55978 U42 s: [] p: 6 w: 55977 U91 s: [] p: 11 w: 55976 U221 s: [] p: 14 w: max(x1 + 111975, x2 + 167951, x3 + 167951) #U101 s: [2,1] p: 0 w: x1 + x2 + 1 activate s: 1 take s: [] p: 15 w: x1 + x2 + 167954 U71 s: [] p: 10 w: 55976 #U81 s: [] p: 0 w: 1 U131 s: [] p: 0 w: 55977 #U222 s: [3] p: 0 w: x3 + 1 #U212 s: [2,1] p: 0 w: x1 + x2 + 1 U101 s: [] p: 10 w: x1 + 111971 pair s: [] p: 4 w: max(x1 + 55981, x2 + 55980) fst s: [1] p: 2 w: x1 U111 s: [] p: 0 w: 55977 U132 s: [] p: 10 w: 55976 #activate s: [] p: 0 w: 1 U152 s: [] p: 11 w: 167950 natsFrom s: [1] p: 7 w: x1 + 55979 #head s: [] p: 0 w: 1 #U121 s: 1 U172 s: [] p: 10 w: max(x1, x2 + 167948, x3 + 167948) splitAt s: [2] p: 12 w: max(x2 + 111965) #U131 s: [] p: 0 w: x2 + 1 #fst s: [] p: 0 w: 1 n__nil s: [] p: 6 w: 1 #U52 s: [] p: 0 w: 1 U12 s: [] p: 6 w: max(x3 + 167945) #U202 s: [1,4] p: 0 w: max(x1 + 1, x3 + 1, x4 + 1) n__natsFrom s: [1] p: 7 w: x1 + 55979 isNatural s: [] p: 0 w: 55978 U222 s: [] p: 13 w: max(x3 + 111966) n__snd s: [1] p: 1 w: x1 + 55979 U201 s: [4] p: 11 w: max(x3 + 111964, x4 + 111965) n__s s: [1] p: 0 w: x1 n__splitAt s: [2] p: 12 w: max(x2 + 111965) #U42 s: [] p: 0 w: 1 #U141 s: [1,2] p: 0 w: x1 + x2 + 1 #U12 s: 1 U141 s: [2] p: 11 w: max(x1 + 111975, x2 + 167951) #U171 s: [2,3,1] p: 0 w: x1 + x2 + x3 + 1 tail s: [1] p: 0 w: x1 + 167952 0 s: [] p: 11 w: 55975 U191 s: [2] p: 12 w: max(x2 + 55983) n__take s: [] p: 15 w: x1 + x2 + 167954 #sel s: [1,2] p: 0 w: x1 + x2 + 1 #U102 s: [] p: 0 w: 1 U171 s: [3,1] p: 10 w: max(x1 + 111973, x2 + 167951, x3 + 167951) #isLNat s: [] p: 0 w: 1 U202 s: [] p: 11 w: max(x3 + 111963, x4 + 111965) sel s: [] p: 11 w: x1 + x2 + 167952 #s s: [] p: 0 w: 1 afterNth s: [] p: 8 w: max(x2 + 167947) n__cons s: [] p: 5 w: max(x1 + 55979, x2) #U211 s: [2,1] p: 0 w: max(x1 + 1, x2 + 1) #isPLNat s: [] p: 0 w: 1 nil s: [] p: 6 w: 1 isLNat s: [] p: 10 w: 167950 n__sel s: [] p: 11 w: x1 + x2 + 167952 #tail s: 1 #U182 s: 1 #splitAt s: 1 U151 s: [] p: 2 w: max(x1 + 111975) #nil s: [] p: 0 w: 0 n__tail s: [1] p: 0 w: x1 + 167952 #afterNth s: 2 #U111 s: [] p: 0 w: 1 U32 s: [2] p: 7 w: max(x2 + 26815) #U221 s: [3,2,1] p: 0 w: x1 + x2 + x3 + 1 n__0 s: [] p: 11 w: 55975 n__afterNth s: [] p: 8 w: max(x2 + 167947) U211 s: [2] p: 11 w: max(x2 + 167951) U203 s: [4,3] p: 7 w: max(x3 + 111962, x4 + 111965) U52 s: [] p: 0 w: 55977 U61 s: [] p: 10 w: 55976 #U51 s: [1,2] p: 0 w: max(x1 + 1, x2 + 1) n__fst s: [1] p: 2 w: x1 #U11 s: [2] p: 0 w: x2 + 1 U31 s: [] p: 9 w: max(x2 + 26816) head s: [] p: 8 w: x1 #snd s: [] p: 0 w: 1 #U41 s: [1,2] p: 0 w: x1 + x2 + 1 cons s: [] p: 5 w: max(x1 + 55979, x2) #natsFrom s: 1 U102 s: [] p: 10 w: 55976 snd s: [1] p: 1 w: x1 + 55979 #U191 s: [1,2] p: 0 w: x1 + x2 + 1 #U21 s: [2,3] p: 0 w: x2 + x3 + 1 U81 s: [] p: 9 w: 167950 #U22 s: [1,2] p: 0 w: x1 + x2 + 1 tt s: [] p: 10 w: 55976 #U71 s: [] p: 0 w: 1 #U151 s: 2 #isNatural s: [1] p: 0 w: x1 + 1 #pair s: [] p: 0 w: max(x2 + 1) U22 s: [2] p: 2 w: max(x2 + 55981) n__head s: [] p: 8 w: x1 U51 s: [1] p: 0 w: max(x1 + 2) #U161 s: [1] p: 0 w: x1 + 1 #U172 s: [3,2,1] p: 0 w: x1 + x2 + x3 + 1 #U203 s: [3,1] p: 0 w: max(x1 + 1, x2 + 1, x3 + 1, x4 + 1) U212 s: [] p: 11 w: max(x2 + 9643) U41 s: [] p: 6 w: max(x1 + 111970) #U31 s: [] p: 0 w: x1 + x3 + 1 #U91 s: [] p: 0 w: 1 #U132 s: 1 U121 s: 1 #U61 s: 1 #U204 s: [1,2] p: 0 w: x1 + x2 + 1 U181 s: [] p: 3 w: max(x2 + 977) USABLE RULES: { 1..8 13..53 56..91 } Removed DPs: #86 Number of SCCs: 2, DPs: 6 SCC { #106 #112 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.