/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__U101(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) 2: a__U11(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) 3: a__U21(tt(),X) -> mark(X) 4: a__U31(tt(),N) -> mark(N) 5: a__U41(tt(),N) -> cons(mark(N),natsFrom(s(N))) 6: a__U51(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) 7: a__U61(tt(),Y) -> mark(Y) 8: a__U71(tt(),XS) -> pair(nil(),mark(XS)) 9: a__U81(tt(),N,X,XS) -> a__U82(a__splitAt(mark(N),mark(XS)),X) 10: a__U82(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) 11: a__U91(tt(),XS) -> mark(XS) 12: a__afterNth(N,XS) -> a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS) 13: a__and(tt(),X) -> mark(X) 14: a__fst(pair(X,Y)) -> a__U21(a__and(a__isLNat(X),isLNat(Y)),X) 15: a__head(cons(N,XS)) -> a__U31(a__and(a__isNatural(N),isLNat(XS)),N) 16: a__isLNat(nil()) -> tt() 17: a__isLNat(afterNth(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) 18: a__isLNat(cons(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) 19: a__isLNat(fst(V1)) -> a__isPLNat(V1) 20: a__isLNat(natsFrom(V1)) -> a__isNatural(V1) 21: a__isLNat(snd(V1)) -> a__isPLNat(V1) 22: a__isLNat(tail(V1)) -> a__isLNat(V1) 23: a__isLNat(take(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) 24: a__isNatural(0()) -> tt() 25: a__isNatural(head(V1)) -> a__isLNat(V1) 26: a__isNatural(s(V1)) -> a__isNatural(V1) 27: a__isNatural(sel(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) 28: a__isPLNat(pair(V1,V2)) -> a__and(a__isLNat(V1),isLNat(V2)) 29: a__isPLNat(splitAt(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2)) 30: a__natsFrom(N) -> a__U41(a__isNatural(N),N) 31: a__sel(N,XS) -> a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) 32: a__snd(pair(X,Y)) -> a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) 33: a__splitAt(0(),XS) -> a__U71(a__isLNat(XS),XS) 34: a__splitAt(s(N),cons(X,XS)) -> a__U81(a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS) 35: a__tail(cons(N,XS)) -> a__U91(a__and(a__isNatural(N),isLNat(XS)),XS) 36: a__take(N,XS) -> a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS) 37: mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) 38: mark(fst(X)) -> a__fst(mark(X)) 39: mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) 40: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) 41: mark(snd(X)) -> a__snd(mark(X)) 42: mark(U21(X1,X2)) -> a__U21(mark(X1),X2) 43: mark(U31(X1,X2)) -> a__U31(mark(X1),X2) 44: mark(U41(X1,X2)) -> a__U41(mark(X1),X2) 45: mark(natsFrom(X)) -> a__natsFrom(mark(X)) 46: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) 47: mark(head(X)) -> a__head(mark(X)) 48: mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) 49: mark(U61(X1,X2)) -> a__U61(mark(X1),X2) 50: mark(U71(X1,X2)) -> a__U71(mark(X1),X2) 51: mark(U81(X1,X2,X3,X4)) -> a__U81(mark(X1),X2,X3,X4) 52: mark(U82(X1,X2)) -> a__U82(mark(X1),X2) 53: mark(U91(X1,X2)) -> a__U91(mark(X1),X2) 54: mark(and(X1,X2)) -> a__and(mark(X1),X2) 55: mark(isNatural(X)) -> a__isNatural(X) 56: mark(isLNat(X)) -> a__isLNat(X) 57: mark(isPLNat(X)) -> a__isPLNat(X) 58: mark(tail(X)) -> a__tail(mark(X)) 59: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) 60: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) 61: mark(tt()) -> tt() 62: mark(cons(X1,X2)) -> cons(mark(X1),X2) 63: mark(s(X)) -> s(mark(X)) 64: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) 65: mark(nil()) -> nil() 66: mark(0()) -> 0() 67: a__U101(X1,X2,X3) -> U101(X1,X2,X3) 68: a__fst(X) -> fst(X) 69: a__splitAt(X1,X2) -> splitAt(X1,X2) 70: a__U11(X1,X2,X3) -> U11(X1,X2,X3) 71: a__snd(X) -> snd(X) 72: a__U21(X1,X2) -> U21(X1,X2) 73: a__U31(X1,X2) -> U31(X1,X2) 74: a__U41(X1,X2) -> U41(X1,X2) 75: a__natsFrom(X) -> natsFrom(X) 76: a__U51(X1,X2,X3) -> U51(X1,X2,X3) 77: a__head(X) -> head(X) 78: a__afterNth(X1,X2) -> afterNth(X1,X2) 79: a__U61(X1,X2) -> U61(X1,X2) 80: a__U71(X1,X2) -> U71(X1,X2) 81: a__U81(X1,X2,X3,X4) -> U81(X1,X2,X3,X4) 82: a__U82(X1,X2) -> U82(X1,X2) 83: a__U91(X1,X2) -> U91(X1,X2) 84: a__and(X1,X2) -> and(X1,X2) 85: a__isNatural(X) -> isNatural(X) 86: a__isLNat(X) -> isLNat(X) 87: a__isPLNat(X) -> isPLNat(X) 88: a__tail(X) -> tail(X) 89: a__take(X1,X2) -> take(X1,X2) 90: a__sel(X1,X2) -> sel(X1,X2) Number of strict rules: 90 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__U11(tt(),N,XS) -> #a__snd(a__splitAt(mark(N),mark(XS))) #2: #a__U11(tt(),N,XS) -> #a__splitAt(mark(N),mark(XS)) #3: #a__U11(tt(),N,XS) -> #mark(N) #4: #a__U11(tt(),N,XS) -> #mark(XS) #5: #mark(U31(X1,X2)) -> #a__U31(mark(X1),X2) #6: #mark(U31(X1,X2)) -> #mark(X1) #7: #a__isPLNat(splitAt(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2)) #8: #a__isPLNat(splitAt(V1,V2)) -> #a__isNatural(V1) #9: #a__tail(cons(N,XS)) -> #a__U91(a__and(a__isNatural(N),isLNat(XS)),XS) #10: #a__tail(cons(N,XS)) -> #a__and(a__isNatural(N),isLNat(XS)) #11: #a__tail(cons(N,XS)) -> #a__isNatural(N) #12: #mark(U51(X1,X2,X3)) -> #a__U51(mark(X1),X2,X3) #13: #mark(U51(X1,X2,X3)) -> #mark(X1) #14: #mark(U21(X1,X2)) -> #a__U21(mark(X1),X2) #15: #mark(U21(X1,X2)) -> #mark(X1) #16: #mark(snd(X)) -> #a__snd(mark(X)) #17: #mark(snd(X)) -> #mark(X) #18: #mark(U101(X1,X2,X3)) -> #a__U101(mark(X1),X2,X3) #19: #mark(U101(X1,X2,X3)) -> #mark(X1) #20: #mark(head(X)) -> #a__head(mark(X)) #21: #mark(head(X)) -> #mark(X) #22: #mark(U91(X1,X2)) -> #a__U91(mark(X1),X2) #23: #mark(U91(X1,X2)) -> #mark(X1) #24: #mark(afterNth(X1,X2)) -> #a__afterNth(mark(X1),mark(X2)) #25: #mark(afterNth(X1,X2)) -> #mark(X1) #26: #mark(afterNth(X1,X2)) -> #mark(X2) #27: #mark(tail(X)) -> #a__tail(mark(X)) #28: #mark(tail(X)) -> #mark(X) #29: #mark(fst(X)) -> #a__fst(mark(X)) #30: #mark(fst(X)) -> #mark(X) #31: #a__U51(tt(),N,XS) -> #a__head(a__afterNth(mark(N),mark(XS))) #32: #a__U51(tt(),N,XS) -> #a__afterNth(mark(N),mark(XS)) #33: #a__U51(tt(),N,XS) -> #mark(N) #34: #a__U51(tt(),N,XS) -> #mark(XS) #35: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2)) #36: #mark(take(X1,X2)) -> #mark(X1) #37: #mark(take(X1,X2)) -> #mark(X2) #38: #mark(isNatural(X)) -> #a__isNatural(X) #39: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3) #40: #mark(U11(X1,X2,X3)) -> #mark(X1) #41: #mark(U81(X1,X2,X3,X4)) -> #a__U81(mark(X1),X2,X3,X4) #42: #mark(U81(X1,X2,X3,X4)) -> #mark(X1) #43: #a__and(tt(),X) -> #mark(X) #44: #a__U81(tt(),N,X,XS) -> #a__U82(a__splitAt(mark(N),mark(XS)),X) #45: #a__U81(tt(),N,X,XS) -> #a__splitAt(mark(N),mark(XS)) #46: #a__U81(tt(),N,X,XS) -> #mark(N) #47: #a__U81(tt(),N,X,XS) -> #mark(XS) #48: #a__U91(tt(),XS) -> #mark(XS) #49: #mark(isPLNat(X)) -> #a__isPLNat(X) #50: #a__isLNat(take(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2)) #51: #a__isLNat(take(V1,V2)) -> #a__isNatural(V1) #52: #mark(natsFrom(X)) -> #a__natsFrom(mark(X)) #53: #mark(natsFrom(X)) -> #mark(X) #54: #a__afterNth(N,XS) -> #a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS) #55: #a__afterNth(N,XS) -> #a__and(a__isNatural(N),isLNat(XS)) #56: #a__afterNth(N,XS) -> #a__isNatural(N) #57: #a__sel(N,XS) -> #a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS) #58: #a__sel(N,XS) -> #a__and(a__isNatural(N),isLNat(XS)) #59: #a__sel(N,XS) -> #a__isNatural(N) #60: #mark(isLNat(X)) -> #a__isLNat(X) #61: #a__fst(pair(X,Y)) -> #a__U21(a__and(a__isLNat(X),isLNat(Y)),X) #62: #a__fst(pair(X,Y)) -> #a__and(a__isLNat(X),isLNat(Y)) #63: #a__fst(pair(X,Y)) -> #a__isLNat(X) #64: #mark(cons(X1,X2)) -> #mark(X1) #65: #a__natsFrom(N) -> #a__U41(a__isNatural(N),N) #66: #a__natsFrom(N) -> #a__isNatural(N) #67: #mark(U82(X1,X2)) -> #a__U82(mark(X1),X2) #68: #mark(U82(X1,X2)) -> #mark(X1) #69: #mark(U61(X1,X2)) -> #a__U61(mark(X1),X2) #70: #mark(U61(X1,X2)) -> #mark(X1) #71: #a__isNatural(head(V1)) -> #a__isLNat(V1) #72: #a__isLNat(natsFrom(V1)) -> #a__isNatural(V1) #73: #a__U61(tt(),Y) -> #mark(Y) #74: #mark(splitAt(X1,X2)) -> #a__splitAt(mark(X1),mark(X2)) #75: #mark(splitAt(X1,X2)) -> #mark(X1) #76: #mark(splitAt(X1,X2)) -> #mark(X2) #77: #a__U82(pair(YS,ZS),X) -> #mark(X) #78: #a__U82(pair(YS,ZS),X) -> #mark(ZS) #79: #mark(pair(X1,X2)) -> #mark(X1) #80: #mark(pair(X1,X2)) -> #mark(X2) #81: #a__splitAt(0(),XS) -> #a__U71(a__isLNat(XS),XS) #82: #a__splitAt(0(),XS) -> #a__isLNat(XS) #83: #a__U41(tt(),N) -> #mark(N) #84: #mark(U41(X1,X2)) -> #a__U41(mark(X1),X2) #85: #mark(U41(X1,X2)) -> #mark(X1) #86: #a__isPLNat(pair(V1,V2)) -> #a__and(a__isLNat(V1),isLNat(V2)) #87: #a__isPLNat(pair(V1,V2)) -> #a__isLNat(V1) #88: #a__isLNat(tail(V1)) -> #a__isLNat(V1) #89: #a__splitAt(s(N),cons(X,XS)) -> #a__U81(a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS) #90: #a__splitAt(s(N),cons(X,XS)) -> #a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))) #91: #a__splitAt(s(N),cons(X,XS)) -> #a__isNatural(N) #92: #a__isNatural(sel(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2)) #93: #a__isNatural(sel(V1,V2)) -> #a__isNatural(V1) #94: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2)) #95: #mark(sel(X1,X2)) -> #mark(X1) #96: #mark(sel(X1,X2)) -> #mark(X2) #97: #a__isLNat(afterNth(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2)) #98: #a__isLNat(afterNth(V1,V2)) -> #a__isNatural(V1) #99: #a__snd(pair(X,Y)) -> #a__U61(a__and(a__isLNat(X),isLNat(Y)),Y) #100: #a__snd(pair(X,Y)) -> #a__and(a__isLNat(X),isLNat(Y)) #101: #a__snd(pair(X,Y)) -> #a__isLNat(X) #102: #a__isLNat(fst(V1)) -> #a__isPLNat(V1) #103: #mark(s(X)) -> #mark(X) #104: #a__isNatural(s(V1)) -> #a__isNatural(V1) #105: #a__take(N,XS) -> #a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS) #106: #a__take(N,XS) -> #a__and(a__isNatural(N),isLNat(XS)) #107: #a__take(N,XS) -> #a__isNatural(N) #108: #a__isLNat(snd(V1)) -> #a__isPLNat(V1) #109: #a__U21(tt(),X) -> #mark(X) #110: #a__U101(tt(),N,XS) -> #a__fst(a__splitAt(mark(N),mark(XS))) #111: #a__U101(tt(),N,XS) -> #a__splitAt(mark(N),mark(XS)) #112: #a__U101(tt(),N,XS) -> #mark(N) #113: #a__U101(tt(),N,XS) -> #mark(XS) #114: #mark(and(X1,X2)) -> #a__and(mark(X1),X2) #115: #mark(and(X1,X2)) -> #mark(X1) #116: #a__U71(tt(),XS) -> #mark(XS) #117: #a__head(cons(N,XS)) -> #a__U31(a__and(a__isNatural(N),isLNat(XS)),N) #118: #a__head(cons(N,XS)) -> #a__and(a__isNatural(N),isLNat(XS)) #119: #a__head(cons(N,XS)) -> #a__isNatural(N) #120: #a__U31(tt(),N) -> #mark(N) #121: #mark(U71(X1,X2)) -> #a__U71(mark(X1),X2) #122: #mark(U71(X1,X2)) -> #mark(X1) #123: #a__isLNat(cons(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2)) #124: #a__isLNat(cons(V1,V2)) -> #a__isNatural(V1) Number of SCCs: 1, DPs: 124 SCC { #1..124 } POLO(Sum)... POLO(max)... succeeded. U21 w: max(x1, x2) #a__U82 w: max(x1, x2 + 1) #a__U71 w: max(x1 + 1, x2) U11 w: max(x1, x2 + 1, x3 + 2) s w: x1 #a__U31 w: max(x1 + 2, x2 + 1) #a__head w: x1 + 3 #a__natsFrom w: x1 + 2 isPLNat w: 0 #a__snd w: x1 a__afterNth w: max(x1 + 2, x2 + 4) U91 w: max(x1 + 4, x2 + 2) a__U82 w: max(x1, x2 + 4) take w: max(x1, x2 + 3) U71 w: max(x1 + 2, x2) and w: max(x1, x2) U101 w: max(x1 + 3, x2, x3 + 2) pair w: max(x1, x2) fst w: x1 natsFrom w: x1 + 5 a__snd w: x1 + 1 #a__U51 w: max(x1 + 9, x2 + 8, x3 + 8) splitAt w: max(x1, x2) #a__U11 w: max(x2, x3) a__U31 w: max(x1 + 3, x2 + 2) a__U51 w: max(x1 + 10, x2 + 9, x3 + 9) a__U81 w: max(x1 + 2, x2, x3 + 4, x4) #a__take w: max(x1, x2 + 3) isNatural w: 0 a__U41 w: max(x1 + 4, x2 + 5) #a__U21 w: max(x2) #a__U81 w: max(x1 + 2, x2, x3 + 3, x4) #a__U61 w: max(x2) a__fst w: x1 tail w: x1 + 3 a__natsFrom w: x1 + 5 #mark w: x1 0 w: 2 #a__and w: max(x2) a__isLNat w: 0 a__U21 w: max(x1, x2) a__U91 w: max(x1 + 4, x2 + 2) sel w: max(x1 + 12, x2 + 11) afterNth w: max(x1 + 2, x2 + 4) nil w: 1 a__splitAt w: max(x1, x2) isLNat w: 0 #a__sel w: max(x1 + 9, x2 + 10) mark w: x1 #a__isLNat w: 0 #a__U101 w: max(x1 + 1, x2, x3) a__U11 w: max(x1, x2 + 1, x3 + 2) a__sel w: max(x1 + 12, x2 + 11) a__isPLNat w: 0 U61 w: max(x1 + 1, x2 + 1) U31 w: max(x1 + 3, x2 + 2) a__U71 w: max(x1 + 2, x2) #a__isPLNat w: 0 head w: x1 + 4 #a__afterNth w: max(x1 + 1, x2 + 3) #a__splitAt w: max(x1, x2) cons w: max(x1 + 4, x2) a__U61 w: max(x1 + 1, x2 + 1) snd w: x1 + 1 a__take w: max(x1, x2 + 3) U81 w: max(x1 + 2, x2, x3 + 4, x4) #a__U41 w: max(x1 + 1, x2 + 1) U82 w: max(x1, x2 + 4) tt w: 0 a__isNatural w: 0 #a__isNatural w: 0 #a__fst w: x1 U51 w: max(x1 + 10, x2 + 9, x3 + 9) a__and w: max(x1, x2) a__tail w: x1 + 3 U41 w: max(x1 + 4, x2 + 5) #a__tail w: x1 + 2 a__U101 w: max(x1 + 3, x2, x3 + 2) #a__U91 w: max(x1 + 2, x2 + 1) a__head w: x1 + 4 USABLE RULES: { 1..90 } Removed DPs: #5 #6 #9..13 #16 #17 #19..28 #31..34 #37 #39 #42 #48 #52..59 #64..66 #69 #70 #77 #82..85 #90 #91 #94..96 #106 #107 #117..120 #122 Number of SCCs: 1, DPs: 59 SCC { #7 #8 #14 #15 #18 #29 #30 #35 #36 #38 #40 #41 #43..47 #49..51 #60..63 #67 #68 #71 #72 #74..76 #78..81 #86..89 #92 #93 #97 #98 #102..105 #108..116 #121 #123 #124 } POLO(Sum)... POLO(max)... succeeded. U21 w: max(x1 + 1, x2 + 3) #a__U82 w: max(x1 + 1) #a__U71 w: max(x1 + 1, x2 + 9) U11 w: max(x1 + 14, x2 + 14, x3 + 14) s w: x1 #a__U31 w: 0 #a__head w: 3 #a__natsFrom w: 2 isPLNat w: 2 #a__snd w: 0 a__afterNth w: max(x1 + 14, x2 + 16) U91 w: max(x2 + 1) a__U82 w: max(x1, x2 + 10) take w: max(x1 + 24, x2 + 22) U71 w: max(x1 + 12, x2 + 13) and w: max(x1, x2) U101 w: max(x1 + 21, x2 + 17, x3 + 16) pair w: max(x1 + 8, x2 + 12) fst w: x1 + 1 natsFrom w: x1 + 3 a__snd w: x1 + 1 #a__U51 w: 0 splitAt w: max(x1 + 9, x2 + 13) #a__U11 w: 0 a__U31 w: max(x2) a__U51 w: max(x1 + 24, x2 + 23, x3 + 23) a__U81 w: max(x1 + 6, x2 + 9, x3 + 11, x4 + 13) #a__take w: max(x1 + 29, x2 + 22) isNatural w: 2 a__U41 w: max(x1 + 1, x2 + 3) #a__U21 w: max(x2 + 10) #a__U81 w: max(x1 + 13, x2 + 13, x3 + 18, x4 + 20) #a__U61 w: 0 a__fst w: x1 + 1 tail w: x1 + 1 a__natsFrom w: x1 + 3 #mark w: x1 + 8 0 w: 5 #a__and w: max(x2 + 8) a__isLNat w: 2 a__U21 w: max(x1 + 1, x2 + 3) a__U91 w: max(x2 + 1) sel w: max(x1 + 26, x2 + 33) afterNth w: max(x1 + 14, x2 + 16) nil w: 1 a__splitAt w: max(x1 + 9, x2 + 13) isLNat w: 2 #a__sel w: 0 mark w: x1 #a__isLNat w: 10 #a__U101 w: max(x1 + 26, x2 + 23, x3 + 21) a__U11 w: max(x1 + 14, x2 + 14, x3 + 14) a__sel w: max(x1 + 26, x2 + 33) a__isPLNat w: 2 U61 w: max(x2 + 10) U31 w: max(x2) a__U71 w: max(x1 + 12, x2 + 13) #a__isPLNat w: 10 head w: x1 + 7 #a__afterNth w: 0 #a__splitAt w: max(x1 + 13, x2 + 20) cons w: max(x1 + 1, x2) a__U61 w: max(x2 + 10) snd w: x1 + 1 a__take w: max(x1 + 24, x2 + 22) U81 w: max(x1 + 6, x2 + 9, x3 + 11, x4 + 13) #a__U41 w: 0 U82 w: max(x1, x2 + 10) tt w: 2 a__isNatural w: 2 #a__isNatural w: 10 #a__fst w: x1 + 3 U51 w: max(x1 + 24, x2 + 23, x3 + 23) a__and w: max(x1, x2) a__tail w: x1 + 1 U41 w: max(x1 + 1, x2 + 3) #a__tail w: 2 a__U101 w: max(x1 + 21, x2 + 17, x3 + 16) #a__U91 w: 0 a__head w: x1 + 7 USABLE RULES: { 1..90 } Removed DPs: #14 #15 #18 #29 #30 #35 #36 #40 #41 #44 #46 #47 #61..63 #67 #74..76 #78..81 #105 #109..113 #116 #121 Number of SCCs: 2, DPs: 28 SCC { #45 #89 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. U21 s: [] p: 4 w: max(x2 + 5) #a__U82 s: [1,2] p: 0 w: x1 + x2 #a__U71 s: [] p: 0 w: x1 + 1 U11 s: [] p: 2 w: max(x3 + 21) s s: [1] p: 14 w: x1 #a__U31 s: [2,1] p: 0 w: x1 + x2 + 1 #a__head s: [] p: 0 w: 0 #a__natsFrom s: [] p: 0 w: 0 isPLNat s: [] p: 9 w: 9 #a__snd s: [] p: 0 w: 0 a__afterNth s: [] p: 2 w: max(x2 + 22) U91 s: [] p: 3 w: max(x2 + 11) a__U82 s: [2] p: 7 w: max(x1, x2 + 17) take s: [] p: 11 w: x1 + x2 + 15 U71 s: [] p: 9 w: max(x2 + 8) and s: 2 U101 s: [1] p: 3 w: max(x1 + 3, x2 + 7, x3 + 15) pair s: [] p: 4 w: max(x1 + 6, x2 + 4) fst s: [1] p: 4 w: x1 + 6 natsFrom s: [] p: 13 w: x1 + 19 a__snd s: [] p: 1 w: x1 + 12 #a__U51 s: [] p: 0 w: x3 + 1 splitAt s: [2] p: 9 w: max(x2 + 8) #a__U11 s: [] p: 0 w: x1 a__U31 s: 2 a__U51 s: [] p: 10 w: max(x1 + 34, x3 + 33) a__U81 s: [] p: 8 w: max(x3 + 17, x4 + 8) #a__take s: [2,1] p: 0 w: x1 + x2 + 1 isNatural s: [] p: 9 w: 9 a__U41 s: [] p: 12 w: max(x1 + 9, x2 + 19) #a__U21 s: [2,1] p: 0 w: x1 + x2 #a__U81 s: [2] p: 14 w: max(x2) #a__U61 s: [] p: 0 w: max(x2) a__fst s: [1] p: 4 w: x1 + 6 tail s: [1] p: 3 w: x1 + 11 a__natsFrom s: [] p: 13 w: x1 + 19 #mark s: [] p: 0 w: 1 0 s: [] p: 9 w: 10 #a__and s: [1,2] p: 0 w: max(x1, x2) a__isLNat s: [] p: 9 w: 9 a__U21 s: [] p: 4 w: max(x2 + 5) a__U91 s: [] p: 3 w: max(x2 + 11) sel s: [] p: 10 w: x2 + 44 afterNth s: [] p: 2 w: max(x2 + 22) nil s: [] p: 13 w: 1 a__splitAt s: [2] p: 9 w: max(x2 + 8) isLNat s: [] p: 9 w: 9 #a__sel s: [1,2] p: 0 w: x1 + x2 + 1 mark s: 1 #a__isLNat s: [] p: 0 w: 1 #a__U101 s: [] p: 0 w: x2 a__U11 s: [] p: 2 w: max(x3 + 21) a__sel s: [] p: 10 w: x2 + 44 a__isPLNat s: [] p: 9 w: 9 U61 s: [2] p: 0 w: max(x1 + 6, x2 + 5) U31 s: 2 a__U71 s: [] p: 9 w: max(x2 + 8) #a__isPLNat s: [] p: 0 w: 0 head s: [] p: 10 w: x1 + 10 #a__afterNth s: [2] p: 0 w: x2 #a__splitAt s: 1 cons s: [1] p: 9 w: max(x1 + 10, x2) a__U61 s: [2] p: 0 w: max(x1 + 6, x2 + 5) snd s: [] p: 1 w: x1 + 12 a__take s: [] p: 11 w: x1 + x2 + 15 U81 s: [] p: 8 w: max(x3 + 17, x4 + 8) #a__U41 s: [] p: 0 w: x1 U82 s: [2] p: 7 w: max(x1, x2 + 17) tt s: [] p: 13 w: 2 a__isNatural s: [] p: 9 w: 9 #a__isNatural s: [] p: 0 w: 0 #a__fst s: [] p: 0 w: 0 U51 s: [] p: 10 w: max(x1 + 34, x3 + 33) a__and s: 2 a__tail s: [1] p: 3 w: x1 + 11 U41 s: [] p: 12 w: max(x1 + 9, x2 + 19) #a__tail s: [] p: 0 w: 1 a__U101 s: [1] p: 3 w: max(x1 + 3, x2 + 7, x3 + 15) #a__U91 s: [2] p: 0 w: x2 + 1 a__head s: [] p: 10 w: x1 + 10 USABLE RULES: { 1..90 } Removed DPs: #45 Number of SCCs: 1, DPs: 26 SCC { #7 #8 #38 #43 #49..51 #60 #68 #71 #72 #86..88 #92 #93 #97 #98 #102..104 #108 #114 #115 #123 #124 } POLO(Sum)... succeeded. U21 w: x1 + x2 + 1 #a__U82 w: 3 #a__U71 w: 2 U11 w: 1 s w: x1 + 1 #a__U31 w: 4 #a__head w: 3 #a__natsFrom w: 4 isPLNat w: x1 + 3 #a__snd w: 4 a__afterNth w: 0 U91 w: x1 + 2 a__U82 w: 3 take w: x1 + x2 + 3 U71 w: x1 + x2 + 3 and w: x1 + x2 + 2 U101 w: x1 + 5 pair w: x1 + x2 + 3 fst w: x1 + 6 natsFrom w: x1 + 2 a__snd w: x1 + 2 #a__U51 w: 3 splitAt w: x1 + x2 + 2 #a__U11 w: 3 a__U31 w: 0 a__U51 w: x3 + 4 a__U81 w: x2 + 2 #a__take w: 4 isNatural w: x1 + 3 a__U41 w: x2 + 5 #a__U21 w: 4 #a__U81 w: 4 #a__U61 w: 3 a__fst w: 5 tail w: x1 + 1 a__natsFrom w: x1 + 4 #mark w: x1 + 2 0 w: 1 #a__and w: x2 + 3 a__isLNat w: 1 a__U21 w: 0 a__U91 w: 1 sel w: x1 + x2 + 5 afterNth w: x1 + x2 + 3 nil w: 0 a__splitAt w: 1 isLNat w: x1 + 2 #a__sel w: 4 mark w: 0 #a__isLNat w: x1 + 3 #a__U101 w: 2 a__U11 w: x2 + 3 a__sel w: x2 + 4 a__isPLNat w: x1 + 2 U61 w: x1 + 1 U31 w: x1 + 1 a__U71 w: 2 #a__isPLNat w: x1 + 4 head w: x1 + 2 #a__afterNth w: 4 #a__splitAt w: 4 cons w: x1 + x2 + 3 a__U61 w: 0 snd w: x1 + 2 a__take w: x1 + x2 + 3 U81 w: x1 + x4 + 3 #a__U41 w: 3 U82 w: x1 + 4 tt w: 3 a__isNatural w: 2 #a__isNatural w: x1 + 4 #a__fst w: 2 U51 w: x2 + 5 a__and w: 0 a__tail w: x1 + 1 U41 w: x1 + 6 #a__tail w: 4 a__U101 w: x2 + x3 + 4 #a__U91 w: 4 a__head w: 1 USABLE RULES: { } Removed DPs: #7 #8 #38 #43 #49..51 #60 #68 #71 #72 #86..88 #92 #93 #97 #98 #102..104 #108 #114 #115 #123 #124 Number of SCCs: 0, DPs: 0