/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(),N,XS) -> fst(splitAt(activate(N),activate(XS))) 2: U11(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS))) 3: U21(tt(),X) -> activate(X) 4: U31(tt(),N) -> activate(N) 5: U41(tt(),N) -> cons(activate(N),n__natsFrom(n__s(activate(N)))) 6: U51(tt(),N,XS) -> head(afterNth(activate(N),activate(XS))) 7: U61(tt(),Y) -> activate(Y) 8: U71(tt(),XS) -> pair(nil(),activate(XS)) 9: U81(tt(),N,X,XS) -> U82(splitAt(activate(N),activate(XS)),activate(X)) 10: U82(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS) 11: U91(tt(),XS) -> activate(XS) 12: afterNth(N,XS) -> U11(and(isNatural(N),n__isLNat(XS)),N,XS) 13: and(tt(),X) -> activate(X) 14: fst(pair(X,Y)) -> U21(and(isLNat(X),n__isLNat(Y)),X) 15: head(cons(N,XS)) -> U31(and(isNatural(N),n__isLNat(activate(XS))),N) 16: isLNat(n__nil()) -> tt() 17: isLNat(n__afterNth(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) 18: isLNat(n__cons(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) 19: isLNat(n__fst(V1)) -> isPLNat(activate(V1)) 20: isLNat(n__natsFrom(V1)) -> isNatural(activate(V1)) 21: isLNat(n__snd(V1)) -> isPLNat(activate(V1)) 22: isLNat(n__tail(V1)) -> isLNat(activate(V1)) 23: isLNat(n__take(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) 24: isNatural(n__0()) -> tt() 25: isNatural(n__head(V1)) -> isLNat(activate(V1)) 26: isNatural(n__s(V1)) -> isNatural(activate(V1)) 27: isNatural(n__sel(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) 28: isPLNat(n__pair(V1,V2)) -> and(isLNat(activate(V1)),n__isLNat(activate(V2))) 29: isPLNat(n__splitAt(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) 30: natsFrom(N) -> U41(isNatural(N),N) 31: sel(N,XS) -> U51(and(isNatural(N),n__isLNat(XS)),N,XS) 32: snd(pair(X,Y)) -> U61(and(isLNat(X),n__isLNat(Y)),Y) 33: splitAt(0(),XS) -> U71(isLNat(XS),XS) 34: splitAt(s(N),cons(X,XS)) -> U81(and(isNatural(N),n__and(n__isNatural(X),n__isLNat(activate(XS)))),N,X,activate(XS)) 35: tail(cons(N,XS)) -> U91(and(isNatural(N),n__isLNat(activate(XS))),activate(XS)) 36: take(N,XS) -> U101(and(isNatural(N),n__isLNat(XS)),N,XS) 37: natsFrom(X) -> n__natsFrom(X) 38: s(X) -> n__s(X) 39: isLNat(X) -> n__isLNat(X) 40: nil() -> n__nil() 41: afterNth(X1,X2) -> n__afterNth(X1,X2) 42: cons(X1,X2) -> n__cons(X1,X2) 43: fst(X) -> n__fst(X) 44: snd(X) -> n__snd(X) 45: tail(X) -> n__tail(X) 46: take(X1,X2) -> n__take(X1,X2) 47: 0() -> n__0() 48: head(X) -> n__head(X) 49: sel(X1,X2) -> n__sel(X1,X2) 50: pair(X1,X2) -> n__pair(X1,X2) 51: splitAt(X1,X2) -> n__splitAt(X1,X2) 52: and(X1,X2) -> n__and(X1,X2) 53: isNatural(X) -> n__isNatural(X) 54: activate(n__natsFrom(X)) -> natsFrom(activate(X)) 55: activate(n__s(X)) -> s(activate(X)) 56: activate(n__isLNat(X)) -> isLNat(X) 57: activate(n__nil()) -> nil() 58: activate(n__afterNth(X1,X2)) -> afterNth(activate(X1),activate(X2)) 59: activate(n__cons(X1,X2)) -> cons(activate(X1),X2) 60: activate(n__fst(X)) -> fst(activate(X)) 61: activate(n__snd(X)) -> snd(activate(X)) 62: activate(n__tail(X)) -> tail(activate(X)) 63: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) 64: activate(n__0()) -> 0() 65: activate(n__head(X)) -> head(activate(X)) 66: activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2)) 67: activate(n__pair(X1,X2)) -> pair(activate(X1),activate(X2)) 68: activate(n__splitAt(X1,X2)) -> splitAt(activate(X1),activate(X2)) 69: activate(n__and(X1,X2)) -> and(activate(X1),X2) 70: activate(n__isNatural(X)) -> isNatural(X) 71: activate(X) -> X Number of strict rules: 71 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #U11(tt(),N,XS) -> #snd(splitAt(activate(N),activate(XS))) #2: #U11(tt(),N,XS) -> #splitAt(activate(N),activate(XS)) #3: #U11(tt(),N,XS) -> #activate(N) #4: #U11(tt(),N,XS) -> #activate(XS) #5: #isPLNat(n__splitAt(V1,V2)) -> #and(isNatural(activate(V1)),n__isLNat(activate(V2))) #6: #isPLNat(n__splitAt(V1,V2)) -> #isNatural(activate(V1)) #7: #isPLNat(n__splitAt(V1,V2)) -> #activate(V1) #8: #isPLNat(n__splitAt(V1,V2)) -> #activate(V2) #9: #tail(cons(N,XS)) -> #U91(and(isNatural(N),n__isLNat(activate(XS))),activate(XS)) #10: #tail(cons(N,XS)) -> #and(isNatural(N),n__isLNat(activate(XS))) #11: #tail(cons(N,XS)) -> #isNatural(N) #12: #tail(cons(N,XS)) -> #activate(XS) #13: #tail(cons(N,XS)) -> #activate(XS) #14: #activate(n__sel(X1,X2)) -> #sel(activate(X1),activate(X2)) #15: #activate(n__sel(X1,X2)) -> #activate(X1) #16: #activate(n__sel(X1,X2)) -> #activate(X2) #17: #activate(n__afterNth(X1,X2)) -> #afterNth(activate(X1),activate(X2)) #18: #activate(n__afterNth(X1,X2)) -> #activate(X1) #19: #activate(n__afterNth(X1,X2)) -> #activate(X2) #20: #activate(n__snd(X)) -> #snd(activate(X)) #21: #activate(n__snd(X)) -> #activate(X) #22: #U51(tt(),N,XS) -> #head(afterNth(activate(N),activate(XS))) #23: #U51(tt(),N,XS) -> #afterNth(activate(N),activate(XS)) #24: #U51(tt(),N,XS) -> #activate(N) #25: #U51(tt(),N,XS) -> #activate(XS) #26: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2) #27: #activate(n__cons(X1,X2)) -> #activate(X1) #28: #activate(n__s(X)) -> #s(activate(X)) #29: #activate(n__s(X)) -> #activate(X) #30: #activate(n__pair(X1,X2)) -> #pair(activate(X1),activate(X2)) #31: #activate(n__pair(X1,X2)) -> #activate(X1) #32: #activate(n__pair(X1,X2)) -> #activate(X2) #33: #and(tt(),X) -> #activate(X) #34: #U81(tt(),N,X,XS) -> #U82(splitAt(activate(N),activate(XS)),activate(X)) #35: #U81(tt(),N,X,XS) -> #splitAt(activate(N),activate(XS)) #36: #U81(tt(),N,X,XS) -> #activate(N) #37: #U81(tt(),N,X,XS) -> #activate(XS) #38: #U81(tt(),N,X,XS) -> #activate(X) #39: #U91(tt(),XS) -> #activate(XS) #40: #activate(n__nil()) -> #nil() #41: #activate(n__isNatural(X)) -> #isNatural(X) #42: #isLNat(n__take(V1,V2)) -> #and(isNatural(activate(V1)),n__isLNat(activate(V2))) #43: #isLNat(n__take(V1,V2)) -> #isNatural(activate(V1)) #44: #isLNat(n__take(V1,V2)) -> #activate(V1) #45: #isLNat(n__take(V1,V2)) -> #activate(V2) #46: #activate(n__and(X1,X2)) -> #and(activate(X1),X2) #47: #activate(n__and(X1,X2)) -> #activate(X1) #48: #afterNth(N,XS) -> #U11(and(isNatural(N),n__isLNat(XS)),N,XS) #49: #afterNth(N,XS) -> #and(isNatural(N),n__isLNat(XS)) #50: #afterNth(N,XS) -> #isNatural(N) #51: #sel(N,XS) -> #U51(and(isNatural(N),n__isLNat(XS)),N,XS) #52: #sel(N,XS) -> #and(isNatural(N),n__isLNat(XS)) #53: #sel(N,XS) -> #isNatural(N) #54: #activate(n__isLNat(X)) -> #isLNat(X) #55: #fst(pair(X,Y)) -> #U21(and(isLNat(X),n__isLNat(Y)),X) #56: #fst(pair(X,Y)) -> #and(isLNat(X),n__isLNat(Y)) #57: #fst(pair(X,Y)) -> #isLNat(X) #58: #activate(n__tail(X)) -> #tail(activate(X)) #59: #activate(n__tail(X)) -> #activate(X) #60: #natsFrom(N) -> #U41(isNatural(N),N) #61: #natsFrom(N) -> #isNatural(N) #62: #isNatural(n__head(V1)) -> #isLNat(activate(V1)) #63: #isNatural(n__head(V1)) -> #activate(V1) #64: #isLNat(n__natsFrom(V1)) -> #isNatural(activate(V1)) #65: #isLNat(n__natsFrom(V1)) -> #activate(V1) #66: #U61(tt(),Y) -> #activate(Y) #67: #U82(pair(YS,ZS),X) -> #pair(cons(activate(X),YS),ZS) #68: #U82(pair(YS,ZS),X) -> #cons(activate(X),YS) #69: #U82(pair(YS,ZS),X) -> #activate(X) #70: #activate(n__0()) -> #0() #71: #splitAt(0(),XS) -> #U71(isLNat(XS),XS) #72: #splitAt(0(),XS) -> #isLNat(XS) #73: #U41(tt(),N) -> #cons(activate(N),n__natsFrom(n__s(activate(N)))) #74: #U41(tt(),N) -> #activate(N) #75: #U41(tt(),N) -> #activate(N) #76: #activate(n__head(X)) -> #head(activate(X)) #77: #activate(n__head(X)) -> #activate(X) #78: #isPLNat(n__pair(V1,V2)) -> #and(isLNat(activate(V1)),n__isLNat(activate(V2))) #79: #isPLNat(n__pair(V1,V2)) -> #isLNat(activate(V1)) #80: #isPLNat(n__pair(V1,V2)) -> #activate(V1) #81: #isPLNat(n__pair(V1,V2)) -> #activate(V2) #82: #isLNat(n__tail(V1)) -> #isLNat(activate(V1)) #83: #isLNat(n__tail(V1)) -> #activate(V1) #84: #splitAt(s(N),cons(X,XS)) -> #U81(and(isNatural(N),n__and(n__isNatural(X),n__isLNat(activate(XS)))),N,X,activate(XS)) #85: #splitAt(s(N),cons(X,XS)) -> #and(isNatural(N),n__and(n__isNatural(X),n__isLNat(activate(XS)))) #86: #splitAt(s(N),cons(X,XS)) -> #isNatural(N) #87: #splitAt(s(N),cons(X,XS)) -> #activate(XS) #88: #splitAt(s(N),cons(X,XS)) -> #activate(XS) #89: #isNatural(n__sel(V1,V2)) -> #and(isNatural(activate(V1)),n__isLNat(activate(V2))) #90: #isNatural(n__sel(V1,V2)) -> #isNatural(activate(V1)) #91: #isNatural(n__sel(V1,V2)) -> #activate(V1) #92: #isNatural(n__sel(V1,V2)) -> #activate(V2) #93: #activate(n__fst(X)) -> #fst(activate(X)) #94: #activate(n__fst(X)) -> #activate(X) #95: #isLNat(n__afterNth(V1,V2)) -> #and(isNatural(activate(V1)),n__isLNat(activate(V2))) #96: #isLNat(n__afterNth(V1,V2)) -> #isNatural(activate(V1)) #97: #isLNat(n__afterNth(V1,V2)) -> #activate(V1) #98: #isLNat(n__afterNth(V1,V2)) -> #activate(V2) #99: #snd(pair(X,Y)) -> #U61(and(isLNat(X),n__isLNat(Y)),Y) #100: #snd(pair(X,Y)) -> #and(isLNat(X),n__isLNat(Y)) #101: #snd(pair(X,Y)) -> #isLNat(X) #102: #isLNat(n__fst(V1)) -> #isPLNat(activate(V1)) #103: #isLNat(n__fst(V1)) -> #activate(V1) #104: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2)) #105: #activate(n__take(X1,X2)) -> #activate(X1) #106: #activate(n__take(X1,X2)) -> #activate(X2) #107: #isNatural(n__s(V1)) -> #isNatural(activate(V1)) #108: #isNatural(n__s(V1)) -> #activate(V1) #109: #activate(n__splitAt(X1,X2)) -> #splitAt(activate(X1),activate(X2)) #110: #activate(n__splitAt(X1,X2)) -> #activate(X1) #111: #activate(n__splitAt(X1,X2)) -> #activate(X2) #112: #take(N,XS) -> #U101(and(isNatural(N),n__isLNat(XS)),N,XS) #113: #take(N,XS) -> #and(isNatural(N),n__isLNat(XS)) #114: #take(N,XS) -> #isNatural(N) #115: #isLNat(n__snd(V1)) -> #isPLNat(activate(V1)) #116: #isLNat(n__snd(V1)) -> #activate(V1) #117: #U21(tt(),X) -> #activate(X) #118: #U101(tt(),N,XS) -> #fst(splitAt(activate(N),activate(XS))) #119: #U101(tt(),N,XS) -> #splitAt(activate(N),activate(XS)) #120: #U101(tt(),N,XS) -> #activate(N) #121: #U101(tt(),N,XS) -> #activate(XS) #122: #activate(n__natsFrom(X)) -> #natsFrom(activate(X)) #123: #activate(n__natsFrom(X)) -> #activate(X) #124: #U71(tt(),XS) -> #pair(nil(),activate(XS)) #125: #U71(tt(),XS) -> #nil() #126: #U71(tt(),XS) -> #activate(XS) #127: #head(cons(N,XS)) -> #U31(and(isNatural(N),n__isLNat(activate(XS))),N) #128: #head(cons(N,XS)) -> #and(isNatural(N),n__isLNat(activate(XS))) #129: #head(cons(N,XS)) -> #isNatural(N) #130: #head(cons(N,XS)) -> #activate(XS) #131: #U31(tt(),N) -> #activate(N) #132: #isLNat(n__cons(V1,V2)) -> #and(isNatural(activate(V1)),n__isLNat(activate(V2))) #133: #isLNat(n__cons(V1,V2)) -> #isNatural(activate(V1)) #134: #isLNat(n__cons(V1,V2)) -> #activate(V1) #135: #isLNat(n__cons(V1,V2)) -> #activate(V2) Number of SCCs: 1, DPs: 125 SCC { #1..25 #27 #29 #31..39 #41..66 #69 #71 #72 #74..123 #126..135 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 U21 w: max(x1, x2 + 7) U11 w: max(x1 + 14, x2 + 14, x3 + 15) #cons w: 0 s w: x1 n__pair w: max(x1 + 3, x2 + 2) #take w: max(x1, x2 + 9) isPLNat w: x1 + 5 U91 w: max(x2 + 1) #U101 w: max(x2, x3 + 8) activate w: x1 n__isLNat w: x1 + 1 #U82 w: max(x2 + 1) take w: max(x1 + 10, x2 + 12) U71 w: max(x2 + 8) #U81 w: max(x2, x3 + 5, x4 + 4) and w: max(x1 + 4, x2) U101 w: max(x2 + 4, x3 + 12) pair w: max(x1 + 3, x2 + 2) fst w: x1 + 4 #activate w: x1 natsFrom w: x1 + 7 #head w: x1 + 3 splitAt w: max(x1, x2 + 8) #fst w: x1 n__nil w: 0 n__natsFrom w: x1 + 7 isNatural w: x1 + 1 n__snd w: x1 + 7 n__s w: x1 n__splitAt w: max(x1, x2 + 8) tail w: x1 + 4 0 w: 2 n__take w: max(x1 + 10, x2 + 12) #sel w: max(x1 + 24, x2 + 24) #isLNat w: x1 + 1 sel w: max(x1 + 25, x2 + 26) #s w: 0 afterNth w: max(x1 + 19, x2 + 18) n__cons w: max(x1 + 4, x2) #isPLNat w: x1 + 2 nil w: 0 isLNat w: x1 + 1 n__sel w: max(x1 + 25, x2 + 26) #tail w: x1 + 3 #splitAt w: max(x1, x2 + 4) #nil w: 0 n__tail w: x1 + 4 #afterNth w: max(x1 + 15, x2 + 17) n__isNatural w: x1 + 1 n__0 w: 2 n__afterNth w: max(x1 + 19, x2 + 18) U61 w: max(x2 + 3) #U51 w: max(x2 + 23, x3 + 23) n__fst w: x1 + 4 #U11 w: max(x1 + 9, x2 + 9, x3 + 16) U31 w: max(x1 + 3, x2 + 7) head w: x1 + 6 #snd w: x1 #U41 w: max(x1 + 1, x2 + 1) cons w: max(x1 + 4, x2) #natsFrom w: x1 + 3 snd w: x1 + 7 #U21 w: max(x2 + 1) U81 w: max(x2, x3 + 7, x4 + 8) U82 w: max(x1, x2 + 7) tt w: 0 n__and w: max(x1 + 4, x2) #U71 w: max(x1 + 2, x2) #isNatural w: x1 #pair w: 0 n__head w: x1 + 6 U51 w: max(x2 + 25, x3 + 24) U41 w: max(x1 + 6, x2 + 7) #U31 w: max(x1 + 1, x2 + 1) #and w: max(x2) #U91 w: max(x1 + 1, x2 + 1) #U61 w: max(x2 + 1) USABLE RULES: { 1..71 } Removed DPs: #1..25 #27 #31 #32 #34 #37..39 #41..45 #47..53 #55..66 #69 #71 #72 #74..83 #85 #87..106 #111 #113 #115..117 #121..123 #127..131 #133..135 Number of SCCs: 1, DPs: 13 SCC { #29 #33 #35 #36 #46 #54 #84 #86 #107..110 #132 } POLO(Sum)... POLO(max)... succeeded. #0 w: 0 U21 w: max(x1 + 3, x2 + 4) U11 w: max(x1 + 16, x2 + 14, x3 + 15) #cons w: 0 s w: x1 n__pair w: max(x1 + 3, x2 + 1) #take w: 0 isPLNat w: 1 U91 w: max(x2 + 1) #U101 w: 0 activate w: x1 n__isLNat w: 1 #U82 w: 0 take w: max(x1 + 7, x2 + 9) U71 w: max(x2 + 8) #U81 w: max(x2 + 3) and w: max(x2) U101 w: max(x2 + 4, x3 + 9) pair w: max(x1 + 3, x2 + 1) fst w: x1 + 1 #activate w: x1 + 1 natsFrom w: x1 + 2 #head w: 3 splitAt w: max(x1 + 3, x2 + 8) #fst w: 0 n__nil w: 1 n__natsFrom w: x1 + 2 isNatural w: 1 n__snd w: x1 + 7 n__s w: x1 n__splitAt w: max(x1 + 3, x2 + 8) tail w: x1 + 4 0 w: 1 n__take w: max(x1 + 7, x2 + 9) #sel w: 0 #isLNat w: 2 sel w: max(x1 + 25, x2 + 26) #s w: 0 afterNth w: max(x1 + 19, x2 + 15) n__cons w: max(x1 + 2, x2) #isPLNat w: 2 nil w: 1 isLNat w: 1 n__sel w: max(x1 + 25, x2 + 26) #tail w: 3 #splitAt w: max(x1 + 3) #nil w: 0 n__tail w: x1 + 4 #afterNth w: 0 n__isNatural w: 1 n__0 w: 1 n__afterNth w: max(x1 + 19, x2 + 15) U61 w: max(x2 + 3) #U51 w: 0 n__fst w: x1 + 1 #U11 w: 0 U31 w: max(x1 + 7, x2 + 8) head w: x1 + 6 #snd w: 0 #U41 w: 0 cons w: max(x1 + 2, x2) #natsFrom w: 3 snd w: x1 + 7 #U21 w: 0 U81 w: max(x2 + 3, x3 + 7, x4 + 8) U82 w: max(x1, x2 + 7) tt w: 0 n__and w: max(x2) #U71 w: 0 #isNatural w: x1 + 2 #pair w: 0 n__head w: x1 + 6 U51 w: max(x2 + 25, x3 + 24) U41 w: max(x2 + 2) #U31 w: 0 #and w: max(x2 + 1) #U91 w: 0 #U61 w: 0 USABLE RULES: { 1..71 } Removed DPs: #36 #86 #108..110 Number of SCCs: 3, DPs: 8 SCC { #107 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #0 s: [] p: 0 w: 0 U21 s: [] p: 6 w: max(x2 + 1) U11 s: [] p: 8 w: max(x3 + 8) #cons s: [2,1] p: 0 w: max(x1, x2 + 1) s s: [1] p: 6 w: x1 n__pair s: [] p: 5 w: max(x1, x2) #take s: [1,2] p: 0 w: x1 + x2 isPLNat s: [] p: 8 w: x1 U91 s: [1,2] p: 3 w: max(x1 + 3, x2 + 3) #U101 s: [1] p: 0 w: max(x1 + 1) activate s: 1 n__isLNat s: [] p: 8 w: x1 #U82 s: [1,2] p: 0 w: x1 + x2 + 1 take s: [] p: 7 w: x2 + 10 U71 s: [2] p: 6 w: max(x1 + 2, x2) #U81 s: [1,2] p: 0 w: max(x1, x2) and s: 2 U101 s: [] p: 6 w: max(x3 + 9) pair s: [] p: 5 w: max(x1, x2) fst s: [] p: 6 w: x1 + 4 #activate s: [] p: 0 w: 1 natsFrom s: [] p: 9 w: x1 + 4 #head s: [] p: 0 w: 1 splitAt s: [] p: 8 w: max(x2 + 4) #fst s: [] p: 0 w: 0 n__nil s: [] p: 0 w: 4 n__natsFrom s: [] p: 9 w: x1 + 4 isNatural s: [] p: 8 w: x1 + 3 n__snd s: [] p: 2 w: x1 + 4 n__s s: [1] p: 6 w: x1 n__splitAt s: [] p: 8 w: max(x2 + 4) tail s: [] p: 4 w: x1 + 4 0 s: [] p: 0 w: 4 n__take s: [] p: 7 w: x2 + 10 #sel s: [] p: 0 w: x2 #isLNat s: [] p: 0 w: 0 sel s: [] p: 4 w: x2 + 15 #s s: [] p: 0 w: 1 afterNth s: [] p: 8 w: max(x2 + 9) n__cons s: [] p: 8 w: max(x1 + 2, x2) #isPLNat s: [] p: 0 w: 0 nil s: [] p: 0 w: 4 isLNat s: [] p: 8 w: x1 n__sel s: [] p: 4 w: x2 + 15 #tail s: [] p: 0 w: 0 #splitAt s: [1] p: 0 w: max(x1 + 1) #nil s: [] p: 0 w: 1 n__tail s: [] p: 4 w: x1 + 4 #afterNth s: [] p: 0 w: x1 n__isNatural s: [] p: 8 w: x1 + 3 n__0 s: [] p: 0 w: 4 n__afterNth s: [] p: 8 w: max(x2 + 9) U61 s: [1,2] p: 1 w: max(x1, x2) #U51 s: [1,2,3] p: 0 w: x1 + x2 + x3 + 1 n__fst s: [] p: 6 w: x1 + 4 #U11 s: [2,3,1] p: 0 w: x1 + x2 + x3 U31 s: [] p: 9 w: max(x1 + 3, x2 + 5) head s: [] p: 10 w: x1 + 4 #snd s: [] p: 0 w: 0 #U41 s: [] p: 0 w: 0 cons s: [] p: 8 w: max(x1 + 2, x2) #natsFrom s: [] p: 0 w: 0 snd s: [] p: 2 w: x1 + 4 #U21 s: [2,1] p: 0 w: x1 + x2 U81 s: [] p: 7 w: max(x1, x3 + 6, x4 + 4) U82 s: [] p: 5 w: max(x1, x2 + 2) tt s: [] p: 1 w: 3 n__and s: 2 #U71 s: [2,1] p: 0 w: x1 + x2 #isNatural s: [1] p: 0 w: x1 + 1 #pair s: [] p: 0 w: max(x2) n__head s: [] p: 10 w: x1 + 4 U51 s: [] p: 3 w: max(x1 + 11, x3 + 14) U41 s: [] p: 8 w: max(x2 + 4) #U31 s: [1,2] p: 0 w: x1 + x2 + 1 #and s: [] p: 0 w: max(x2 + 1) #U91 s: [] p: 0 w: x1 + 1 #U61 s: [] p: 0 w: x2 + 1 USABLE RULES: { 1..71 } Removed DPs: #107 Number of SCCs: 2, DPs: 7 SCC { #35 #84 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #0 s: [] p: 0 w: 0 U21 s: [1,2] p: 9 w: max(x1 + 1, x2 + 1) U11 s: [] p: 10 w: max(x2 + 13, x3 + 15) #cons s: [2,1] p: 0 w: max(x1, x2 + 1) s s: [1] p: 8 w: x1 n__pair s: [] p: 2 w: max(x1, x2) #take s: [1,2] p: 0 w: x1 + x2 isPLNat s: [] p: 5 w: x1 U91 s: [] p: 3 w: max(x1 + 3, x2 + 3) #U101 s: [1] p: 0 w: max(x1 + 1) activate s: 1 n__isLNat s: [] p: 5 w: x1 #U82 s: [1,2] p: 0 w: x1 + x2 + 1 take s: [] p: 11 w: x1 + x2 + 14 U71 s: [] p: 3 w: max(x2 + 5) #U81 s: [2,1] p: 6 w: max(x1, x2 + 1, x3 + 2, x4) and s: 2 U101 s: [] p: 10 w: max(x2 + 13, x3 + 9) pair s: [] p: 2 w: max(x1, x2) fst s: [] p: 10 w: x1 + 2 #activate s: [] p: 0 w: 1 natsFrom s: [] p: 10 w: x1 + 4 #head s: [] p: 0 w: 1 splitAt s: [] p: 3 w: max(x1 + 10, x2 + 6) #fst s: [] p: 0 w: 0 n__nil s: [] p: 0 w: 4 n__natsFrom s: [] p: 10 w: x1 + 4 isNatural s: 1 n__snd s: [] p: 4 w: x1 + 2 n__s s: [1] p: 8 w: x1 n__splitAt s: [] p: 3 w: max(x1 + 10, x2 + 6) tail s: [] p: 8 w: x1 + 4 0 s: [] p: 0 w: 6 n__take s: [] p: 11 w: x1 + x2 + 14 #sel s: [] p: 0 w: x2 #isLNat s: [] p: 0 w: 0 sel s: [] p: 8 w: x1 + x2 + 24 #s s: [] p: 0 w: 1 afterNth s: [2] p: 10 w: max(x1 + 14, x2 + 16) n__cons s: [] p: 5 w: max(x1 + 2, x2) #isPLNat s: [] p: 0 w: 0 nil s: [] p: 0 w: 4 isLNat s: [] p: 5 w: x1 n__sel s: [] p: 8 w: x1 + x2 + 24 #tail s: [] p: 0 w: 0 #splitAt s: [1] p: 6 w: max(x1 + 1, x2) #nil s: [] p: 0 w: 1 n__tail s: [] p: 8 w: x1 + 4 #afterNth s: [] p: 0 w: x1 n__isNatural s: 1 n__0 s: [] p: 0 w: 6 n__afterNth s: [2] p: 10 w: max(x1 + 14, x2 + 16) U61 s: [] p: 4 w: max(x1, x2 + 1) #U51 s: [1,2,3] p: 0 w: x1 + x2 + x3 + 1 n__fst s: [] p: 10 w: x1 + 2 #U11 s: [2,3,1] p: 0 w: x1 + x2 + x3 U31 s: [] p: 5 w: max(x1 + 3, x2 + 3) head s: [] p: 5 w: x1 + 4 #snd s: [] p: 0 w: 0 #U41 s: [] p: 0 w: 0 cons s: [] p: 5 w: max(x1 + 2, x2) #natsFrom s: [] p: 0 w: 0 snd s: [] p: 4 w: x1 + 2 #U21 s: [2,1] p: 0 w: x1 + x2 U81 s: [] p: 3 w: max(x2 + 10, x3 + 7, x4 + 6) U82 s: [] p: 2 w: max(x1, x2 + 2) tt s: [] p: 1 w: 3 n__and s: 2 #U71 s: [2,1] p: 0 w: x1 + x2 #isNatural s: [] p: 0 w: 1 #pair s: [] p: 0 w: max(x2) n__head s: [] p: 5 w: x1 + 4 U51 s: [] p: 5 w: max(x1 + 14, x2 + 19, x3 + 21) U41 s: [] p: 9 w: max(x1, x2 + 4) #U31 s: [1,2] p: 0 w: x1 + x2 + 1 #and s: [] p: 0 w: max(x2 + 1) #U91 s: [] p: 0 w: x1 + 1 #U61 s: [] p: 0 w: x2 + 1 USABLE RULES: { 1..71 } Removed DPs: #35 #84 Number of SCCs: 1, DPs: 5 SCC { #29 #33 #46 #54 #132 } POLO(Sum)... succeeded. #0 w: 0 U21 w: x1 + x2 + 4 U11 w: x1 + x3 + 2 #cons w: 0 s w: 9 n__pair w: 2 #take w: 1 isPLNat w: x1 + 5 U91 w: x2 + 2 #U101 w: 1 activate w: x1 + 2 n__isLNat w: 1 #U82 w: 1 take w: 0 U71 w: x1 + x2 #U81 w: 0 and w: x1 + 2 U101 w: x1 + x2 + x3 pair w: x1 + x2 + 1 fst w: x1 + 3 #activate w: x1 + 1 natsFrom w: x1 + 2 #head w: 1 splitAt w: x2 + 3 #fst w: 1 n__nil w: 1 n__natsFrom w: x1 + 1 isNatural w: x1 + 4 n__snd w: 1 n__s w: x1 + 6 n__splitAt w: 2 tail w: x1 + 2 0 w: 1 n__take w: x1 + x2 + 4 #sel w: 1 #isLNat w: 2 sel w: x1 + 2 #s w: 0 afterNth w: 7 n__cons w: 1 #isPLNat w: 1 nil w: 4 isLNat w: x1 + 4 n__sel w: x2 + 1 #tail w: 1 #splitAt w: 0 #nil w: 0 n__tail w: 1 #afterNth w: 1 n__isNatural w: 1 n__0 w: 2 n__afterNth w: x1 + x2 + 4 U61 w: 0 #U51 w: 1 n__fst w: 2 #U11 w: 0 U31 w: x1 + 3 head w: 0 #snd w: 1 #U41 w: 1 cons w: x1 + x2 + 2 #natsFrom w: 1 snd w: x1 + 5 #U21 w: 1 U81 w: x1 + x4 + 2 U82 w: 4 tt w: 7 n__and w: x1 + x2 + 3 #U71 w: 1 #isNatural w: 1 #pair w: 0 n__head w: x1 + 1 U51 w: x1 + x2 + x3 U41 w: x1 #U31 w: 1 #and w: x2 + 1 #U91 w: 1 #U61 w: 1 USABLE RULES: { } Removed DPs: #29 #46 Number of SCCs: 1, DPs: 3 SCC { #33 #54 #132 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.