/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: U101(tt(),V1,V2) -> U102(isNatural(activate(V1)),activate(V2)) 2: U102(tt(),V2) -> U103(isLNat(activate(V2))) 3: U103(tt()) -> tt() 4: U11(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS))) 5: U111(tt(),V1) -> U112(isLNat(activate(V1))) 6: U112(tt()) -> tt() 7: U121(tt(),V1) -> U122(isNatural(activate(V1))) 8: U122(tt()) -> tt() 9: U131(tt(),V1,V2) -> U132(isNatural(activate(V1)),activate(V2)) 10: U132(tt(),V2) -> U133(isLNat(activate(V2))) 11: U133(tt()) -> tt() 12: U141(tt(),V1,V2) -> U142(isLNat(activate(V1)),activate(V2)) 13: U142(tt(),V2) -> U143(isLNat(activate(V2))) 14: U143(tt()) -> tt() 15: U151(tt(),V1,V2) -> U152(isNatural(activate(V1)),activate(V2)) 16: U152(tt(),V2) -> U153(isLNat(activate(V2))) 17: U153(tt()) -> tt() 18: U161(tt(),N) -> cons(activate(N),n__natsFrom(n__s(activate(N)))) 19: U171(tt(),N,XS) -> head(afterNth(activate(N),activate(XS))) 20: U181(tt(),Y) -> activate(Y) 21: U191(tt(),XS) -> pair(nil(),activate(XS)) 22: U201(tt(),N,X,XS) -> U202(splitAt(activate(N),activate(XS)),activate(X)) 23: U202(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS) 24: U21(tt(),X) -> activate(X) 25: U211(tt(),XS) -> activate(XS) 26: U221(tt(),N,XS) -> fst(splitAt(activate(N),activate(XS))) 27: U31(tt(),N) -> activate(N) 28: U41(tt(),V1,V2) -> U42(isNatural(activate(V1)),activate(V2)) 29: U42(tt(),V2) -> U43(isLNat(activate(V2))) 30: U43(tt()) -> tt() 31: U51(tt(),V1,V2) -> U52(isNatural(activate(V1)),activate(V2)) 32: U52(tt(),V2) -> U53(isLNat(activate(V2))) 33: U53(tt()) -> tt() 34: U61(tt(),V1) -> U62(isPLNat(activate(V1))) 35: U62(tt()) -> tt() 36: U71(tt(),V1) -> U72(isNatural(activate(V1))) 37: U72(tt()) -> tt() 38: U81(tt(),V1) -> U82(isPLNat(activate(V1))) 39: U82(tt()) -> tt() 40: U91(tt(),V1) -> U92(isLNat(activate(V1))) 41: U92(tt()) -> tt() 42: afterNth(N,XS) -> U11(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) 43: and(tt(),X) -> activate(X) 44: fst(pair(X,Y)) -> U21(and(and(isLNat(X),n__isLNatKind(X)),n__and(n__isLNat(Y),n__isLNatKind(Y))),X) 45: head(cons(N,XS)) -> U31(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))),N) 46: isLNat(n__nil()) -> tt() 47: isLNat(n__afterNth(V1,V2)) -> U41(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) 48: isLNat(n__cons(V1,V2)) -> U51(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) 49: isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)),activate(V1)) 50: isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)),activate(V1)) 51: isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)),activate(V1)) 52: isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)),activate(V1)) 53: isLNat(n__take(V1,V2)) -> U101(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) 54: isLNatKind(n__nil()) -> tt() 55: isLNatKind(n__afterNth(V1,V2)) -> and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) 56: isLNatKind(n__cons(V1,V2)) -> and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) 57: isLNatKind(n__fst(V1)) -> isPLNatKind(activate(V1)) 58: isLNatKind(n__natsFrom(V1)) -> isNaturalKind(activate(V1)) 59: isLNatKind(n__snd(V1)) -> isPLNatKind(activate(V1)) 60: isLNatKind(n__tail(V1)) -> isLNatKind(activate(V1)) 61: isLNatKind(n__take(V1,V2)) -> and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) 62: isNatural(n__0()) -> tt() 63: isNatural(n__head(V1)) -> U111(isLNatKind(activate(V1)),activate(V1)) 64: isNatural(n__s(V1)) -> U121(isNaturalKind(activate(V1)),activate(V1)) 65: isNatural(n__sel(V1,V2)) -> U131(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) 66: isNaturalKind(n__0()) -> tt() 67: isNaturalKind(n__head(V1)) -> isLNatKind(activate(V1)) 68: isNaturalKind(n__s(V1)) -> isNaturalKind(activate(V1)) 69: isNaturalKind(n__sel(V1,V2)) -> and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) 70: isPLNat(n__pair(V1,V2)) -> U141(and(isLNatKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) 71: isPLNat(n__splitAt(V1,V2)) -> U151(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) 72: isPLNatKind(n__pair(V1,V2)) -> and(isLNatKind(activate(V1)),n__isLNatKind(activate(V2))) 73: isPLNatKind(n__splitAt(V1,V2)) -> and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) 74: natsFrom(N) -> U161(and(isNatural(N),n__isNaturalKind(N)),N) 75: sel(N,XS) -> U171(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) 76: snd(pair(X,Y)) -> U181(and(and(isLNat(X),n__isLNatKind(X)),n__and(n__isLNat(Y),n__isLNatKind(Y))),Y) 77: splitAt(0(),XS) -> U191(and(isLNat(XS),n__isLNatKind(XS)),XS) 78: splitAt(s(N),cons(X,XS)) -> U201(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__and(n__isNatural(X),n__isNaturalKind(X)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS))))),N,X,activate(XS)) 79: tail(cons(N,XS)) -> U211(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))),activate(XS)) 80: take(N,XS) -> U221(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) 81: natsFrom(X) -> n__natsFrom(X) 82: s(X) -> n__s(X) 83: isNaturalKind(X) -> n__isNaturalKind(X) 84: and(X1,X2) -> n__and(X1,X2) 85: isLNat(X) -> n__isLNat(X) 86: isLNatKind(X) -> n__isLNatKind(X) 87: nil() -> n__nil() 88: afterNth(X1,X2) -> n__afterNth(X1,X2) 89: cons(X1,X2) -> n__cons(X1,X2) 90: fst(X) -> n__fst(X) 91: snd(X) -> n__snd(X) 92: tail(X) -> n__tail(X) 93: take(X1,X2) -> n__take(X1,X2) 94: 0() -> n__0() 95: head(X) -> n__head(X) 96: sel(X1,X2) -> n__sel(X1,X2) 97: pair(X1,X2) -> n__pair(X1,X2) 98: splitAt(X1,X2) -> n__splitAt(X1,X2) 99: isNatural(X) -> n__isNatural(X) 100: activate(n__natsFrom(X)) -> natsFrom(activate(X)) 101: activate(n__s(X)) -> s(activate(X)) 102: activate(n__isNaturalKind(X)) -> isNaturalKind(X) 103: activate(n__and(X1,X2)) -> and(activate(X1),X2) 104: activate(n__isLNat(X)) -> isLNat(X) 105: activate(n__isLNatKind(X)) -> isLNatKind(X) 106: activate(n__nil()) -> nil() 107: activate(n__afterNth(X1,X2)) -> afterNth(activate(X1),activate(X2)) 108: activate(n__cons(X1,X2)) -> cons(activate(X1),X2) 109: activate(n__fst(X)) -> fst(activate(X)) 110: activate(n__snd(X)) -> snd(activate(X)) 111: activate(n__tail(X)) -> tail(activate(X)) 112: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) 113: activate(n__0()) -> 0() 114: activate(n__head(X)) -> head(activate(X)) 115: activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2)) 116: activate(n__pair(X1,X2)) -> pair(activate(X1),activate(X2)) 117: activate(n__splitAt(X1,X2)) -> splitAt(activate(X1),activate(X2)) 118: activate(n__isNatural(X)) -> isNatural(X) 119: activate(X) -> X Number of strict rules: 119 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U102(tt(),V2) -> #U103(isLNat(activate(V2))) #2: #U102(tt(),V2) -> #isLNat(activate(V2)) #3: #U102(tt(),V2) -> #activate(V2) #4: #and(tt(),X) -> #activate(X) #5: #U42(tt(),V2) -> #U43(isLNat(activate(V2))) #6: #U42(tt(),V2) -> #isLNat(activate(V2)) #7: #U42(tt(),V2) -> #activate(V2) #8: #afterNth(N,XS) -> #U11(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) #9: #afterNth(N,XS) -> #and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))) #10: #afterNth(N,XS) -> #and(isNatural(N),n__isNaturalKind(N)) #11: #afterNth(N,XS) -> #isNatural(N) #12: #activate(n__sel(X1,X2)) -> #sel(activate(X1),activate(X2)) #13: #activate(n__sel(X1,X2)) -> #activate(X1) #14: #activate(n__sel(X1,X2)) -> #activate(X2) #15: #activate(n__head(X)) -> #head(activate(X)) #16: #activate(n__head(X)) -> #activate(X) #17: #isPLNatKind(n__splitAt(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #18: #isPLNatKind(n__splitAt(V1,V2)) -> #isNaturalKind(activate(V1)) #19: #isPLNatKind(n__splitAt(V1,V2)) -> #activate(V1) #20: #isPLNatKind(n__splitAt(V1,V2)) -> #activate(V2) #21: #isLNat(n__afterNth(V1,V2)) -> #U41(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) #22: #isLNat(n__afterNth(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #23: #isLNat(n__afterNth(V1,V2)) -> #isNaturalKind(activate(V1)) #24: #isLNat(n__afterNth(V1,V2)) -> #activate(V1) #25: #isLNat(n__afterNth(V1,V2)) -> #activate(V2) #26: #isLNat(n__afterNth(V1,V2)) -> #activate(V1) #27: #isLNat(n__afterNth(V1,V2)) -> #activate(V2) #28: #isLNat(n__take(V1,V2)) -> #U101(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) #29: #isLNat(n__take(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #30: #isLNat(n__take(V1,V2)) -> #isNaturalKind(activate(V1)) #31: #isLNat(n__take(V1,V2)) -> #activate(V1) #32: #isLNat(n__take(V1,V2)) -> #activate(V2) #33: #isLNat(n__take(V1,V2)) -> #activate(V1) #34: #isLNat(n__take(V1,V2)) -> #activate(V2) #35: #isPLNat(n__splitAt(V1,V2)) -> #U151(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) #36: #isPLNat(n__splitAt(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #37: #isPLNat(n__splitAt(V1,V2)) -> #isNaturalKind(activate(V1)) #38: #isPLNat(n__splitAt(V1,V2)) -> #activate(V1) #39: #isPLNat(n__splitAt(V1,V2)) -> #activate(V2) #40: #isPLNat(n__splitAt(V1,V2)) -> #activate(V1) #41: #isPLNat(n__splitAt(V1,V2)) -> #activate(V2) #42: #isLNat(n__cons(V1,V2)) -> #U51(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) #43: #isLNat(n__cons(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #44: #isLNat(n__cons(V1,V2)) -> #isNaturalKind(activate(V1)) #45: #isLNat(n__cons(V1,V2)) -> #activate(V1) #46: #isLNat(n__cons(V1,V2)) -> #activate(V2) #47: #isLNat(n__cons(V1,V2)) -> #activate(V1) #48: #isLNat(n__cons(V1,V2)) -> #activate(V2) #49: #sel(N,XS) -> #U171(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) #50: #sel(N,XS) -> #and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))) #51: #sel(N,XS) -> #and(isNatural(N),n__isNaturalKind(N)) #52: #sel(N,XS) -> #isNatural(N) #53: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2)) #54: #activate(n__take(X1,X2)) -> #activate(X1) #55: #activate(n__take(X1,X2)) -> #activate(X2) #56: #natsFrom(N) -> #U161(and(isNatural(N),n__isNaturalKind(N)),N) #57: #natsFrom(N) -> #and(isNatural(N),n__isNaturalKind(N)) #58: #natsFrom(N) -> #isNatural(N) #59: #isLNatKind(n__natsFrom(V1)) -> #isNaturalKind(activate(V1)) #60: #isLNatKind(n__natsFrom(V1)) -> #activate(V1) #61: #activate(n__0()) -> #0() #62: #isLNatKind(n__take(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #63: #isLNatKind(n__take(V1,V2)) -> #isNaturalKind(activate(V1)) #64: #isLNatKind(n__take(V1,V2)) -> #activate(V1) #65: #isLNatKind(n__take(V1,V2)) -> #activate(V2) #66: #U81(tt(),V1) -> #U82(isPLNat(activate(V1))) #67: #U81(tt(),V1) -> #isPLNat(activate(V1)) #68: #U81(tt(),V1) -> #activate(V1) #69: #activate(n__pair(X1,X2)) -> #pair(activate(X1),activate(X2)) #70: #activate(n__pair(X1,X2)) -> #activate(X1) #71: #activate(n__pair(X1,X2)) -> #activate(X2) #72: #isLNatKind(n__snd(V1)) -> #isPLNatKind(activate(V1)) #73: #isLNatKind(n__snd(V1)) -> #activate(V1) #74: #activate(n__snd(X)) -> #snd(activate(X)) #75: #activate(n__snd(X)) -> #activate(X) #76: #isLNatKind(n__afterNth(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #77: #isLNatKind(n__afterNth(V1,V2)) -> #isNaturalKind(activate(V1)) #78: #isLNatKind(n__afterNth(V1,V2)) -> #activate(V1) #79: #isLNatKind(n__afterNth(V1,V2)) -> #activate(V2) #80: #isNaturalKind(n__head(V1)) -> #isLNatKind(activate(V1)) #81: #isNaturalKind(n__head(V1)) -> #activate(V1) #82: #U91(tt(),V1) -> #U92(isLNat(activate(V1))) #83: #U91(tt(),V1) -> #isLNat(activate(V1)) #84: #U91(tt(),V1) -> #activate(V1) #85: #activate(n__afterNth(X1,X2)) -> #afterNth(activate(X1),activate(X2)) #86: #activate(n__afterNth(X1,X2)) -> #activate(X1) #87: #activate(n__afterNth(X1,X2)) -> #activate(X2) #88: #isLNat(n__snd(V1)) -> #U81(isPLNatKind(activate(V1)),activate(V1)) #89: #isLNat(n__snd(V1)) -> #isPLNatKind(activate(V1)) #90: #isLNat(n__snd(V1)) -> #activate(V1) #91: #isLNat(n__snd(V1)) -> #activate(V1) #92: #U142(tt(),V2) -> #U143(isLNat(activate(V2))) #93: #U142(tt(),V2) -> #isLNat(activate(V2)) #94: #U142(tt(),V2) -> #activate(V2) #95: #U131(tt(),V1,V2) -> #U132(isNatural(activate(V1)),activate(V2)) #96: #U131(tt(),V1,V2) -> #isNatural(activate(V1)) #97: #U131(tt(),V1,V2) -> #activate(V1) #98: #U131(tt(),V1,V2) -> #activate(V2) #99: #isLNatKind(n__fst(V1)) -> #isPLNatKind(activate(V1)) #100: #isLNatKind(n__fst(V1)) -> #activate(V1) #101: #snd(pair(X,Y)) -> #U181(and(and(isLNat(X),n__isLNatKind(X)),n__and(n__isLNat(Y),n__isLNatKind(Y))),Y) #102: #snd(pair(X,Y)) -> #and(and(isLNat(X),n__isLNatKind(X)),n__and(n__isLNat(Y),n__isLNatKind(Y))) #103: #snd(pair(X,Y)) -> #and(isLNat(X),n__isLNatKind(X)) #104: #snd(pair(X,Y)) -> #isLNat(X) #105: #activate(n__fst(X)) -> #fst(activate(X)) #106: #activate(n__fst(X)) -> #activate(X) #107: #U21(tt(),X) -> #activate(X) #108: #isPLNat(n__pair(V1,V2)) -> #U141(and(isLNatKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) #109: #isPLNat(n__pair(V1,V2)) -> #and(isLNatKind(activate(V1)),n__isLNatKind(activate(V2))) #110: #isPLNat(n__pair(V1,V2)) -> #isLNatKind(activate(V1)) #111: #isPLNat(n__pair(V1,V2)) -> #activate(V1) #112: #isPLNat(n__pair(V1,V2)) -> #activate(V2) #113: #isPLNat(n__pair(V1,V2)) -> #activate(V1) #114: #isPLNat(n__pair(V1,V2)) -> #activate(V2) #115: #U202(pair(YS,ZS),X) -> #pair(cons(activate(X),YS),ZS) #116: #U202(pair(YS,ZS),X) -> #cons(activate(X),YS) #117: #U202(pair(YS,ZS),X) -> #activate(X) #118: #activate(n__isNatural(X)) -> #isNatural(X) #119: #splitAt(s(N),cons(X,XS)) -> #U201(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__and(n__isNatural(X),n__isNaturalKind(X)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS))))),N,X,activate(XS)) #120: #splitAt(s(N),cons(X,XS)) -> #and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__and(n__isNatural(X),n__isNaturalKind(X)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS))))) #121: #splitAt(s(N),cons(X,XS)) -> #and(isNatural(N),n__isNaturalKind(N)) #122: #splitAt(s(N),cons(X,XS)) -> #isNatural(N) #123: #splitAt(s(N),cons(X,XS)) -> #activate(XS) #124: #splitAt(s(N),cons(X,XS)) -> #activate(XS) #125: #splitAt(s(N),cons(X,XS)) -> #activate(XS) #126: #head(cons(N,XS)) -> #U31(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))),N) #127: #head(cons(N,XS)) -> #and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))) #128: #head(cons(N,XS)) -> #and(isNatural(N),n__isNaturalKind(N)) #129: #head(cons(N,XS)) -> #isNatural(N) #130: #head(cons(N,XS)) -> #activate(XS) #131: #head(cons(N,XS)) -> #activate(XS) #132: #isNaturalKind(n__sel(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #133: #isNaturalKind(n__sel(V1,V2)) -> #isNaturalKind(activate(V1)) #134: #isNaturalKind(n__sel(V1,V2)) -> #activate(V1) #135: #isNaturalKind(n__sel(V1,V2)) -> #activate(V2) #136: #activate(n__s(X)) -> #s(activate(X)) #137: #activate(n__s(X)) -> #activate(X) #138: #U141(tt(),V1,V2) -> #U142(isLNat(activate(V1)),activate(V2)) #139: #U141(tt(),V1,V2) -> #isLNat(activate(V1)) #140: #U141(tt(),V1,V2) -> #activate(V1) #141: #U141(tt(),V1,V2) -> #activate(V2) #142: #U51(tt(),V1,V2) -> #U52(isNatural(activate(V1)),activate(V2)) #143: #U51(tt(),V1,V2) -> #isNatural(activate(V1)) #144: #U51(tt(),V1,V2) -> #activate(V1) #145: #U51(tt(),V1,V2) -> #activate(V2) #146: #tail(cons(N,XS)) -> #U211(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))),activate(XS)) #147: #tail(cons(N,XS)) -> #and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))) #148: #tail(cons(N,XS)) -> #and(isNatural(N),n__isNaturalKind(N)) #149: #tail(cons(N,XS)) -> #isNatural(N) #150: #tail(cons(N,XS)) -> #activate(XS) #151: #tail(cons(N,XS)) -> #activate(XS) #152: #tail(cons(N,XS)) -> #activate(XS) #153: #isLNatKind(n__cons(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #154: #isLNatKind(n__cons(V1,V2)) -> #isNaturalKind(activate(V1)) #155: #isLNatKind(n__cons(V1,V2)) -> #activate(V1) #156: #isLNatKind(n__cons(V1,V2)) -> #activate(V2) #157: #activate(n__tail(X)) -> #tail(activate(X)) #158: #activate(n__tail(X)) -> #activate(X) #159: #activate(n__nil()) -> #nil() #160: #isLNat(n__tail(V1)) -> #U91(isLNatKind(activate(V1)),activate(V1)) #161: #isLNat(n__tail(V1)) -> #isLNatKind(activate(V1)) #162: #isLNat(n__tail(V1)) -> #activate(V1) #163: #isLNat(n__tail(V1)) -> #activate(V1) #164: #isLNat(n__fst(V1)) -> #U61(isPLNatKind(activate(V1)),activate(V1)) #165: #isLNat(n__fst(V1)) -> #isPLNatKind(activate(V1)) #166: #isLNat(n__fst(V1)) -> #activate(V1) #167: #isLNat(n__fst(V1)) -> #activate(V1) #168: #U211(tt(),XS) -> #activate(XS) #169: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2) #170: #activate(n__cons(X1,X2)) -> #activate(X1) #171: #U181(tt(),Y) -> #activate(Y) #172: #U121(tt(),V1) -> #U122(isNatural(activate(V1))) #173: #U121(tt(),V1) -> #isNatural(activate(V1)) #174: #U121(tt(),V1) -> #activate(V1) #175: #U132(tt(),V2) -> #U133(isLNat(activate(V2))) #176: #U132(tt(),V2) -> #isLNat(activate(V2)) #177: #U132(tt(),V2) -> #activate(V2) #178: #isNatural(n__s(V1)) -> #U121(isNaturalKind(activate(V1)),activate(V1)) #179: #isNatural(n__s(V1)) -> #isNaturalKind(activate(V1)) #180: #isNatural(n__s(V1)) -> #activate(V1) #181: #isNatural(n__s(V1)) -> #activate(V1) #182: #isPLNatKind(n__pair(V1,V2)) -> #and(isLNatKind(activate(V1)),n__isLNatKind(activate(V2))) #183: #isPLNatKind(n__pair(V1,V2)) -> #isLNatKind(activate(V1)) #184: #isPLNatKind(n__pair(V1,V2)) -> #activate(V1) #185: #isPLNatKind(n__pair(V1,V2)) -> #activate(V2) #186: #U111(tt(),V1) -> #U112(isLNat(activate(V1))) #187: #U111(tt(),V1) -> #isLNat(activate(V1)) #188: #U111(tt(),V1) -> #activate(V1) #189: #fst(pair(X,Y)) -> #U21(and(and(isLNat(X),n__isLNatKind(X)),n__and(n__isLNat(Y),n__isLNatKind(Y))),X) #190: #fst(pair(X,Y)) -> #and(and(isLNat(X),n__isLNatKind(X)),n__and(n__isLNat(Y),n__isLNatKind(Y))) #191: #fst(pair(X,Y)) -> #and(isLNat(X),n__isLNatKind(X)) #192: #fst(pair(X,Y)) -> #isLNat(X) #193: #isNatural(n__sel(V1,V2)) -> #U131(and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))),activate(V1),activate(V2)) #194: #isNatural(n__sel(V1,V2)) -> #and(isNaturalKind(activate(V1)),n__isLNatKind(activate(V2))) #195: #isNatural(n__sel(V1,V2)) -> #isNaturalKind(activate(V1)) #196: #isNatural(n__sel(V1,V2)) -> #activate(V1) #197: #isNatural(n__sel(V1,V2)) -> #activate(V2) #198: #isNatural(n__sel(V1,V2)) -> #activate(V1) #199: #isNatural(n__sel(V1,V2)) -> #activate(V2) #200: #U41(tt(),V1,V2) -> #U42(isNatural(activate(V1)),activate(V2)) #201: #U41(tt(),V1,V2) -> #isNatural(activate(V1)) #202: #U41(tt(),V1,V2) -> #activate(V1) #203: #U41(tt(),V1,V2) -> #activate(V2) #204: #U201(tt(),N,X,XS) -> #U202(splitAt(activate(N),activate(XS)),activate(X)) #205: #U201(tt(),N,X,XS) -> #splitAt(activate(N),activate(XS)) #206: #U201(tt(),N,X,XS) -> #activate(N) #207: #U201(tt(),N,X,XS) -> #activate(XS) #208: #U201(tt(),N,X,XS) -> #activate(X) #209: #U61(tt(),V1) -> #U62(isPLNat(activate(V1))) #210: #U61(tt(),V1) -> #isPLNat(activate(V1)) #211: #U61(tt(),V1) -> #activate(V1) #212: #U31(tt(),N) -> #activate(N) #213: #isLNatKind(n__tail(V1)) -> #isLNatKind(activate(V1)) #214: #isLNatKind(n__tail(V1)) -> #activate(V1) #215: #activate(n__splitAt(X1,X2)) -> #splitAt(activate(X1),activate(X2)) #216: #activate(n__splitAt(X1,X2)) -> #activate(X1) #217: #activate(n__splitAt(X1,X2)) -> #activate(X2) #218: #U52(tt(),V2) -> #U53(isLNat(activate(V2))) #219: #U52(tt(),V2) -> #isLNat(activate(V2)) #220: #U52(tt(),V2) -> #activate(V2) #221: #U171(tt(),N,XS) -> #head(afterNth(activate(N),activate(XS))) #222: #U171(tt(),N,XS) -> #afterNth(activate(N),activate(XS)) #223: #U171(tt(),N,XS) -> #activate(N) #224: #U171(tt(),N,XS) -> #activate(XS) #225: #isNatural(n__head(V1)) -> #U111(isLNatKind(activate(V1)),activate(V1)) #226: #isNatural(n__head(V1)) -> #isLNatKind(activate(V1)) #227: #isNatural(n__head(V1)) -> #activate(V1) #228: #isNatural(n__head(V1)) -> #activate(V1) #229: #activate(n__isLNatKind(X)) -> #isLNatKind(X) #230: #U221(tt(),N,XS) -> #fst(splitAt(activate(N),activate(XS))) #231: #U221(tt(),N,XS) -> #splitAt(activate(N),activate(XS)) #232: #U221(tt(),N,XS) -> #activate(N) #233: #U221(tt(),N,XS) -> #activate(XS) #234: #activate(n__natsFrom(X)) -> #natsFrom(activate(X)) #235: #activate(n__natsFrom(X)) -> #activate(X) #236: #isNaturalKind(n__s(V1)) -> #isNaturalKind(activate(V1)) #237: #isNaturalKind(n__s(V1)) -> #activate(V1) #238: #U71(tt(),V1) -> #U72(isNatural(activate(V1))) #239: #U71(tt(),V1) -> #isNatural(activate(V1)) #240: #U71(tt(),V1) -> #activate(V1) #241: #U191(tt(),XS) -> #pair(nil(),activate(XS)) #242: #U191(tt(),XS) -> #nil() #243: #U191(tt(),XS) -> #activate(XS) #244: #U152(tt(),V2) -> #U153(isLNat(activate(V2))) #245: #U152(tt(),V2) -> #isLNat(activate(V2)) #246: #U152(tt(),V2) -> #activate(V2) #247: #splitAt(0(),XS) -> #U191(and(isLNat(XS),n__isLNatKind(XS)),XS) #248: #splitAt(0(),XS) -> #and(isLNat(XS),n__isLNatKind(XS)) #249: #splitAt(0(),XS) -> #isLNat(XS) #250: #U101(tt(),V1,V2) -> #U102(isNatural(activate(V1)),activate(V2)) #251: #U101(tt(),V1,V2) -> #isNatural(activate(V1)) #252: #U101(tt(),V1,V2) -> #activate(V1) #253: #U101(tt(),V1,V2) -> #activate(V2) #254: #U151(tt(),V1,V2) -> #U152(isNatural(activate(V1)),activate(V2)) #255: #U151(tt(),V1,V2) -> #isNatural(activate(V1)) #256: #U151(tt(),V1,V2) -> #activate(V1) #257: #U151(tt(),V1,V2) -> #activate(V2) #258: #activate(n__isNaturalKind(X)) -> #isNaturalKind(X) #259: #activate(n__and(X1,X2)) -> #and(activate(X1),X2) #260: #activate(n__and(X1,X2)) -> #activate(X1) #261: #U11(tt(),N,XS) -> #snd(splitAt(activate(N),activate(XS))) #262: #U11(tt(),N,XS) -> #splitAt(activate(N),activate(XS)) #263: #U11(tt(),N,XS) -> #activate(N) #264: #U11(tt(),N,XS) -> #activate(XS) #265: #activate(n__isLNat(X)) -> #isLNat(X) #266: #take(N,XS) -> #U221(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) #267: #take(N,XS) -> #and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))) #268: #take(N,XS) -> #and(isNatural(N),n__isNaturalKind(N)) #269: #take(N,XS) -> #isNatural(N) #270: #isLNat(n__natsFrom(V1)) -> #U71(isNaturalKind(activate(V1)),activate(V1)) #271: #isLNat(n__natsFrom(V1)) -> #isNaturalKind(activate(V1)) #272: #isLNat(n__natsFrom(V1)) -> #activate(V1) #273: #isLNat(n__natsFrom(V1)) -> #activate(V1) #274: #U161(tt(),N) -> #cons(activate(N),n__natsFrom(n__s(activate(N)))) #275: #U161(tt(),N) -> #activate(N) #276: #U161(tt(),N) -> #activate(N) Number of SCCs: 1, DPs: 254 SCC { #2..4 #6..60 #62..65 #67 #68 #70..81 #83..91 #93..114 #117..135 #137..158 #160..168 #170 #171 #173 #174 #176..185 #187..208 #210..217 #219..237 #239 #240 #243 #245..273 #275 #276 } POLO(Sum)... POLO(max)... succeeded. #U201 w: max(x1 + 24, x2 + 38, x3 + 64, x4 + 48) #isLNatKind w: x1 + 20 #0 w: 0 #U72 w: 0 U21 w: max(x2 + 12) U161 w: max(x1, x2 + 16) n__isLNatKind w: x1 + 2 U11 w: max(x2 + 44, x3 + 42) #cons w: 0 s w: x1 n__pair w: max(x1 + 15, x2) U143 w: x1 + 12 #U142 w: max(x1 + 38, x2 + 27) #take w: max(x1 + 61, x2 + 59) isPLNatKind w: x1 + 4 U142 w: max(x1, x2 + 1) #U152 w: max(x1 + 16, x2 + 22) #U181 w: max(x1 + 18, x2 + 19) isPLNat w: 1 U42 w: max(x2 + 15) U91 w: max(x1 + 3) U221 w: max(x1 + 36, x2 + 44, x3 + 44) #U101 w: max(x2 + 69, x3 + 23) activate w: x1 n__isLNat w: x1 + 4 #U82 w: 0 take w: max(x1 + 49, x2 + 44) U71 w: max(x1, x2 + 16) #U81 w: max(x1 + 15, x2 + 30) and w: max(x1 + 2, x2) #U92 w: 0 #U133 w: 0 U131 w: max(x3 + 73) U101 w: max(x1, x2 + 16, x3 + 19) pair w: max(x1 + 15, x2) fst w: x1 + 11 U111 w: max(x1, x2 + 18) U132 w: max(x2 + 4) U43 w: 15 #activate w: x1 + 18 U152 w: 0 U103 w: 18 #U53 w: 0 natsFrom w: x1 + 16 #head w: x1 + 27 #U43 w: 0 #U121 w: max(x2 + 20) splitAt w: max(x1 + 33, x2 + 31) isNaturalKind w: x1 + 8 #U131 w: max(x2 + 26, x3 + 23) U72 w: x1 + 8 n__isNaturalKind w: x1 + 8 #fst w: x1 + 26 #U143 w: 0 n__nil w: 13 #U52 w: max(x1 + 14, x2 + 21) #U103 w: 0 #isPLNatKind w: x1 + 30 #U202 w: max(x1 + 4, x2 + 19) n__natsFrom w: x1 + 16 isNatural w: x1 + 8 n__snd w: x1 + 11 n__s w: x1 U201 w: max(x2 + 33, x3 + 46, x4 + 31) n__splitAt w: max(x1 + 33, x2 + 31) #U42 w: max(x1 + 16, x2 + 22) #U141 w: max(x1 + 26, x2 + 43, x3 + 28) U141 w: 0 #U171 w: max(x1 + 60, x2 + 75, x3 + 79) tail w: x1 + 8 #U62 w: 0 0 w: 7 U191 w: max(x2 + 28) n__take w: max(x1 + 49, x2 + 44) #sel w: max(x1 + 78, x2 + 80) #U102 w: max(x1 + 16, x2 + 22) U153 w: x1 U171 w: max(x2 + 56, x3 + 65) #isLNat w: x1 + 21 U202 w: max(x1, x2 + 31) sel w: max(x1 + 64, x2 + 65) #s w: 0 afterNth w: max(x1 + 46, x2 + 47) n__cons w: max(x1 + 16, x2) #U211 w: max(x2 + 19) #isPLNat w: x1 + 29 nil w: 13 isLNat w: x1 + 4 U62 w: 15 #U153 w: 0 n__sel w: max(x1 + 64, x2 + 65) #tail w: x1 + 25 #isNaturalKind w: x1 + 19 #splitAt w: max(x1 + 38, x2 + 48) U151 w: max(x2 + 2) #nil w: 0 U133 w: x1 n__tail w: x1 + 8 #afterNth w: max(x1 + 60, x2 + 62) #U111 w: max(x1 + 7, x2 + 22) #U221 w: max(x2 + 60, x3 + 58) n__isNatural w: x1 + 8 n__0 w: 7 n__afterNth w: max(x1 + 46, x2 + 47) U211 w: max(x2) isLNatKind w: x1 + 2 U52 w: max(x1 + 9) U61 w: max(x2 + 15) #U51 w: max(x1 + 12, x2 + 22, x3 + 21) n__fst w: x1 + 11 #U11 w: max(x1 + 44, x2 + 59, x3 + 61) U31 w: max(x2 + 1) U92 w: 15 head w: x1 + 10 U112 w: 15 #snd w: x1 + 25 #U41 w: max(x2 + 25, x3 + 23) cons w: max(x1 + 16, x2) #natsFrom w: x1 + 27 U102 w: max(x1 + 8, x2 + 17) snd w: x1 + 11 #U191 w: max(x1 + 4, x2 + 46) #U21 w: max(x1 + 4, x2 + 27) U81 w: max(x2 + 15) U82 w: 15 #U112 w: 0 tt w: 15 n__and w: max(x1 + 2, x2) #U71 w: max(x1 + 6, x2 + 21) #U151 w: max(x2 + 61, x3 + 23) #isNatural w: x1 + 20 #pair w: 0 n__head w: x1 + 10 U51 w: max(x1 + 1, x2 + 17, x3 + 1) #U161 w: max(x1 + 4, x2 + 19) #U122 w: 0 U53 w: 24 U41 w: max(x3 + 15) #U31 w: max(x1 + 10, x2 + 19) #and w: max(x1 + 14, x2 + 18) #U91 w: max(x1 + 7, x2 + 22) #U132 w: max(x1 + 7, x2 + 22) U121 w: max(x1, x2 + 8) #U61 w: max(x1 + 15, x2 + 31) U181 w: max(x1 + 4, x2) U122 w: x1 USABLE RULES: { 1..11 18..69 72..119 } Removed DPs: #2 #3 #6..41 #43..60 #62..65 #67 #68 #70 #72..81 #83..91 #93..114 #117 #118 #120..135 #138..141 #143..152 #154..158 #160..168 #170 #171 #174 #176 #177 #179..185 #187..204 #206..208 #210..217 #220..228 #230..235 #237 #239 #240 #243 #245..258 #260..273 #275 #276 Number of SCCs: 5, DPs: 14 SCC { #236 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #U201 s: [3,1] p: 0 w: max(x1, x3) #isLNatKind s: [] p: 0 w: 0 #0 s: [] p: 0 w: 0 #U72 s: [] p: 0 w: 0 U21 s: [2] p: 9 w: max(x2 + 1) U161 s: [] p: 15 w: max(x2 + 14) n__isLNatKind s: [] p: 9 w: 15 U11 s: [] p: 7 w: max(x1 + 19, x2 + 8, x3 + 44) #cons s: [] p: 0 w: max(x1 + 1) s s: [1] p: 16 w: x1 n__pair s: [] p: 2 w: max(x1 + 2, x2 + 3) U143 s: [] p: 1 w: x1 #U142 s: [] p: 0 w: x2 #take s: [] p: 0 w: x1 + 1 isPLNatKind s: [] p: 9 w: 15 U142 s: [] p: 1 w: 0 #U152 s: [] p: 0 w: x1 #U181 s: [] p: 0 w: x2 + 1 isPLNat s: [] p: 11 w: 0 U42 s: [] p: 7 w: max(x1 + 1) U91 s: [2] p: 1 w: max(x2 + 17) U221 s: [] p: 11 w: max(x1 + 35, x3 + 35) #U101 s: [3] p: 0 w: x3 + 1 activate s: 1 n__isLNat s: [] p: 13 w: x1 + 11 #U82 s: [] p: 0 w: 1 take s: [] p: 12 w: x1 + x2 + 51 U71 s: [] p: 9 w: max(x2 + 15) #U81 s: [2] p: 0 w: x2 + 1 and s: 2 #U92 s: [] p: 0 w: 0 #U133 s: [] p: 0 w: 1 U131 s: [] p: 2 w: 0 U101 s: [2] p: 12 w: max(x1 + 13, x2 + 52, x3 + 13) pair s: [] p: 2 w: max(x1 + 2, x2 + 3) fst s: [] p: 10 w: x1 U111 s: [] p: 1 w: 0 U132 s: [] p: 2 w: 0 U43 s: [] p: 6 w: 0 #activate s: [] p: 0 w: 0 U152 s: [1] p: 14 w: max(x1 + 1, x2 + 12) U103 s: [] p: 2 w: 0 #U53 s: [] p: 0 w: 1 natsFrom s: [] p: 15 w: x1 + 14 #head s: [] p: 0 w: 0 #U43 s: [] p: 0 w: 1 #U121 s: [1,2] p: 0 w: max(x1, x2) splitAt s: [] p: 6 w: max(x2 + 34) isNaturalKind s: [] p: 9 w: 15 #U131 s: [3,1] p: 0 w: x1 + x2 + x3 + 1 U72 s: [] p: 1 w: 0 n__isNaturalKind s: [] p: 9 w: 15 #fst s: [] p: 0 w: 0 #U143 s: [] p: 0 w: 0 n__nil s: [] p: 10 w: 0 #U52 s: [1] p: 0 w: max(x1 + 1) #U103 s: [] p: 0 w: 1 #isPLNatKind s: [] p: 0 w: 0 #U202 s: [2,1] p: 0 w: x1 + x2 n__natsFrom s: [] p: 15 w: x1 + 14 isNatural s: [] p: 2 w: 0 n__snd s: [] p: 4 w: x1 + 7 n__s s: [1] p: 16 w: x1 U201 s: [1] p: 2 w: max(x1 + 31, x3 + 35, x4 + 34) n__splitAt s: [] p: 6 w: max(x2 + 34) #U42 s: [1] p: 0 w: x1 #U141 s: [3] p: 0 w: x3 + 1 U141 s: [3,2,1] p: 9 w: max(x1 + 12, x2 + 12, x3 + 12) #U171 s: [3,1,2] p: 0 w: x1 + x2 + x3 tail s: [1] p: 14 w: x1 + 16 #U62 s: [] p: 0 w: 1 0 s: [] p: 10 w: 5 U191 s: [1] p: 2 w: max(x1 + 4, x2 + 6) n__take s: [] p: 12 w: x1 + x2 + 51 #sel s: [2,1] p: 0 w: x1 + x2 + 1 #U102 s: [1,2] p: 0 w: x1 + x2 U153 s: [] p: 14 w: 0 U171 s: [] p: 14 w: max(x2 + 46, x3 + 46) #isLNat s: [] p: 0 w: 0 U202 s: [] p: 2 w: max(x1, x2 + 16) sel s: [] p: 14 w: x1 + x2 + 47 #s s: [] p: 0 w: 1 afterNth s: [] p: 8 w: max(x1 + 35, x2 + 45) n__cons s: [] p: 14 w: max(x1 + 13, x2) #U211 s: [2,1] p: 0 w: x1 + x2 #isPLNat s: [] p: 0 w: 0 nil s: [] p: 10 w: 0 isLNat s: [] p: 13 w: x1 + 11 U62 s: [] p: 9 w: 1 #U153 s: [] p: 0 w: 0 n__sel s: [] p: 14 w: x1 + x2 + 47 #tail s: [] p: 0 w: 0 #isNaturalKind s: [1] p: 0 w: x1 + 1 #splitAt s: [] p: 0 w: max(x1 + 1) U151 s: [] p: 6 w: 0 #nil s: [] p: 0 w: 0 U133 s: [] p: 2 w: 0 n__tail s: [1] p: 14 w: x1 + 16 #afterNth s: [1,2] p: 0 w: x1 + x2 #U111 s: [] p: 0 w: x2 + 1 #U221 s: [] p: 0 w: x1 + 1 n__isNatural s: [] p: 2 w: 0 n__0 s: [] p: 10 w: 5 n__afterNth s: [] p: 8 w: max(x1 + 35, x2 + 45) U211 s: [2] p: 13 w: max(x2) isLNatKind s: [] p: 9 w: 15 U52 s: [] p: 3 w: 0 U61 s: [] p: 10 w: max(x2 + 2) #U51 s: [1,3,2] p: 0 w: max(x1, x2 + 1, x3) n__fst s: [] p: 10 w: x1 #U11 s: [1] p: 0 w: x1 U31 s: [2] p: 0 w: max(x2 + 13) U92 s: [] p: 1 w: 0 head s: [1] p: 0 w: x1 U112 s: [] p: 1 w: 0 #snd s: [] p: 0 w: 1 #U41 s: [2,1,3] p: 0 w: x1 + x2 + x3 cons s: [] p: 14 w: max(x1 + 13, x2) #natsFrom s: [] p: 0 w: 0 U102 s: [] p: 10 w: max(x1 + 12) snd s: [] p: 4 w: x1 + 7 #U191 s: [2] p: 0 w: x2 #U21 s: [] p: 0 w: x1 U81 s: [1] p: 11 w: max(x1 + 2, x2 + 8) U82 s: [] p: 12 w: 1 #U112 s: [] p: 0 w: 0 tt s: [] p: 1 w: 0 n__and s: 2 #U71 s: [1,2] p: 0 w: x1 + x2 + 1 #U151 s: [1,3] p: 0 w: x1 + x2 + x3 + 1 #isNatural s: [] p: 0 w: 0 #pair s: [1,2] p: 0 w: max(x1, x2 + 1) n__head s: [1] p: 0 w: x1 U51 s: [] p: 9 w: max(x1 + 1, x2 + 12) #U161 s: [2,1] p: 0 w: x1 + x2 #U122 s: [] p: 0 w: 1 U53 s: [] p: 2 w: 0 U41 s: [] p: 8 w: max(x1 + 30, x2 + 2) #U31 s: [] p: 0 w: x1 + 1 #and s: [] p: 0 w: max(x2) #U91 s: [2,1] p: 0 w: x1 + x2 #U132 s: [1,2] p: 0 w: x1 + x2 U121 s: [] p: 2 w: 0 #U61 s: [] p: 0 w: x1 U181 s: [] p: 3 w: max(x2 + 4) U122 s: [] p: 1 w: 0 USABLE RULES: { 1..11 16..69 72..119 } Removed DPs: #236 Number of SCCs: 4, DPs: 13 SCC { #173 #178 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #U201 s: [3,1] p: 0 w: max(x1, x3) #isLNatKind s: [] p: 0 w: 0 #0 s: [] p: 0 w: 0 #U72 s: [] p: 0 w: 0 U21 s: [2] p: 3 w: max(x2 + 12) U161 s: [] p: 8 w: max(x2 + 14) n__isLNatKind s: [] p: 12 w: 11 U11 s: [] p: 11 w: max(x1 + 29, x2 + 54, x3 + 28) #cons s: [] p: 0 w: max(x1 + 1) s s: [1] p: 13 w: x1 n__pair s: [] p: 4 w: max(x1 + 12, x2 + 14) U143 s: [] p: 1 w: x1 #U142 s: [] p: 0 w: x2 #take s: [] p: 0 w: x1 + 1 isPLNatKind s: [] p: 12 w: 11 U142 s: [] p: 1 w: 0 #U152 s: [] p: 0 w: x1 #U181 s: [] p: 0 w: x2 + 1 isPLNat s: [] p: 12 w: 0 U42 s: [] p: 3 w: max(x1 + 1) U91 s: [] p: 12 w: max(x1 + 11) U221 s: [] p: 6 w: max(x2 + 54, x3 + 52) #U101 s: [3] p: 0 w: x3 + 1 activate s: 1 n__isLNat s: [1] p: 7 w: x1 + 60 #U82 s: [] p: 0 w: 1 take s: [] p: 6 w: x1 + x2 + 65 U71 s: [] p: 5 w: max(x2 + 57) #U81 s: [2] p: 0 w: x2 + 1 and s: 2 #U92 s: [] p: 0 w: 0 #U133 s: [] p: 0 w: 1 U131 s: [1] p: 3 w: max(x1 + 49, x2 + 61) U101 s: [] p: 10 w: max(x1 + 53, x3 + 63) pair s: [] p: 4 w: max(x1 + 12, x2 + 14) fst s: 1 U111 s: [] p: 1 w: max(x1 + 51) U132 s: [] p: 2 w: max(x1 + 4) U43 s: [] p: 2 w: 11 #activate s: [] p: 0 w: 0 U152 s: [] p: 12 w: max(x1 + 50, x2 + 61) U103 s: [1] p: 2 w: x1 + 1 #U53 s: [] p: 0 w: 1 natsFrom s: [] p: 9 w: x1 + 14 #head s: [] p: 0 w: 0 #U43 s: [] p: 0 w: 1 #U121 s: [2] p: 0 w: max(x2) splitAt s: [] p: 5 w: max(x1 + 53, x2 + 27) isNaturalKind s: [] p: 12 w: 11 #U131 s: [3,1] p: 0 w: x1 + x2 + x3 + 1 U72 s: [] p: 1 w: 10 n__isNaturalKind s: [] p: 12 w: 11 #fst s: [] p: 0 w: 0 #U143 s: [] p: 0 w: 0 n__nil s: [] p: 12 w: 11 #U52 s: [1] p: 0 w: max(x1 + 1) #U103 s: [] p: 0 w: 1 #isPLNatKind s: [] p: 0 w: 0 #U202 s: [2,1] p: 0 w: x1 + x2 n__natsFrom s: [] p: 9 w: x1 + 14 isNatural s: [] p: 4 w: x1 + 56 n__snd s: 1 n__s s: [1] p: 13 w: x1 U201 s: [1] p: 4 w: max(x1 + 41, x2 + 53, x3 + 40, x4 + 27) n__splitAt s: [] p: 5 w: max(x1 + 53, x2 + 27) #U42 s: [1] p: 0 w: x1 #U141 s: [3] p: 0 w: x3 + 1 U141 s: [] p: 6 w: max(x1 + 50, x2 + 61, x3 + 61) #U171 s: [3,1,2] p: 0 w: x1 + x2 + x3 tail s: [] p: 11 w: x1 + 23 #U62 s: [] p: 0 w: 1 0 s: [] p: 3 w: 8 U191 s: [] p: 4 w: max(x1 + 16, x2 + 27) n__take s: [] p: 6 w: x1 + x2 + 65 #sel s: [2,1] p: 0 w: x1 + x2 + 1 #U102 s: [1,2] p: 0 w: x1 + x2 U153 s: [] p: 12 w: x1 U171 s: [] p: 12 w: max(x1 + 53, x2 + 63, x3 + 63) #isLNat s: [] p: 0 w: 0 U202 s: [] p: 4 w: max(x1, x2 + 26) sel s: [2] p: 12 w: x1 + x2 + 65 #s s: [] p: 0 w: 1 afterNth s: [] p: 11 w: max(x1 + 55, x2 + 29) n__cons s: [] p: 8 w: max(x1 + 13, x2) #U211 s: [2,1] p: 0 w: x1 + x2 #isPLNat s: [] p: 0 w: 0 nil s: [] p: 12 w: 11 isLNat s: [1] p: 7 w: x1 + 60 U62 s: [] p: 5 w: 11 #U153 s: [] p: 0 w: 0 n__sel s: [2] p: 12 w: x1 + x2 + 65 #tail s: [] p: 0 w: 0 #isNaturalKind s: [] p: 0 w: 1 #splitAt s: [] p: 0 w: max(x1 + 1) U151 s: [] p: 5 w: 0 #nil s: [] p: 0 w: 0 U133 s: [] p: 2 w: 11 n__tail s: [] p: 11 w: x1 + 23 #afterNth s: [1,2] p: 0 w: x1 + x2 #U111 s: [] p: 0 w: x2 + 1 #U221 s: [] p: 0 w: x1 + 1 n__isNatural s: [] p: 4 w: x1 + 56 n__0 s: [] p: 3 w: 8 n__afterNth s: [] p: 11 w: max(x1 + 55, x2 + 29) U211 s: [2] p: 7 w: max(x2 + 22) isLNatKind s: [] p: 12 w: 11 U52 s: [] p: 3 w: max(x1 + 2) U61 s: [] p: 6 w: max(x2 + 59) #U51 s: [1,3,2] p: 0 w: max(x1, x2 + 1, x3) n__fst s: 1 #U11 s: [1] p: 0 w: x1 U31 s: [2] p: 0 w: max(x1 + 9, x2) U92 s: [] p: 1 w: 10 head s: [1] p: 0 w: x1 + 7 U112 s: [] p: 1 w: 60 #snd s: [] p: 0 w: 1 #U41 s: [2,1,3] p: 0 w: x1 + x2 + x3 cons s: [] p: 8 w: max(x1 + 13, x2) #natsFrom s: [] p: 0 w: 0 U102 s: [2] p: 9 w: max(x2 + 62) snd s: 1 #U191 s: [2] p: 0 w: x2 #U21 s: [] p: 0 w: x1 U81 s: [2] p: 12 w: max(x1 + 2, x2 + 18) U82 s: [] p: 13 w: 11 #U112 s: [] p: 0 w: 0 tt s: [] p: 1 w: 10 n__and s: 2 #U71 s: [1,2] p: 0 w: x1 + x2 + 1 #U151 s: [1,3] p: 0 w: x1 + x2 + x3 + 1 #isNatural s: [1] p: 0 w: x1 #pair s: [1,2] p: 0 w: max(x1, x2 + 1) n__head s: [1] p: 0 w: x1 + 7 U51 s: [] p: 7 w: max(x1 + 62, x2 + 59) #U161 s: [2,1] p: 0 w: x1 + x2 #U122 s: [] p: 0 w: 1 U53 s: [] p: 2 w: 11 U41 s: [] p: 7 w: max(x1 + 48, x2 + 58) #U31 s: [] p: 0 w: x1 + 1 #and s: [] p: 0 w: max(x2) #U91 s: [2,1] p: 0 w: x1 + x2 #U132 s: [1,2] p: 0 w: x1 + x2 U121 s: [] p: 4 w: max(x1 + 1) #U61 s: [] p: 0 w: x1 U181 s: [] p: 12 w: max(x2 + 13) U122 s: [] p: 1 w: 10 USABLE RULES: { 1..11 17..69 72..119 } Removed DPs: #178 Number of SCCs: 3, DPs: 11 SCC { #42 #142 #219 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.