/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We split firstr-order part and higher-order part, and do modular checking by a general modularity. ******** FO SN check ******** Check SN using NaTT (Nagoya Termination Tool) Input TRS: 1: active(u101(tt(),X,Y)) -> mark(u102(isNatural(X),Y)) 2: active(u102(tt(),U)) -> mark(u103(isLNat(U))) 3: active(u103(tt())) -> mark(tt()) 4: active(u11(tt(),V,W)) -> mark(snd(splitAt(V,W))) 5: active(u111(tt(),P)) -> mark(u112(isLNat(P))) 6: active(u112(tt())) -> mark(tt()) 7: active(u121(tt(),X1)) -> mark(u122(isNatural(X1))) 8: active(u122(tt())) -> mark(tt()) 9: active(u131(tt(),Y1,U1)) -> mark(u132(isNatural(Y1),U1)) 10: active(u132(tt(),V1)) -> mark(u133(isLNat(V1))) 11: active(u133(tt())) -> mark(tt()) 12: active(u141(tt(),W1,P1)) -> mark(u142(isLNat(W1),P1)) 13: active(u142(tt(),X2)) -> mark(u143(isLNat(X2))) 14: active(u143(tt())) -> mark(tt()) 15: active(u151(tt(),Y2,U2)) -> mark(u152(isNatural(Y2),U2)) 16: active(u152(tt(),V2)) -> mark(u153(isLNat(V2))) 17: active(u153(tt())) -> mark(tt()) 18: active(u161(tt(),W2)) -> mark(cons(W2,natsFrom(s(W2)))) 19: active(u171(tt(),P2,X3)) -> mark(head(afterNth(P2,X3))) 20: active(u181(tt(),Y3)) -> mark(Y3) 21: active(u191(tt(),U3)) -> mark(pair(nil(),U3)) 22: active(u201(tt(),V3,W3,P3)) -> mark(u202(splitAt(V3,P3),W3)) 23: active(u202(pair(X4,Y4),U4)) -> mark(pair(cons(U4,X4),Y4)) 24: active(u21(tt(),V4)) -> mark(V4) 25: active(u211(tt(),W4)) -> mark(W4) 26: active(u221(tt(),P4,X5)) -> mark(fst(splitAt(P4,X5))) 27: active(u31(tt(),Y5)) -> mark(Y5) 28: active(u41(tt(),U5,V5)) -> mark(u42(isNatural(U5),V5)) 29: active(u42(tt(),W5)) -> mark(u43(isLNat(W5))) 30: active(u43(tt())) -> mark(tt()) 31: active(u51(tt(),P5,X6)) -> mark(u52(isNatural(P5),X6)) 32: active(u52(tt(),Y6)) -> mark(u53(isLNat(Y6))) 33: active(u53(tt())) -> mark(tt()) 34: active(u61(tt(),U6)) -> mark(u62(isPLNat(U6))) 35: active(u62(tt())) -> mark(tt()) 36: active(u71(tt(),V6)) -> mark(u72(isNatural(V6))) 37: active(u72(tt())) -> mark(tt()) 38: active(u81(tt(),W6)) -> mark(u82(isPLNat(W6))) 39: active(u82(tt())) -> mark(tt()) 40: active(u91(tt(),P6)) -> mark(u92(isLNat(P6))) 41: active(u92(tt())) -> mark(tt()) 42: active(afterNth(X7,Y7)) -> mark(u11(and(and(isNatural(X7),isNaturalKind(X7)),and(isLNat(Y7),isLNatKind(Y7))),X7,Y7)) 43: active(and(tt(),U7)) -> mark(U7) 44: active(fst(pair(V7,W7))) -> mark(u21(and(and(isLNat(V7),isLNatKind(V7)),and(isLNat(W7),isLNatKind(W7))),V7)) 45: active(head(cons(P7,X8))) -> mark(u31(and(and(isNatural(P7),isNaturalKind(P7)),and(isLNat(X8),isLNatKind(X8))),P7)) 46: active(isLNat(nil())) -> mark(tt()) 47: active(isLNat(afterNth(Y8,U8))) -> mark(u41(and(isNaturalKind(Y8),isLNatKind(U8)),Y8,U8)) 48: active(isLNat(cons(V8,W8))) -> mark(u51(and(isNaturalKind(V8),isLNatKind(W8)),V8,W8)) 49: active(isLNat(fst(P8))) -> mark(u61(isPLNatKind(P8),P8)) 50: active(isLNat(natsFrom(X9))) -> mark(u71(isNaturalKind(X9),X9)) 51: active(isLNat(snd(Y9))) -> mark(u81(isPLNatKind(Y9),Y9)) 52: active(isLNat(tail(U9))) -> mark(u91(isLNatKind(U9),U9)) 53: active(isLNat(take(V9,W9))) -> mark(u101(and(isNaturalKind(V9),isLNatKind(W9)),V9,W9)) 54: active(isLNatKind(nil())) -> mark(tt()) 55: active(isLNatKind(afterNth(P9,X10))) -> mark(and(isNaturalKind(P9),isLNatKind(X10))) 56: active(isLNatKind(cons(Y10,U10))) -> mark(and(isNaturalKind(Y10),isLNatKind(U10))) 57: active(isLNatKind(fst(V10))) -> mark(isPLNatKind(V10)) 58: active(isLNatKind(natsFrom(W10))) -> mark(isNaturalKind(W10)) 59: active(isLNatKind(snd(P10))) -> mark(isPLNatKind(P10)) 60: active(isLNatKind(tail(X11))) -> mark(isLNatKind(X11)) 61: active(isLNatKind(take(Y11,U11))) -> mark(and(isNaturalKind(Y11),isLNatKind(U11))) 62: active(isNatural(0())) -> mark(tt()) 63: active(isNatural(head(V11))) -> mark(u111(isLNatKind(V11),V11)) 64: active(isNatural(s(W11))) -> mark(u121(isNaturalKind(W11),W11)) 65: active(isNatural(sel(P11,X12))) -> mark(u131(and(isNaturalKind(P11),isLNatKind(X12)),P11,X12)) 66: active(isNaturalKind(0())) -> mark(tt()) 67: active(isNaturalKind(head(Y12))) -> mark(isLNatKind(Y12)) 68: active(isNaturalKind(s(U12))) -> mark(isNaturalKind(U12)) 69: active(isNaturalKind(sel(V12,W12))) -> mark(and(isNaturalKind(V12),isLNatKind(W12))) 70: active(isPLNat(pair(P12,X13))) -> mark(u141(and(isLNatKind(P12),isLNatKind(X13)),P12,X13)) 71: active(isPLNat(splitAt(Y13,U13))) -> mark(u151(and(isNaturalKind(Y13),isLNatKind(U13)),Y13,U13)) 72: active(isPLNatKind(pair(V13,W13))) -> mark(and(isLNatKind(V13),isLNatKind(W13))) 73: active(isPLNatKind(splitAt(P13,X14))) -> mark(and(isNaturalKind(P13),isLNatKind(X14))) 74: active(natsFrom(Y14)) -> mark(u161(and(isNatural(Y14),isNaturalKind(Y14)),Y14)) 75: active(sel(U14,V14)) -> mark(u171(and(and(isNatural(U14),isNaturalKind(U14)),and(isLNat(V14),isLNatKind(V14))),U14,V14)) 76: active(snd(pair(W14,P14))) -> mark(u181(and(and(isLNat(W14),isLNatKind(W14)),and(isLNat(P14),isLNatKind(P14))),P14)) 77: active(splitAt(0(),X15)) -> mark(u191(and(isLNat(X15),isLNatKind(X15)),X15)) 78: active(splitAt(s(Y15),cons(U15,V15))) -> mark(u201(and(and(isNatural(Y15),isNaturalKind(Y15)),and(and(isNatural(U15),isNaturalKind(U15)),and(isLNat(V15),isLNatKind(V15)))),Y15,U15,V15)) 79: active(tail(cons(W15,P15))) -> mark(u211(and(and(isNatural(W15),isNaturalKind(W15)),and(isLNat(P15),isLNatKind(P15))),P15)) 80: active(take(X16,Y16)) -> mark(u221(and(and(isNatural(X16),isNaturalKind(X16)),and(isLNat(Y16),isLNatKind(Y16))),X16,Y16)) 81: mark(u101(U16,V16,W16)) -> active(u101(mark(U16),V16,W16)) 82: mark(tt()) -> active(tt()) 83: mark(u102(P16,X17)) -> active(u102(mark(P16),X17)) 84: mark(isNatural(Y17)) -> active(isNatural(Y17)) 85: mark(u103(U17)) -> active(u103(mark(U17))) 86: mark(isLNat(V17)) -> active(isLNat(V17)) 87: mark(u11(W17,P17,X18)) -> active(u11(mark(W17),P17,X18)) 88: mark(snd(Y18)) -> active(snd(mark(Y18))) 89: mark(splitAt(U18,V18)) -> active(splitAt(mark(U18),mark(V18))) 90: mark(u111(W18,P18)) -> active(u111(mark(W18),P18)) 91: mark(u112(X19)) -> active(u112(mark(X19))) 92: mark(u121(Y19,U19)) -> active(u121(mark(Y19),U19)) 93: mark(u122(V19)) -> active(u122(mark(V19))) 94: mark(u131(W19,P19,X20)) -> active(u131(mark(W19),P19,X20)) 95: mark(u132(Y20,U20)) -> active(u132(mark(Y20),U20)) 96: mark(u133(V20)) -> active(u133(mark(V20))) 97: mark(u141(W20,P20,X21)) -> active(u141(mark(W20),P20,X21)) 98: mark(u142(Y21,U21)) -> active(u142(mark(Y21),U21)) 99: mark(u143(V21)) -> active(u143(mark(V21))) 100: mark(u151(W21,P21,X22)) -> active(u151(mark(W21),P21,X22)) 101: mark(u152(Y22,U22)) -> active(u152(mark(Y22),U22)) 102: mark(u153(V22)) -> active(u153(mark(V22))) 103: mark(u161(W22,P22)) -> active(u161(mark(W22),P22)) 104: mark(cons(X23,Y23)) -> active(cons(mark(X23),Y23)) 105: mark(natsFrom(U23)) -> active(natsFrom(mark(U23))) 106: mark(s(V23)) -> active(s(mark(V23))) 107: mark(u171(W23,P23,X24)) -> active(u171(mark(W23),P23,X24)) 108: mark(head(Y24)) -> active(head(mark(Y24))) 109: mark(afterNth(U24,V24)) -> active(afterNth(mark(U24),mark(V24))) 110: mark(u181(W24,P24)) -> active(u181(mark(W24),P24)) 111: mark(u191(X25,Y25)) -> active(u191(mark(X25),Y25)) 112: mark(pair(U25,V25)) -> active(pair(mark(U25),mark(V25))) 113: mark(nil()) -> active(nil()) 114: mark(u201(W25,P25,X26,Y26)) -> active(u201(mark(W25),P25,X26,Y26)) 115: mark(u202(U26,V26)) -> active(u202(mark(U26),V26)) 116: mark(u21(W26,P26)) -> active(u21(mark(W26),P26)) 117: mark(u211(X27,Y27)) -> active(u211(mark(X27),Y27)) 118: mark(u221(U27,V27,W27)) -> active(u221(mark(U27),V27,W27)) 119: mark(fst(P27)) -> active(fst(mark(P27))) 120: mark(u31(X28,Y28)) -> active(u31(mark(X28),Y28)) 121: mark(u41(U28,V28,W28)) -> active(u41(mark(U28),V28,W28)) 122: mark(u42(P28,X29)) -> active(u42(mark(P28),X29)) 123: mark(u43(Y29)) -> active(u43(mark(Y29))) 124: mark(u51(U29,V29,W29)) -> active(u51(mark(U29),V29,W29)) 125: mark(u52(P29,X30)) -> active(u52(mark(P29),X30)) 126: mark(u53(Y30)) -> active(u53(mark(Y30))) 127: mark(u61(U30,V30)) -> active(u61(mark(U30),V30)) 128: mark(u62(W30)) -> active(u62(mark(W30))) 129: mark(isPLNat(P30)) -> active(isPLNat(P30)) 130: mark(u71(X31,Y31)) -> active(u71(mark(X31),Y31)) 131: mark(u72(U31)) -> active(u72(mark(U31))) 132: mark(u81(V31,W31)) -> active(u81(mark(V31),W31)) 133: mark(u82(P31)) -> active(u82(mark(P31))) 134: mark(u91(X32,Y32)) -> active(u91(mark(X32),Y32)) 135: mark(u92(U32)) -> active(u92(mark(U32))) 136: mark(and(V32,W32)) -> active(and(mark(V32),W32)) 137: mark(isNaturalKind(P32)) -> active(isNaturalKind(P32)) 138: mark(isLNatKind(X33)) -> active(isLNatKind(X33)) 139: mark(isPLNatKind(Y33)) -> active(isPLNatKind(Y33)) 140: mark(tail(U33)) -> active(tail(mark(U33))) 141: mark(take(V33,W33)) -> active(take(mark(V33),mark(W33))) 142: mark(0()) -> active(0()) 143: mark(sel(P33,X34)) -> active(sel(mark(P33),mark(X34))) 144: u101(mark(Y34),U34,V34) -> u101(Y34,U34,V34) 145: u101(W34,mark(P34),X35) -> u101(W34,P34,X35) 146: u101(Y35,U35,mark(V35)) -> u101(Y35,U35,V35) 147: u101(active(W35),P35,X36) -> u101(W35,P35,X36) 148: u101(Y36,active(U36),V36) -> u101(Y36,U36,V36) 149: u101(W36,P36,active(X37)) -> u101(W36,P36,X37) 150: u102(mark(Y37),U37) -> u102(Y37,U37) 151: u102(V37,mark(W37)) -> u102(V37,W37) 152: u102(active(P37),X38) -> u102(P37,X38) 153: u102(Y38,active(U38)) -> u102(Y38,U38) 154: isNatural(mark(V38)) -> isNatural(V38) 155: isNatural(active(W38)) -> isNatural(W38) 156: u103(mark(P38)) -> u103(P38) 157: u103(active(X39)) -> u103(X39) 158: isLNat(mark(Y39)) -> isLNat(Y39) 159: isLNat(active(U39)) -> isLNat(U39) 160: u11(mark(V39),W39,P39) -> u11(V39,W39,P39) 161: u11(X40,mark(Y40),U40) -> u11(X40,Y40,U40) 162: u11(V40,W40,mark(P40)) -> u11(V40,W40,P40) 163: u11(active(X41),Y41,U41) -> u11(X41,Y41,U41) 164: u11(V41,active(W41),P41) -> u11(V41,W41,P41) 165: u11(X42,Y42,active(U42)) -> u11(X42,Y42,U42) 166: snd(mark(V42)) -> snd(V42) 167: snd(active(W42)) -> snd(W42) 168: splitAt(mark(P42),X43) -> splitAt(P42,X43) 169: splitAt(Y43,mark(U43)) -> splitAt(Y43,U43) 170: splitAt(active(V43),W43) -> splitAt(V43,W43) 171: splitAt(P43,active(X44)) -> splitAt(P43,X44) 172: u111(mark(Y44),U44) -> u111(Y44,U44) 173: u111(V44,mark(W44)) -> u111(V44,W44) 174: u111(active(P44),X45) -> u111(P44,X45) 175: u111(Y45,active(U45)) -> u111(Y45,U45) 176: u112(mark(V45)) -> u112(V45) 177: u112(active(W45)) -> u112(W45) 178: u121(mark(P45),X46) -> u121(P45,X46) 179: u121(Y46,mark(U46)) -> u121(Y46,U46) 180: u121(active(V46),W46) -> u121(V46,W46) 181: u121(P46,active(X47)) -> u121(P46,X47) 182: u122(mark(Y47)) -> u122(Y47) 183: u122(active(U47)) -> u122(U47) 184: u131(mark(V47),W47,P47) -> u131(V47,W47,P47) 185: u131(X48,mark(Y48),U48) -> u131(X48,Y48,U48) 186: u131(V48,W48,mark(P48)) -> u131(V48,W48,P48) 187: u131(active(X49),Y49,U49) -> u131(X49,Y49,U49) 188: u131(V49,active(W49),P49) -> u131(V49,W49,P49) 189: u131(X50,Y50,active(U50)) -> u131(X50,Y50,U50) 190: u132(mark(V50),W50) -> u132(V50,W50) 191: u132(P50,mark(X51)) -> u132(P50,X51) 192: u132(active(Y51),U51) -> u132(Y51,U51) 193: u132(V51,active(W51)) -> u132(V51,W51) 194: u133(mark(P51)) -> u133(P51) 195: u133(active(X52)) -> u133(X52) 196: u141(mark(Y52),U52,V52) -> u141(Y52,U52,V52) 197: u141(W52,mark(P52),X53) -> u141(W52,P52,X53) 198: u141(Y53,U53,mark(V53)) -> u141(Y53,U53,V53) 199: u141(active(W53),P53,X54) -> u141(W53,P53,X54) 200: u141(Y54,active(U54),V54) -> u141(Y54,U54,V54) 201: u141(W54,P54,active(X55)) -> u141(W54,P54,X55) 202: u142(mark(Y55),U55) -> u142(Y55,U55) 203: u142(V55,mark(W55)) -> u142(V55,W55) 204: u142(active(P55),X56) -> u142(P55,X56) 205: u142(Y56,active(U56)) -> u142(Y56,U56) 206: u143(mark(V56)) -> u143(V56) 207: u143(active(W56)) -> u143(W56) 208: u151(mark(P56),X57,Y57) -> u151(P56,X57,Y57) 209: u151(U57,mark(V57),W57) -> u151(U57,V57,W57) 210: u151(P57,X58,mark(Y58)) -> u151(P57,X58,Y58) 211: u151(active(U58),V58,W58) -> u151(U58,V58,W58) 212: u151(P58,active(X59),Y59) -> u151(P58,X59,Y59) 213: u151(U59,V59,active(W59)) -> u151(U59,V59,W59) 214: u152(mark(P59),X60) -> u152(P59,X60) 215: u152(Y60,mark(U60)) -> u152(Y60,U60) 216: u152(active(V60),W60) -> u152(V60,W60) 217: u152(P60,active(X61)) -> u152(P60,X61) 218: u153(mark(Y61)) -> u153(Y61) 219: u153(active(U61)) -> u153(U61) 220: u161(mark(V61),W61) -> u161(V61,W61) 221: u161(P61,mark(X62)) -> u161(P61,X62) 222: u161(active(Y62),U62) -> u161(Y62,U62) 223: u161(V62,active(W62)) -> u161(V62,W62) 224: cons(mark(P62),X63) -> cons(P62,X63) 225: cons(Y63,mark(U63)) -> cons(Y63,U63) 226: cons(active(V63),W63) -> cons(V63,W63) 227: cons(P63,active(X64)) -> cons(P63,X64) 228: natsFrom(mark(Y64)) -> natsFrom(Y64) 229: natsFrom(active(U64)) -> natsFrom(U64) 230: s(mark(V64)) -> s(V64) 231: s(active(W64)) -> s(W64) 232: u171(mark(P64),X65,Y65) -> u171(P64,X65,Y65) 233: u171(U65,mark(V65),W65) -> u171(U65,V65,W65) 234: u171(P65,X66,mark(Y66)) -> u171(P65,X66,Y66) 235: u171(active(U66),V66,W66) -> u171(U66,V66,W66) 236: u171(P66,active(X67),Y67) -> u171(P66,X67,Y67) 237: u171(U67,V67,active(W67)) -> u171(U67,V67,W67) 238: head(mark(P67)) -> head(P67) 239: head(active(X68)) -> head(X68) 240: afterNth(mark(Y68),U68) -> afterNth(Y68,U68) 241: afterNth(V68,mark(W68)) -> afterNth(V68,W68) 242: afterNth(active(P68),X69) -> afterNth(P68,X69) 243: afterNth(Y69,active(U69)) -> afterNth(Y69,U69) 244: u181(mark(V69),W69) -> u181(V69,W69) 245: u181(P69,mark(X70)) -> u181(P69,X70) 246: u181(active(Y70),U70) -> u181(Y70,U70) 247: u181(V70,active(W70)) -> u181(V70,W70) 248: u191(mark(P70),X71) -> u191(P70,X71) 249: u191(Y71,mark(U71)) -> u191(Y71,U71) 250: u191(active(V71),W71) -> u191(V71,W71) 251: u191(P71,active(X72)) -> u191(P71,X72) 252: pair(mark(Y72),U72) -> pair(Y72,U72) 253: pair(V72,mark(W72)) -> pair(V72,W72) 254: pair(active(P72),X73) -> pair(P72,X73) 255: pair(Y73,active(U73)) -> pair(Y73,U73) 256: u201(mark(V73),W73,P73,X74) -> u201(V73,W73,P73,X74) 257: u201(Y74,mark(U74),V74,W74) -> u201(Y74,U74,V74,W74) 258: u201(P74,X75,mark(Y75),U75) -> u201(P74,X75,Y75,U75) 259: u201(V75,W75,P75,mark(X76)) -> u201(V75,W75,P75,X76) 260: u201(active(Y76),U76,V76,W76) -> u201(Y76,U76,V76,W76) 261: u201(P76,active(X77),Y77,U77) -> u201(P76,X77,Y77,U77) 262: u201(V77,W77,active(P77),X78) -> u201(V77,W77,P77,X78) 263: u201(Y78,U78,V78,active(W78)) -> u201(Y78,U78,V78,W78) 264: u202(mark(P78),X79) -> u202(P78,X79) 265: u202(Y79,mark(U79)) -> u202(Y79,U79) 266: u202(active(V79),W79) -> u202(V79,W79) 267: u202(P79,active(X80)) -> u202(P79,X80) 268: u21(mark(Y80),U80) -> u21(Y80,U80) 269: u21(V80,mark(W80)) -> u21(V80,W80) 270: u21(active(P80),X81) -> u21(P80,X81) 271: u21(Y81,active(U81)) -> u21(Y81,U81) 272: u211(mark(V81),W81) -> u211(V81,W81) 273: u211(P81,mark(X82)) -> u211(P81,X82) 274: u211(active(Y82),U82) -> u211(Y82,U82) 275: u211(V82,active(W82)) -> u211(V82,W82) 276: u221(mark(P82),X83,Y83) -> u221(P82,X83,Y83) 277: u221(U83,mark(V83),W83) -> u221(U83,V83,W83) 278: u221(P83,X84,mark(Y84)) -> u221(P83,X84,Y84) 279: u221(active(U84),V84,W84) -> u221(U84,V84,W84) 280: u221(P84,active(X85),Y85) -> u221(P84,X85,Y85) 281: u221(U85,V85,active(W85)) -> u221(U85,V85,W85) 282: fst(mark(P85)) -> fst(P85) 283: fst(active(X86)) -> fst(X86) 284: u31(mark(Y86),U86) -> u31(Y86,U86) 285: u31(V86,mark(W86)) -> u31(V86,W86) 286: u31(active(P86),X87) -> u31(P86,X87) 287: u31(Y87,active(U87)) -> u31(Y87,U87) 288: u41(mark(V87),W87,P87) -> u41(V87,W87,P87) 289: u41(X88,mark(Y88),U88) -> u41(X88,Y88,U88) 290: u41(V88,W88,mark(P88)) -> u41(V88,W88,P88) 291: u41(active(X89),Y89,U89) -> u41(X89,Y89,U89) 292: u41(V89,active(W89),P89) -> u41(V89,W89,P89) 293: u41(X90,Y90,active(U90)) -> u41(X90,Y90,U90) 294: u42(mark(V90),W90) -> u42(V90,W90) 295: u42(P90,mark(X91)) -> u42(P90,X91) 296: u42(active(Y91),U91) -> u42(Y91,U91) 297: u42(V91,active(W91)) -> u42(V91,W91) 298: u43(mark(P91)) -> u43(P91) 299: u43(active(X92)) -> u43(X92) 300: u51(mark(Y92),U92,V92) -> u51(Y92,U92,V92) 301: u51(W92,mark(P92),X93) -> u51(W92,P92,X93) 302: u51(Y93,U93,mark(V93)) -> u51(Y93,U93,V93) 303: u51(active(W93),P93,X94) -> u51(W93,P93,X94) 304: u51(Y94,active(U94),V94) -> u51(Y94,U94,V94) 305: u51(W94,P94,active(X95)) -> u51(W94,P94,X95) 306: u52(mark(Y95),U95) -> u52(Y95,U95) 307: u52(V95,mark(W95)) -> u52(V95,W95) 308: u52(active(P95),X96) -> u52(P95,X96) 309: u52(Y96,active(U96)) -> u52(Y96,U96) 310: u53(mark(V96)) -> u53(V96) 311: u53(active(W96)) -> u53(W96) 312: u61(mark(P96),X97) -> u61(P96,X97) 313: u61(Y97,mark(U97)) -> u61(Y97,U97) 314: u61(active(V97),W97) -> u61(V97,W97) 315: u61(P97,active(X98)) -> u61(P97,X98) 316: u62(mark(Y98)) -> u62(Y98) 317: u62(active(U98)) -> u62(U98) 318: isPLNat(mark(V98)) -> isPLNat(V98) 319: isPLNat(active(W98)) -> isPLNat(W98) 320: u71(mark(P98),X99) -> u71(P98,X99) 321: u71(Y99,mark(U99)) -> u71(Y99,U99) 322: u71(active(V99),W99) -> u71(V99,W99) 323: u71(P99,active(X100)) -> u71(P99,X100) 324: u72(mark(Y100)) -> u72(Y100) 325: u72(active(U100)) -> u72(U100) 326: u81(mark(V100),W100) -> u81(V100,W100) 327: u81(P100,mark(X101)) -> u81(P100,X101) 328: u81(active(Y101),U101) -> u81(Y101,U101) 329: u81(V101,active(W101)) -> u81(V101,W101) 330: u82(mark(P101)) -> u82(P101) 331: u82(active(X102)) -> u82(X102) 332: u91(mark(Y102),U102) -> u91(Y102,U102) 333: u91(V102,mark(W102)) -> u91(V102,W102) 334: u91(active(P102),X103) -> u91(P102,X103) 335: u91(Y103,active(U103)) -> u91(Y103,U103) 336: u92(mark(V103)) -> u92(V103) 337: u92(active(W103)) -> u92(W103) 338: and(mark(P103),X104) -> and(P103,X104) 339: and(Y104,mark(U104)) -> and(Y104,U104) 340: and(active(V104),W104) -> and(V104,W104) 341: and(P104,active(X105)) -> and(P104,X105) 342: isNaturalKind(mark(Y105)) -> isNaturalKind(Y105) 343: isNaturalKind(active(U105)) -> isNaturalKind(U105) 344: isLNatKind(mark(V105)) -> isLNatKind(V105) 345: isLNatKind(active(W105)) -> isLNatKind(W105) 346: isPLNatKind(mark(P105)) -> isPLNatKind(P105) 347: isPLNatKind(active(X106)) -> isPLNatKind(X106) 348: tail(mark(Y106)) -> tail(Y106) 349: tail(active(U106)) -> tail(U106) 350: take(mark(V106),W106) -> take(V106,W106) 351: take(P106,mark(X107)) -> take(P106,X107) 352: take(active(Y107),U107) -> take(Y107,U107) 353: take(V107,active(W107)) -> take(V107,W107) 354: sel(mark(P107),X108) -> sel(P107,X108) 355: sel(Y108,mark(U108)) -> sel(Y108,U108) 356: sel(active(V108),W108) -> sel(V108,W108) 357: sel(P108,active(X109)) -> sel(P108,X109) 358: _(X1,X2) -> X1 359: _(X1,X2) -> X2 Number of strict rules: 359 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(u102(tt(),U)) -> #mark(u103(isLNat(U))) #2: #active(u102(tt(),U)) -> #u103(isLNat(U)) #3: #active(u102(tt(),U)) -> #isLNat(U) #4: #mark(isLNat(V17)) -> #active(isLNat(V17)) #5: #active(and(tt(),U7)) -> #mark(U7) #6: #active(u42(tt(),W5)) -> #mark(u43(isLNat(W5))) #7: #active(u42(tt(),W5)) -> #u43(isLNat(W5)) #8: #active(u42(tt(),W5)) -> #isLNat(W5) #9: #head(mark(P67)) -> #head(P67) #10: #u92(mark(V103)) -> #u92(V103) #11: #u201(Y78,U78,V78,active(W78)) -> #u201(Y78,U78,V78,W78) #12: #active(u62(tt())) -> #mark(tt()) #13: #and(active(V104),W104) -> #and(V104,W104) #14: #mark(u102(P16,X17)) -> #active(u102(mark(P16),X17)) #15: #mark(u102(P16,X17)) -> #u102(mark(P16),X17) #16: #mark(u102(P16,X17)) -> #mark(P16) #17: #active(isNaturalKind(0())) -> #mark(tt()) #18: #u112(active(W45)) -> #u112(W45) #19: #active(isLNat(nil())) -> #mark(tt()) #20: #natsFrom(active(U64)) -> #natsFrom(U64) #21: #u72(mark(Y100)) -> #u72(Y100) #22: #u31(Y87,active(U87)) -> #u31(Y87,U87) #23: #pair(V72,mark(W72)) -> #pair(V72,W72) #24: #active(afterNth(X7,Y7)) -> #mark(u11(and(and(isNatural(X7),isNaturalKind(X7)),and(isLNat(Y7),isLNatKind(Y7))),X7,Y7)) #25: #active(afterNth(X7,Y7)) -> #u11(and(and(isNatural(X7),isNaturalKind(X7)),and(isLNat(Y7),isLNatKind(Y7))),X7,Y7) #26: #active(afterNth(X7,Y7)) -> #and(and(isNatural(X7),isNaturalKind(X7)),and(isLNat(Y7),isLNatKind(Y7))) #27: #active(afterNth(X7,Y7)) -> #and(isNatural(X7),isNaturalKind(X7)) #28: #active(afterNth(X7,Y7)) -> #isNatural(X7) #29: #active(afterNth(X7,Y7)) -> #isNaturalKind(X7) #30: #active(afterNth(X7,Y7)) -> #and(isLNat(Y7),isLNatKind(Y7)) #31: #active(afterNth(X7,Y7)) -> #isLNat(Y7) #32: #active(afterNth(X7,Y7)) -> #isLNatKind(Y7) #33: #u41(V88,W88,mark(P88)) -> #u41(V88,W88,P88) #34: #mark(u202(U26,V26)) -> #active(u202(mark(U26),V26)) #35: #mark(u202(U26,V26)) -> #u202(mark(U26),V26) #36: #mark(u202(U26,V26)) -> #mark(U26) #37: #u171(mark(P64),X65,Y65) -> #u171(P64,X65,Y65) #38: #u141(Y53,U53,mark(V53)) -> #u141(Y53,U53,V53) #39: #u101(W36,P36,active(X37)) -> #u101(W36,P36,X37) #40: #mark(u132(Y20,U20)) -> #active(u132(mark(Y20),U20)) #41: #mark(u132(Y20,U20)) -> #u132(mark(Y20),U20) #42: #mark(u132(Y20,U20)) -> #mark(Y20) #43: #fst(active(X86)) -> #fst(X86) #44: #active(u92(tt())) -> #mark(tt()) #45: #u81(P100,mark(X101)) -> #u81(P100,X101) #46: #u191(mark(P70),X71) -> #u191(P70,X71) #47: #u202(Y79,mark(U79)) -> #u202(Y79,U79) #48: #pair(mark(Y72),U72) -> #pair(Y72,U72) #49: #active(u72(tt())) -> #mark(tt()) #50: #mark(u201(W25,P25,X26,Y26)) -> #active(u201(mark(W25),P25,X26,Y26)) #51: #mark(u201(W25,P25,X26,Y26)) -> #u201(mark(W25),P25,X26,Y26) #52: #mark(u201(W25,P25,X26,Y26)) -> #mark(W25) #53: #mark(u143(V21)) -> #active(u143(mark(V21))) #54: #mark(u143(V21)) -> #u143(mark(V21)) #55: #mark(u143(V21)) -> #mark(V21) #56: #s(mark(V64)) -> #s(V64) #57: #u11(active(X41),Y41,U41) -> #u11(X41,Y41,U41) #58: #mark(u141(W20,P20,X21)) -> #active(u141(mark(W20),P20,X21)) #59: #mark(u141(W20,P20,X21)) -> #u141(mark(W20),P20,X21) #60: #mark(u141(W20,P20,X21)) -> #mark(W20) #61: #fst(mark(P85)) -> #fst(P85) #62: #mark(u112(X19)) -> #active(u112(mark(X19))) #63: #mark(u112(X19)) -> #u112(mark(X19)) #64: #mark(u112(X19)) -> #mark(X19) #65: #active(isPLNatKind(splitAt(P13,X14))) -> #mark(and(isNaturalKind(P13),isLNatKind(X14))) #66: #active(isPLNatKind(splitAt(P13,X14))) -> #and(isNaturalKind(P13),isLNatKind(X14)) #67: #active(isPLNatKind(splitAt(P13,X14))) -> #isNaturalKind(P13) #68: #active(isPLNatKind(splitAt(P13,X14))) -> #isLNatKind(X14) #69: #active(isLNat(afterNth(Y8,U8))) -> #mark(u41(and(isNaturalKind(Y8),isLNatKind(U8)),Y8,U8)) #70: #active(isLNat(afterNth(Y8,U8))) -> #u41(and(isNaturalKind(Y8),isLNatKind(U8)),Y8,U8) #71: #active(isLNat(afterNth(Y8,U8))) -> #and(isNaturalKind(Y8),isLNatKind(U8)) #72: #active(isLNat(afterNth(Y8,U8))) -> #isNaturalKind(Y8) #73: #active(isLNat(afterNth(Y8,U8))) -> #isLNatKind(U8) #74: #u53(active(W96)) -> #u53(W96) #75: #u153(mark(Y61)) -> #u153(Y61) #76: #u132(P50,mark(X51)) -> #u132(P50,X51) #77: #afterNth(mark(Y68),U68) -> #afterNth(Y68,U68) #78: #active(isLNat(take(V9,W9))) -> #mark(u101(and(isNaturalKind(V9),isLNatKind(W9)),V9,W9)) #79: #active(isLNat(take(V9,W9))) -> #u101(and(isNaturalKind(V9),isLNatKind(W9)),V9,W9) #80: #active(isLNat(take(V9,W9))) -> #and(isNaturalKind(V9),isLNatKind(W9)) #81: #active(isLNat(take(V9,W9))) -> #isNaturalKind(V9) #82: #active(isLNat(take(V9,W9))) -> #isLNatKind(W9) #83: #u201(active(Y76),U76,V76,W76) -> #u201(Y76,U76,V76,W76) #84: #u41(X90,Y90,active(U90)) -> #u41(X90,Y90,U90) #85: #u111(V44,mark(W44)) -> #u111(V44,W44) #86: #u171(P65,X66,mark(Y66)) -> #u171(P65,X66,Y66) #87: #active(isPLNat(splitAt(Y13,U13))) -> #mark(u151(and(isNaturalKind(Y13),isLNatKind(U13)),Y13,U13)) #88: #active(isPLNat(splitAt(Y13,U13))) -> #u151(and(isNaturalKind(Y13),isLNatKind(U13)),Y13,U13) #89: #active(isPLNat(splitAt(Y13,U13))) -> #and(isNaturalKind(Y13),isLNatKind(U13)) #90: #active(isPLNat(splitAt(Y13,U13))) -> #isNaturalKind(Y13) #91: #active(isPLNat(splitAt(Y13,U13))) -> #isLNatKind(U13) #92: #u101(active(W35),P35,X36) -> #u101(W35,P35,X36) #93: #mark(isPLNatKind(Y33)) -> #active(isPLNatKind(Y33)) #94: #active(isLNat(cons(V8,W8))) -> #mark(u51(and(isNaturalKind(V8),isLNatKind(W8)),V8,W8)) #95: #active(isLNat(cons(V8,W8))) -> #u51(and(isNaturalKind(V8),isLNatKind(W8)),V8,W8) #96: #active(isLNat(cons(V8,W8))) -> #and(isNaturalKind(V8),isLNatKind(W8)) #97: #active(isLNat(cons(V8,W8))) -> #isNaturalKind(V8) #98: #active(isLNat(cons(V8,W8))) -> #isLNatKind(W8) #99: #u202(P79,active(X80)) -> #u202(P79,X80) #100: #mark(u43(Y29)) -> #active(u43(mark(Y29))) #101: #mark(u43(Y29)) -> #u43(mark(Y29)) #102: #mark(u43(Y29)) -> #mark(Y29) #103: #active(sel(U14,V14)) -> #mark(u171(and(and(isNatural(U14),isNaturalKind(U14)),and(isLNat(V14),isLNatKind(V14))),U14,V14)) #104: #active(sel(U14,V14)) -> #u171(and(and(isNatural(U14),isNaturalKind(U14)),and(isLNat(V14),isLNatKind(V14))),U14,V14) #105: #active(sel(U14,V14)) -> #and(and(isNatural(U14),isNaturalKind(U14)),and(isLNat(V14),isLNatKind(V14))) #106: #active(sel(U14,V14)) -> #and(isNatural(U14),isNaturalKind(U14)) #107: #active(sel(U14,V14)) -> #isNatural(U14) #108: #active(sel(U14,V14)) -> #isNaturalKind(U14) #109: #active(sel(U14,V14)) -> #and(isLNat(V14),isLNatKind(V14)) #110: #active(sel(U14,V14)) -> #isLNat(V14) #111: #active(sel(U14,V14)) -> #isLNatKind(V14) #112: #pair(Y73,active(U73)) -> #pair(Y73,U73) #113: #u121(mark(P45),X46) -> #u121(P45,X46) #114: #mark(pair(U25,V25)) -> #active(pair(mark(U25),mark(V25))) #115: #mark(pair(U25,V25)) -> #pair(mark(U25),mark(V25)) #116: #mark(pair(U25,V25)) -> #mark(U25) #117: #mark(pair(U25,V25)) -> #mark(V25) #118: #active(natsFrom(Y14)) -> #mark(u161(and(isNatural(Y14),isNaturalKind(Y14)),Y14)) #119: #active(natsFrom(Y14)) -> #u161(and(isNatural(Y14),isNaturalKind(Y14)),Y14) #120: #active(natsFrom(Y14)) -> #and(isNatural(Y14),isNaturalKind(Y14)) #121: #active(natsFrom(Y14)) -> #isNatural(Y14) #122: #active(natsFrom(Y14)) -> #isNaturalKind(Y14) #123: #splitAt(active(V43),W43) -> #splitAt(V43,W43) #124: #active(isLNatKind(natsFrom(W10))) -> #mark(isNaturalKind(W10)) #125: #active(isLNatKind(natsFrom(W10))) -> #isNaturalKind(W10) #126: #u221(P83,X84,mark(Y84)) -> #u221(P83,X84,Y84) #127: #u201(mark(V73),W73,P73,X74) -> #u201(V73,W73,P73,X74) #128: #mark(isLNatKind(X33)) -> #active(isLNatKind(X33)) #129: #mark(nil()) -> #active(nil()) #130: #isLNat(mark(Y39)) -> #isLNat(Y39) #131: #active(isLNatKind(take(Y11,U11))) -> #mark(and(isNaturalKind(Y11),isLNatKind(U11))) #132: #active(isLNatKind(take(Y11,U11))) -> #and(isNaturalKind(Y11),isLNatKind(U11)) #133: #active(isLNatKind(take(Y11,U11))) -> #isNaturalKind(Y11) #134: #active(isLNatKind(take(Y11,U11))) -> #isLNatKind(U11) #135: #active(u81(tt(),W6)) -> #mark(u82(isPLNat(W6))) #136: #active(u81(tt(),W6)) -> #u82(isPLNat(W6)) #137: #active(u81(tt(),W6)) -> #isPLNat(W6) #138: #tail(mark(Y106)) -> #tail(Y106) #139: #isNaturalKind(mark(Y105)) -> #isNaturalKind(Y105) #140: #u102(V37,mark(W37)) -> #u102(V37,W37) #141: #isNatural(mark(V38)) -> #isNatural(V38) #142: #u51(mark(Y92),U92,V92) -> #u51(Y92,U92,V92) #143: #mark(u21(W26,P26)) -> #active(u21(mark(W26),P26)) #144: #mark(u21(W26,P26)) -> #u21(mark(W26),P26) #145: #mark(u21(W26,P26)) -> #mark(W26) #146: #u52(active(P95),X96) -> #u52(P95,X96) #147: #isNatural(active(W38)) -> #isNatural(W38) #148: #active(u112(tt())) -> #mark(tt()) #149: #u61(active(V97),W97) -> #u61(V97,W97) #150: #u161(V62,active(W62)) -> #u161(V62,W62) #151: #u141(mark(Y52),U52,V52) -> #u141(Y52,U52,V52) #152: #u71(Y99,mark(U99)) -> #u71(Y99,U99) #153: #u11(X42,Y42,active(U42)) -> #u11(X42,Y42,U42) #154: #active(isLNatKind(snd(P10))) -> #mark(isPLNatKind(P10)) #155: #active(isLNatKind(snd(P10))) -> #isPLNatKind(P10) #156: #isLNatKind(active(W105)) -> #isLNatKind(W105) #157: #and(Y104,mark(U104)) -> #and(Y104,U104) #158: #u132(V51,active(W51)) -> #u132(V51,W51) #159: #mark(u181(W24,P24)) -> #active(u181(mark(W24),P24)) #160: #mark(u181(W24,P24)) -> #u181(mark(W24),P24) #161: #mark(u181(W24,P24)) -> #mark(W24) #162: #mark(u81(V31,W31)) -> #active(u81(mark(V31),W31)) #163: #mark(u81(V31,W31)) -> #u81(mark(V31),W31) #164: #mark(u81(V31,W31)) -> #mark(V31) #165: #active(isLNatKind(afterNth(P9,X10))) -> #mark(and(isNaturalKind(P9),isLNatKind(X10))) #166: #active(isLNatKind(afterNth(P9,X10))) -> #and(isNaturalKind(P9),isLNatKind(X10)) #167: #active(isLNatKind(afterNth(P9,X10))) -> #isNaturalKind(P9) #168: #active(isLNatKind(afterNth(P9,X10))) -> #isLNatKind(X10) #169: #active(isNaturalKind(head(Y12))) -> #mark(isLNatKind(Y12)) #170: #active(isNaturalKind(head(Y12))) -> #isLNatKind(Y12) #171: #u151(P57,X58,mark(Y58)) -> #u151(P57,X58,Y58) #172: #active(u91(tt(),P6)) -> #mark(u92(isLNat(P6))) #173: #active(u91(tt(),P6)) -> #u92(isLNat(P6)) #174: #active(u91(tt(),P6)) -> #isLNat(P6) #175: #u21(mark(Y80),U80) -> #u21(Y80,U80) #176: #u82(active(X102)) -> #u82(X102) #177: #u71(active(V99),W99) -> #u71(V99,W99) #178: #mark(u111(W18,P18)) -> #active(u111(mark(W18),P18)) #179: #mark(u111(W18,P18)) -> #u111(mark(W18),P18) #180: #mark(u111(W18,P18)) -> #mark(W18) #181: #u51(Y94,active(U94),V94) -> #u51(Y94,U94,V94) #182: #u62(mark(Y98)) -> #u62(Y98) #183: #u191(Y71,mark(U71)) -> #u191(Y71,U71) #184: #u101(Y35,U35,mark(V35)) -> #u101(Y35,U35,V35) #185: #isPLNatKind(active(X106)) -> #isPLNatKind(X106) #186: #u61(mark(P96),X97) -> #u61(P96,X97) #187: #mark(u171(W23,P23,X24)) -> #active(u171(mark(W23),P23,X24)) #188: #mark(u171(W23,P23,X24)) -> #u171(mark(W23),P23,X24) #189: #mark(u171(W23,P23,X24)) -> #mark(W23) #190: #active(isLNat(snd(Y9))) -> #mark(u81(isPLNatKind(Y9),Y9)) #191: #active(isLNat(snd(Y9))) -> #u81(isPLNatKind(Y9),Y9) #192: #active(isLNat(snd(Y9))) -> #isPLNatKind(Y9) #193: #isLNatKind(mark(V105)) -> #isLNatKind(V105) #194: #u161(mark(V61),W61) -> #u161(V61,W61) #195: #active(u142(tt(),X2)) -> #mark(u143(isLNat(X2))) #196: #active(u142(tt(),X2)) -> #u143(isLNat(X2)) #197: #active(u142(tt(),X2)) -> #isLNat(X2) #198: #active(u131(tt(),Y1,U1)) -> #mark(u132(isNatural(Y1),U1)) #199: #active(u131(tt(),Y1,U1)) -> #u132(isNatural(Y1),U1) #200: #active(u131(tt(),Y1,U1)) -> #isNatural(Y1) #201: #u142(mark(Y55),U55) -> #u142(Y55,U55) #202: #active(u133(tt())) -> #mark(tt()) #203: #u152(mark(P59),X60) -> #u152(P59,X60) #204: #mark(u142(Y21,U21)) -> #active(u142(mark(Y21),U21)) #205: #mark(u142(Y21,U21)) -> #u142(mark(Y21),U21) #206: #mark(u142(Y21,U21)) -> #mark(Y21) #207: #u43(active(X92)) -> #u43(X92) #208: #u201(Y74,mark(U74),V74,W74) -> #u201(Y74,U74,V74,W74) #209: #u103(mark(P38)) -> #u103(P38) #210: #active(isLNatKind(fst(V10))) -> #mark(isPLNatKind(V10)) #211: #active(isLNatKind(fst(V10))) -> #isPLNatKind(V10) #212: #u181(P69,mark(X70)) -> #u181(P69,X70) #213: #u141(W52,mark(P52),X53) -> #u141(W52,P52,X53) #214: #active(snd(pair(W14,P14))) -> #mark(u181(and(and(isLNat(W14),isLNatKind(W14)),and(isLNat(P14),isLNatKind(P14))),P14)) #215: #active(snd(pair(W14,P14))) -> #u181(and(and(isLNat(W14),isLNatKind(W14)),and(isLNat(P14),isLNatKind(P14))),P14) #216: #active(snd(pair(W14,P14))) -> #and(and(isLNat(W14),isLNatKind(W14)),and(isLNat(P14),isLNatKind(P14))) #217: #active(snd(pair(W14,P14))) -> #and(isLNat(W14),isLNatKind(W14)) #218: #active(snd(pair(W14,P14))) -> #isLNat(W14) #219: #active(snd(pair(W14,P14))) -> #isLNatKind(W14) #220: #active(snd(pair(W14,P14))) -> #and(isLNat(P14),isLNatKind(P14)) #221: #active(snd(pair(W14,P14))) -> #isLNat(P14) #222: #active(snd(pair(W14,P14))) -> #isLNatKind(P14) #223: #snd(active(W42)) -> #snd(W42) #224: #u132(mark(V50),W50) -> #u132(V50,W50) #225: #mark(afterNth(U24,V24)) -> #active(afterNth(mark(U24),mark(V24))) #226: #mark(afterNth(U24,V24)) -> #afterNth(mark(U24),mark(V24)) #227: #mark(afterNth(U24,V24)) -> #mark(U24) #228: #mark(afterNth(U24,V24)) -> #mark(V24) #229: #mark(u131(W19,P19,X20)) -> #active(u131(mark(W19),P19,X20)) #230: #mark(u131(W19,P19,X20)) -> #u131(mark(W19),P19,X20) #231: #mark(u131(W19,P19,X20)) -> #mark(W19) #232: #take(P106,mark(X107)) -> #take(P106,X107) #233: #active(u21(tt(),V4)) -> #mark(V4) #234: #u92(active(W103)) -> #u92(W103) #235: #mark(u91(X32,Y32)) -> #active(u91(mark(X32),Y32)) #236: #mark(u91(X32,Y32)) -> #u91(mark(X32),Y32) #237: #mark(u91(X32,Y32)) -> #mark(X32) #238: #active(isPLNat(pair(P12,X13))) -> #mark(u141(and(isLNatKind(P12),isLNatKind(X13)),P12,X13)) #239: #active(isPLNat(pair(P12,X13))) -> #u141(and(isLNatKind(P12),isLNatKind(X13)),P12,X13) #240: #active(isPLNat(pair(P12,X13))) -> #and(isLNatKind(P12),isLNatKind(X13)) #241: #active(isPLNat(pair(P12,X13))) -> #isLNatKind(P12) #242: #active(isPLNat(pair(P12,X13))) -> #isLNatKind(X13) #243: #u211(P81,mark(X82)) -> #u211(P81,X82) #244: #u31(V86,mark(W86)) -> #u31(V86,W86) #245: #active(u202(pair(X4,Y4),U4)) -> #mark(pair(cons(U4,X4),Y4)) #246: #active(u202(pair(X4,Y4),U4)) -> #pair(cons(U4,X4),Y4) #247: #active(u202(pair(X4,Y4),U4)) -> #cons(U4,X4) #248: #sel(active(V108),W108) -> #sel(V108,W108) #249: #u171(P66,active(X67),Y67) -> #u171(P66,X67,Y67) #250: #mark(u62(W30)) -> #active(u62(mark(W30))) #251: #mark(u62(W30)) -> #u62(mark(W30)) #252: #mark(u62(W30)) -> #mark(W30) #253: #mark(u101(U16,V16,W16)) -> #active(u101(mark(U16),V16,W16)) #254: #mark(u101(U16,V16,W16)) -> #u101(mark(U16),V16,W16) #255: #mark(u101(U16,V16,W16)) -> #mark(U16) #256: #u51(active(W93),P93,X94) -> #u51(W93,P93,X94) #257: #mark(u221(U27,V27,W27)) -> #active(u221(mark(U27),V27,W27)) #258: #mark(u221(U27,V27,W27)) -> #u221(mark(U27),V27,W27) #259: #mark(u221(U27,V27,W27)) -> #mark(U27) #260: #active(splitAt(s(Y15),cons(U15,V15))) -> #mark(u201(and(and(isNatural(Y15),isNaturalKind(Y15)),and(and(isNatural(U15),isNaturalKind(U15)),and(isLNat(V15),isLNatKind(V15)))),Y15,U15,V15)) #261: #active(splitAt(s(Y15),cons(U15,V15))) -> #u201(and(and(isNatural(Y15),isNaturalKind(Y15)),and(and(isNatural(U15),isNaturalKind(U15)),and(isLNat(V15),isLNatKind(V15)))),Y15,U15,V15) #262: #active(splitAt(s(Y15),cons(U15,V15))) -> #and(and(isNatural(Y15),isNaturalKind(Y15)),and(and(isNatural(U15),isNaturalKind(U15)),and(isLNat(V15),isLNatKind(V15)))) #263: #active(splitAt(s(Y15),cons(U15,V15))) -> #and(isNatural(Y15),isNaturalKind(Y15)) #264: #active(splitAt(s(Y15),cons(U15,V15))) -> #isNatural(Y15) #265: #active(splitAt(s(Y15),cons(U15,V15))) -> #isNaturalKind(Y15) #266: #active(splitAt(s(Y15),cons(U15,V15))) -> #and(and(isNatural(U15),isNaturalKind(U15)),and(isLNat(V15),isLNatKind(V15))) #267: #active(splitAt(s(Y15),cons(U15,V15))) -> #and(isNatural(U15),isNaturalKind(U15)) #268: #active(splitAt(s(Y15),cons(U15,V15))) -> #isNatural(U15) #269: #active(splitAt(s(Y15),cons(U15,V15))) -> #isNaturalKind(U15) #270: #active(splitAt(s(Y15),cons(U15,V15))) -> #and(isLNat(V15),isLNatKind(V15)) #271: #active(splitAt(s(Y15),cons(U15,V15))) -> #isLNat(V15) #272: #active(splitAt(s(Y15),cons(U15,V15))) -> #isLNatKind(V15) #273: #active(head(cons(P7,X8))) -> #mark(u31(and(and(isNatural(P7),isNaturalKind(P7)),and(isLNat(X8),isLNatKind(X8))),P7)) #274: #active(head(cons(P7,X8))) -> #u31(and(and(isNatural(P7),isNaturalKind(P7)),and(isLNat(X8),isLNatKind(X8))),P7) #275: #active(head(cons(P7,X8))) -> #and(and(isNatural(P7),isNaturalKind(P7)),and(isLNat(X8),isLNatKind(X8))) #276: #active(head(cons(P7,X8))) -> #and(isNatural(P7),isNaturalKind(P7)) #277: #active(head(cons(P7,X8))) -> #isNatural(P7) #278: #active(head(cons(P7,X8))) -> #isNaturalKind(P7) #279: #active(head(cons(P7,X8))) -> #and(isLNat(X8),isLNatKind(X8)) #280: #active(head(cons(P7,X8))) -> #isLNat(X8) #281: #active(head(cons(P7,X8))) -> #isLNatKind(X8) #282: #u41(mark(V87),W87,P87) -> #u41(V87,W87,P87) #283: #mark(u133(V20)) -> #active(u133(mark(V20))) #284: #mark(u133(V20)) -> #u133(mark(V20)) #285: #mark(u133(V20)) -> #mark(V20) #286: #u142(V55,mark(W55)) -> #u142(V55,W55) #287: #isPLNatKind(mark(P105)) -> #isPLNatKind(P105) #288: #u141(W54,P54,active(X55)) -> #u141(W54,P54,X55) #289: #active(isNaturalKind(sel(V12,W12))) -> #mark(and(isNaturalKind(V12),isLNatKind(W12))) #290: #active(isNaturalKind(sel(V12,W12))) -> #and(isNaturalKind(V12),isLNatKind(W12)) #291: #active(isNaturalKind(sel(V12,W12))) -> #isNaturalKind(V12) #292: #active(isNaturalKind(sel(V12,W12))) -> #isLNatKind(W12) #293: #u151(U57,mark(V57),W57) -> #u151(U57,V57,W57) #294: #mark(u152(Y22,U22)) -> #active(u152(mark(Y22),U22)) #295: #mark(u152(Y22,U22)) -> #u152(mark(Y22),U22) #296: #mark(u152(Y22,U22)) -> #mark(Y22) #297: #active(u141(tt(),W1,P1)) -> #mark(u142(isLNat(W1),P1)) #298: #active(u141(tt(),W1,P1)) -> #u142(isLNat(W1),P1) #299: #active(u141(tt(),W1,P1)) -> #isLNat(W1) #300: #active(u51(tt(),P5,X6)) -> #mark(u52(isNatural(P5),X6)) #301: #active(u51(tt(),P5,X6)) -> #u52(isNatural(P5),X6) #302: #active(u51(tt(),P5,X6)) -> #isNatural(P5) #303: #and(P104,active(X105)) -> #and(P104,X105) #304: #u11(V41,active(W41),P41) -> #u11(V41,W41,P41) #305: #u21(active(P80),X81) -> #u21(P80,X81) #306: #u152(P60,active(X61)) -> #u152(P60,X61) #307: #active(tail(cons(W15,P15))) -> #mark(u211(and(and(isNatural(W15),isNaturalKind(W15)),and(isLNat(P15),isLNatKind(P15))),P15)) #308: #active(tail(cons(W15,P15))) -> #u211(and(and(isNatural(W15),isNaturalKind(W15)),and(isLNat(P15),isLNatKind(P15))),P15) #309: #active(tail(cons(W15,P15))) -> #and(and(isNatural(W15),isNaturalKind(W15)),and(isLNat(P15),isLNatKind(P15))) #310: #active(tail(cons(W15,P15))) -> #and(isNatural(W15),isNaturalKind(W15)) #311: #active(tail(cons(W15,P15))) -> #isNatural(W15) #312: #active(tail(cons(W15,P15))) -> #isNaturalKind(W15) #313: #active(tail(cons(W15,P15))) -> #and(isLNat(P15),isLNatKind(P15)) #314: #active(tail(cons(W15,P15))) -> #isLNat(P15) #315: #active(tail(cons(W15,P15))) -> #isLNatKind(P15) #316: #active(isLNatKind(cons(Y10,U10))) -> #mark(and(isNaturalKind(Y10),isLNatKind(U10))) #317: #active(isLNatKind(cons(Y10,U10))) -> #and(isNaturalKind(Y10),isLNatKind(U10)) #318: #active(isLNatKind(cons(Y10,U10))) -> #isNaturalKind(Y10) #319: #active(isLNatKind(cons(Y10,U10))) -> #isLNatKind(U10) #320: #u41(active(X89),Y89,U89) -> #u41(X89,Y89,U89) #321: #mark(splitAt(U18,V18)) -> #active(splitAt(mark(U18),mark(V18))) #322: #mark(splitAt(U18,V18)) -> #splitAt(mark(U18),mark(V18)) #323: #mark(splitAt(U18,V18)) -> #mark(U18) #324: #mark(splitAt(U18,V18)) -> #mark(V18) #325: #mark(u82(P31)) -> #active(u82(mark(P31))) #326: #mark(u82(P31)) -> #u82(mark(P31)) #327: #mark(u82(P31)) -> #mark(P31) #328: #mark(tt()) -> #active(tt()) #329: #u221(U83,mark(V83),W83) -> #u221(U83,V83,W83) #330: #u202(active(V79),W79) -> #u202(V79,W79) #331: #mark(u191(X25,Y25)) -> #active(u191(mark(X25),Y25)) #332: #mark(u191(X25,Y25)) -> #u191(mark(X25),Y25) #333: #mark(u191(X25,Y25)) -> #mark(X25) #334: #active(u143(tt())) -> #mark(tt()) #335: #u143(mark(V56)) -> #u143(V56) #336: #mark(s(V23)) -> #active(s(mark(V23))) #337: #mark(s(V23)) -> #s(mark(V23)) #338: #mark(s(V23)) -> #mark(V23) #339: #u31(mark(Y86),U86) -> #u31(Y86,U86) #340: #u131(X48,mark(Y48),U48) -> #u131(X48,Y48,U48) #341: #active(isNatural(0())) -> #mark(tt()) #342: #active(u43(tt())) -> #mark(tt()) #343: #u191(active(V71),W71) -> #u191(V71,W71) #344: #u91(V102,mark(W102)) -> #u91(V102,W102) #345: #u141(Y ... 0 #u42 w: 0 #snd w: 0 cons w: 0 u142 w: 0 #natsFrom w: 0 #active w: 0 #u31 w: 0 snd w: 0 u112 w: 0 u42 w: 0 tt w: 0 #u53 w: 0 #u131 w: 0 u152 w: 0 #isNatural w: 0 #pair w: 0 u71 w: 0 #u181 w: 0 #u153 w: 0 #u43 w: 0 #u62 w: 0 u31 w: 0 #and w: 0 u141 w: 0 #u121 w: 0 #u111 w: 0 #u71 w: 0 #u132 w: 0 #u92 w: 0 USABLE RULES: { } Removed DPs: #11 #208 #409 #477 #520 #626 Number of SCCs: 2, DPs: 170 SCC { #83 #127 } POLO(Sum)... succeeded. #isLNatKind w: 0 u81 w: 0 #u101 w: 0 #u191 w: 0 u62 w: 0 #u152 w: 0 #u103 w: 0 #u82 w: 0 #u201 w: x1 u133 w: 0 #cons w: 0 s w: 0 u132 w: 0 u91 w: 0 #u52 w: 0 #take w: 0 u111 w: 0 u53 w: 0 isPLNatKind w: 0 u191 w: 0 isPLNat w: 0 #u141 w: 0 #u161 w: 0 u102 w: 0 u121 w: 0 #u51 w: 0 u181 w: 0 u153 w: 0 take w: 0 #u21 w: 0 u122 w: 0 and w: 0 u103 w: 0 pair w: 0 fst w: 0 u131 w: 0 natsFrom w: 0 #u102 w: 0 #head w: 0 #u61 w: 0 splitAt w: 0 isNaturalKind w: 0 u52 w: 0 #u151 w: 0 #fst w: 0 #u11 w: 0 u61 w: 0 u92 w: 0 #u81 w: 0 #u143 w: 0 u221 w: 0 _ w: 0 #isPLNatKind w: 0 #u91 w: 0 u151 w: 0 u202 w: 0 isNatural w: 0 u41 w: 0 #u72 w: 0 u211 w: 0 #u112 w: 0 u51 w: 0 tail w: 0 #mark w: 0 0 w: 0 #sel w: 0 #u171 w: 0 u11 w: 0 #isLNat w: 0 sel w: 0 #s w: 0 afterNth w: 0 #u211 w: 0 #isPLNat w: 0 nil w: 0 isLNat w: 0 #isNaturalKind w: 0 #tail w: 0 #splitAt w: 0 mark w: x1 + 1 u101 w: 0 #afterNth w: 0 #u122 w: 0 u72 w: 0 u21 w: 0 u201 w: 0 u143 w: 0 #u41 w: 0 isLNatKind w: 0 u43 w: 0 #u221 w: 0 u82 w: 0 #_ w: 0 u161 w: 0 #u202 w: 0 #u142 w: 0 #u133 w: 0 u171 w: 0 active w: x1 + 724 head w: 0 #u42 w: 0 #snd w: 0 cons w: 0 u142 w: 0 #natsFrom w: 0 #active w: 0 #u31 w: 0 snd w: 0 u112 w: 0 u42 w: 0 tt w: 0 #u53 w: 0 #u131 w: 0 u152 w: 0 #isNatural w: 0 #pair w: 0 u71 w: 0 #u181 w: 0 #u153 w: 0 #u43 w: 0 #u62 w: 0 u31 w: 0 #and w: 0 u141 w: 0 #u121 w: 0 #u111 w: 0 #u71 w: 0 #u132 w: 0 #u92 w: 0 USABLE RULES: { } Removed DPs: #83 #127 Number of SCCs: 1, DPs: 168 SCC { #1 #4..6 #14 #16 #24 #34 #36 #40 #42 #50 #52 #55 #58 #60 #64 #65 #69 #78 #87 #93 #94 #102 #103 #116..118 #124 #128 #131 #135 #143 #145 #154 #159 #161 #162 #164 #165 #169 #172 #178 #180 #187 #189 #190 #195 #198 #204 #206 #210 #214 #225 #227..229 #231 #233 #235 #237 #238 #245 #252 #253 #255 #257 #259 #260 #273 #285 #289 #294 #296 #297 #300 #307 #316 #321 #323 #324 #327 #331 #333 #338 #346 #349 #352 #354 #356 #358 #360 #361 #365 #371 #373 #375 #376 #383 #385 #387 #391 #393 #398 #400 #403 #405 #410 #416 #418 #419 #422 #433 #439 #447 #451 #453 #460 #465 #466 #468 #476 #478 #486 #490 #492 #504 #507 #511 #513 #514 #516 #518 #529 #534 #538 #540 #541 #544 #546 #549 #553 #555 #558 #563 #564 #567 #569 #577 #582 #585 #587 #588 #590 #604 #606..608 #610 #614 #621 #623 #625 #628 #636 #638 #647 #650 } POLO(Sum)... POLO(max)... succeeded. #isLNatKind w: 0 u81 w: max(x1 + 1, x2 + 15) #u101 w: 0 #u191 w: 0 u62 w: x1 + 6 #u152 w: 0 #u103 w: 0 #u82 w: 0 #u201 w: 0 u133 w: x1 + 1368 #cons w: 0 s w: x1 u132 w: max(x1 + 10960, x2 + 4577) u91 w: max(x1 + 541, x2 + 2020) #u52 w: 0 #take w: 0 u111 w: max(x1 + 10211, x2 + 32900) u53 w: x1 isPLNatKind w: 3 u191 w: max(x1 + 19, x2 + 17) isPLNat w: x1 + 6 #u141 w: 0 #u161 w: 0 u102 w: max(x1 + 11240, x2 + 10840) u121 w: max(x1 + 1, x2 + 5) #u51 w: 0 u181 w: max(x1 + 10, x2 + 3) u153 w: x1 + 7 take w: max(x1 + 18694, x2 + 19767) #u21 w: 0 u122 w: x1 and w: max(x1, x2) u103 w: x1 + 5838 pair w: max(x1 + 2, x2 + 14) fst w: x1 + 21 u131 w: max(x1 + 6534, x2 + 27242, x3 + 6535) natsFrom w: x1 + 14872 #u102 w: 0 #head w: 0 #u61 w: 0 splitAt w: max(x1 + 40, x2 + 23) isNaturalKind w: 3 u52 w: max(x1 + 2, x2 + 1) #u151 w: 0 #fst w: 0 #u11 w: 0 u61 w: max(x1 + 6, x2 + 19) u92 w: x1 + 253 #u81 w: 0 #u143 w: 0 u221 w: max(x1 + 8485, x2 + 1026, x3 + 48) _ w: 0 #isPLNatKind w: 0 #u91 w: 0 u151 w: max(x1 + 6, x2 + 28, x3 + 26) u202 w: max(x1, x2 + 18) isNatural w: x1 + 5 u41 w: max(x1 + 4612, x2 + 4578, x3 + 4577) #u72 w: 0 u211 w: max(x1 + 6282, x2 + 7380) #u112 w: 0 u51 w: max(x1 + 8, x2 + 7, x3 + 1) tail w: x1 + 13935 #mark w: x1 0 w: 4632 #sel w: 0 #u171 w: 0 u11 w: max(x1 + 4886, x2 + 1007, x3 + 41) #isLNat w: 0 sel w: max(x1 + 43483, x2 + 45972) #s w: 0 afterNth w: max(x1 + 7180, x2 + 4888) #u211 w: 0 #isPLNat w: 0 nil w: 2 isLNat w: x1 + 1 #isNaturalKind w: 0 #tail w: 0 #splitAt w: 0 mark w: x1 u101 w: max(x1 + 11244, x2 + 11247, x3 + 11246) #afterNth w: 0 #u122 w: 0 u72 w: x1 + 2251 u21 w: max(x1 + 19, x2 + 13) u201 w: max(x1 + 17, x2 + 40, x3 + 30, x4 + 23) u143 w: x1 + 1 #u41 w: 0 isLNatKind w: 3 u43 w: x1 + 1353 #u221 w: 0 u82 w: x1 + 1 #_ w: 0 u161 w: max(x1 + 5, x2 + 14872) #u202 w: 0 #u142 w: 0 #u133 w: 0 u171 w: max(x1 + 43478, x2 + 43483, x3 + 43477) active w: x1 head w: x1 + 36296 #u42 w: 0 #snd w: 0 cons w: max(x1 + 10, x2) u142 w: max(x1 + 4, x2 + 3) #natsFrom w: 0 #active w: x1 #u31 w: 0 snd w: x1 + 15 u112 w: x1 + 5177 u42 w: max(x1 + 1758, x2 + 1745) tt w: 2 #u53 w: 0 #u131 w: 0 u152 w: max(x1 + 20, x2 + 19) #isNatural w: 0 #pair w: 0 u71 w: max(x1 + 7513, x2 + 5321) #u181 w: 0 #u153 w: 0 #u43 w: 0 #u62 w: 0 u31 w: max(x1 + 678, x2 + 677) #and w: 0 u141 w: max(x1 + 15, x2 + 8, x3 + 9) #u121 w: 0 #u111 w: 0 #u71 w: 0 #u132 w: 0 #u92 w: 0 USABLE RULES: { 1..357 } Removed DPs: #1 #6 #16 #24 #42 #52 #55 #60 #64 #69 #78 #87 #102 #116 #117 #135 #145 #161 #164 #172 #180 #189 #190 #195 #198 #206 #214 #227 #228 #231 #233 #237 #252 #255 #259 #273 #285 #296 #297 #307 #323 #324 #327 #333 #346 #349 #352 #356 #360 #365 #375 #387 #393 #400 #418 #419 #422 #433 #439 #453 #460 #468 #476 #492 #507 #513 #514 #518 #529 #534 #540 #541 #546 #549 #555 #563 #564 #567 #569 #577 #582 #587 #590 #606 #607 #610 #614 #621 #625 #628 #636 #638 #647 Number of SCCs: 1, DPs: 36 SCC { #4 #5 #36 #50 #65 #93 #94 #124 #128 #131 #154 #165 #169 #210 #260 #289 #300 #316 #321 #338 #371 #376 #383 #385 #391 #403 #405 #410 #447 #465 #478 #486 #504 #516 #558 #588 } POLO(Sum)... POLO(max)... succeeded. #isLNatKind w: 0 u81 w: max(x2 + 2) #u101 w: 0 #u191 w: 0 u62 w: 0 #u152 w: 0 #u103 w: 0 #u82 w: 0 #u201 w: 0 u133 w: 0 #cons w: 0 s w: x1 u132 w: 0 u91 w: max(x1 + 6861, x2 + 7179) #u52 w: 0 #take w: 0 u111 w: 0 u53 w: x1 isPLNatKind w: x1 u191 w: max(x1 + 74, x2 + 73) isPLNat w: x1 + 11220 #u141 w: 0 #u161 w: 0 u102 w: 0 u121 w: 0 #u51 w: 0 u181 w: max(x1 + 2, x2 + 1) u153 w: 1526 take w: max(x1 + 3969, x2 + 9300) #u21 w: 0 u122 w: x1 and w: max(x1 + 24, x2) u103 w: 0 pair w: max(x1 + 72, x2 + 70) fst w: x1 + 1042 u131 w: 0 natsFrom w: x1 #u102 w: 0 #head w: 0 #u61 w: 0 splitAt w: max(x1 + 568, x2 + 121) isNaturalKind w: x1 + 15 u52 w: max(x2 + 23) #u151 w: 0 #fst w: 0 #u11 w: 0 u61 w: 0 u92 w: 6862 #u81 w: 0 #u143 w: 0 u221 w: max(x1 + 2789, x2 + 2788, x3 + 2787) _ w: 0 #isPLNatKind w: 0 #u91 w: 0 u151 w: max(x2 + 2140, x3 + 1955) u202 w: max(x1, x2 + 81) isNatural w: 0 u41 w: max(x3 + 2168) #u72 w: 0 u211 w: max(x1 + 14922, x2 + 14941) #u112 w: 0 u51 w: max(x2 + 5, x3 + 23) tail w: x1 + 14970 #mark w: x1 0 w: 4620 #sel w: 0 #u171 w: 0 u11 w: max(x1 + 1856, x2 + 571, x3 + 124) #isLNat w: 0 sel w: max(x1 + 25901, x2 + 25901) #s w: 0 afterNth w: max(x1 + 1903, x2 + 12687) #u211 w: 0 #isPLNat w: 0 nil w: 1 isLNat w: x1 + 23 #isNaturalKind w: 0 #tail w: 0 #splitAt w: 0 mark w: x1 u101 w: 0 #afterNth w: 0 #u122 w: 0 u72 w: 0 u21 w: max(x2 + 753) u201 w: max(x2 + 568, x3 + 94, x4 + 121) u143 w: 0 #u41 w: 0 isLNatKind w: x1 + 47 u43 w: x1 #u221 w: 0 u82 w: 0 #_ w: 0 u161 w: max(x2) #u202 w: 0 #u142 w: 0 #u133 w: 0 u171 w: max(x2 + 25901, x3 + 25900) active w: x1 head w: x1 + 6478 #u42 w: 0 #snd w: 0 cons w: max(x1, x2) u142 w: 0 #natsFrom w: 0 #active w: x1 #u31 w: 0 snd w: x1 + 3 u112 w: 0 u42 w: max(x2 + 183) tt w: 0 #u53 w: 0 #u131 w: 0 u152 w: max(x2 + 1708) #isNatural w: 0 #pair w: 0 u71 w: max(x1 + 4, x2 + 3) #u181 w: 0 #u153 w: 0 #u43 w: 0 #u62 w: 0 u31 w: max(x2 + 2420) #and w: 0 u141 w: max(x2 + 4075) #u121 w: 0 #u111 w: 0 #u71 w: 0 #u132 w: 0 #u92 w: 0 USABLE RULES: { 1..357 } Removed DPs: #65 #124 #131 #154 #165 #169 #210 #289 #385 #410 #486 Number of SCCs: 2, DPs: 24 SCC { #478 #558 } POLO(Sum)... succeeded. #isLNatKind w: 0 u81 w: x2 + 5158 #u101 w: 0 #u191 w: 0 u62 w: 7210 #u152 w: 0 #u103 w: 0 #u82 w: 0 #u201 w: 0 u133 w: x1 + 25412 #cons w: 0 s w: x1 + 54079 u132 w: 25543 u91 w: x2 + 318 #u52 w: 0 #take w: 0 u111 w: x2 + 38293 u53 w: 9174 isPLNatKind w: 33262 u191 w: x2 + 18387 isPLNat w: x1 + 1251 #u141 w: 0 #u161 w: 0 u102 w: x2 + 3572 u121 w: 42250 #u51 w: 0 u181 w: x2 + 24903 u153 w: 26763 take w: 8496 #u21 w: 0 u122 w: 45560 and w: x2 + 27250 u103 w: 1793 pair w: 18390 fst w: 14098 u131 w: x2 + x3 + 16054 natsFrom w: 7379 #u102 w: 0 #head w: 0 #u61 w: 0 splitAt w: 18384 isNaturalKind w: x1 + 18137 u52 w: x2 + 11477 #u151 w: 0 #fst w: 0 #u11 w: 0 u61 w: x2 + 6697 u92 w: 229 #u81 w: 0 #u143 w: 0 u221 w: x2 + 9847 _ w: 0 #isPLNatKind w: 0 #u91 w: 0 u151 w: x2 + 26853 u202 w: x2 + 28384 isNatural w: x1 + 9973 u41 w: x3 + 7590 #u72 w: 0 u211 w: x2 + 324 #u112 w: 0 u51 w: x2 + x3 + 11282 tail w: 321 #mark w: x1 + 1 0 w: 2006 #sel w: 0 #u171 w: 0 u11 w: x2 + 26809 #isLNat w: 0 sel w: 4469 #s w: 0 afterNth w: 25391 #u211 w: 0 #isPLNat w: 0 nil w: 30968 isLNat w: 133 #isNaturalKind w: 0 #tail w: 0 #splitAt w: 0 mark w: x1 + 3505 u101 w: x2 + x3 + 6998 #afterNth w: 0 #u122 w: 0 u72 w: 14032 u21 w: x2 + 18363 u201 w: x2 + x4 + 23051 u143 w: x1 + 8218 #u41 w: 0 isLNatKind w: x1 + 9903 u43 w: x1 + 12516 #u221 w: 0 u82 w: 180 #_ w: 0 u161 w: x2 + 37968 #u202 w: 0 #u142 w: 0 #u133 w: 0 u171 w: x3 + 13408 active w: x1 + 3507 head w: 22876 #u42 w: 0 #snd w: 0 cons w: x2 + 27974 u142 w: 8349 #natsFrom w: 0 #active w: x1 #u31 w: 0 snd w: 23356 u112 w: 46988 u42 w: 12647 tt w: 46991 #u53 w: 0 #u131 w: 0 u152 w: 21763 #isNatural w: 0 #pair w: 0 u71 w: 8450 #u181 w: 0 #u153 w: 0 #u43 w: 0 #u62 w: 0 u31 w: x2 + 32083 #and w: 0 u141 w: 12402 #u121 w: 0 #u111 w: 0 #u71 w: 0 #u132 w: 0 #u92 w: 0 USABLE RULES: { 144..155 158..175 178..181 184..193 196..205 208..217 220..229 232..297 300..309 312..315 318..323 326..329 332..335 338..357 } Removed DPs: #478 #558 Number of SCCs: 1, DPs: 22 SCC { #4 #5 #36 #50 #94 #128 #260 #300 #316 #321 #338 #371 #376 #383 #391 #403 #405 #447 #465 #504 #516 #588 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #isLNatKind s: [] p: 0 u81 s: [1] p: 10 #u101 s: [2,3] p: 0 #u191 s: [2] p: 0 u62 s: [] p: 3 #u152 s: [2] p: 0 #u103 s: [] p: 0 #u82 s: [] p: 0 #u201 s: [2,3,4,1] p: 0 u133 s: 1 #cons s: [1] p: 0 s s: [1] p: 4 u132 s: [] p: 11 u91 s: [2] p: 2 #u52 s: [] p: 0 #take s: [] p: 0 u111 s: [1,2] p: 11 u53 s: 1 isPLNatKind s: [] p: 11 u191 s: 2 isPLNat s: 1 #u141 s: [2,3,1] p: 0 #u161 s: [1] p: 0 u102 s: [2] p: 3 u121 s: [] p: 4 #u51 s: [2,1,3] p: 0 u181 s: 1 u153 s: [1] p: 3 take s: [2] p: 6 #u21 s: [2] p: 0 u122 s: 1 and s: 2 u103 s: [] p: 8 pair s: [1,2] p: 6 fst s: 1 u131 s: 1 natsFrom s: [] p: 7 #u102 s: [] p: 0 #head s: [] p: 0 #u61 s: [] p: 0 splitAt s: [] p: 7 isNaturalKind s: [] p: 6 u52 s: [] p: 5 #u151 s: [1,3] p: 0 #fst s: [] p: 0 #u11 s: [1,3,2] p: 0 u61 s: 2 u92 s: [] p: 3 #u81 s: [2] p: 0 #u143 s: [] p: 0 u221 s: [3,2,1] p: 3 _ s: [] p: 0 #isPLNatKind s: [] p: 0 #u91 s: [2] p: 0 u151 s: 2 u202 s: 1 isNatural s: [] p: 4 u41 s: [] p: 11 #u72 s: [] p: 0 u211 s: [1,2] p: 2 #u112 s: [] p: 0 u51 s: [] p: 5 tail s: [] p: 1 #mark s: 1 0 s: [] p: 10 #sel s: [1,2] p: 0 #u171 s: [2] p: 0 u11 s: [2,1,3] p: 8 #isLNat s: [] p: 0 sel s: [2] p: 6 #s s: [] p: 0 afterNth s: [1] p: 0 #u211 s: [] p: 0 #isPLNat s: [] p: 0 nil s: [] p: 3 isLNat s: [] p: 5 #isNaturalKind s: [] p: 0 #tail s: [] p: 0 #splitAt s: [2,1] p: 0 mark s: [1] p: 3 u101 s: [1,2,3] p: 11 #afterNth s: [2] p: 0 #u122 s: [] p: 0 u72 s: [] p: 3 u21 s: [1,2] p: 5 u201 s: [] p: 7 u143 s: [] p: 3 #u41 s: [3,1,2] p: 0 isLNatKind s: [] p: 6 u43 s: 1 #u221 s: [3] p: 0 u82 s: [] p: 10 #_ s: [2,1] p: 0 u161 s: [1] p: 5 #u202 s: [2] p: 0 #u142 s: [1] p: 0 #u133 s: [] p: 0 u171 s: [2] p: 1 active s: [1] p: 11 head s: [] p: 2 #u42 s: [1] p: 0 #snd s: [] p: 0 cons s: [2] p: 6 u142 s: [1] p: 3 #natsFrom s: [] p: 0 #active s: 1 #u31 s: [] p: 0 snd s: [] p: 8 u112 s: [1] p: 9 u42 s: [] p: 0 tt s: [] p: 9 #u53 s: [] p: 0 #u131 s: [] p: 0 u152 s: 1 #isNatural s: [] p: 0 #pair s: [] p: 0 u71 s: [1,2] p: 11 #u181 s: [1,2] p: 0 #u153 s: [] p: 0 #u43 s: [] p: 0 #u62 s: [] p: 0 u31 s: [] p: 1 #and s: [] p: 0 u141 s: [1,3] p: 3 #u121 s: [] p: 0 #u111 s: [1,2] p: 0 #u71 s: [] p: 0 #u132 s: [1,2] p: 0 #u92 s: [] p: 0 USABLE RULES: { 154 155 158..175 178..181 184..189 202..205 208..217 230..237 240..271 284..297 300..309 320..323 326..329 332..335 338..341 344..347 350..357 } Removed DPs: #338 Number of SCCs: 1, DPs: 21 SCC { #4 #5 #36 #50 #94 #128 #260 #300 #316 #321 #371 #376 #383 #391 #403 #405 #447 #465 #504 #516 #588 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #isLNatKind s: [] p: 0 u81 s: [1] p: 8 #u101 s: [2,3] p: 0 #u191 s: [2] p: 0 u62 s: [] p: 3 #u152 s: [2] p: 0 #u103 s: [] p: 0 #u82 s: [] p: 0 #u201 s: [2,3,4,1] p: 0 u133 s: 1 #cons s: [1] p: 0 s s: [1] p: 5 u132 s: [] p: 9 u91 s: [2] p: 2 #u52 s: [] p: 0 #take s: [] p: 0 u111 s: [1,2] p: 9 u53 s: 1 isPLNatKind s: [] p: 9 u191 s: 2 isPLNat s: 1 #u141 s: [2,3,1] p: 0 #u161 s: [1] p: 0 u102 s: [2] p: 3 u121 s: [2] p: 5 #u51 s: [2,1,3] p: 0 u181 s: 1 u153 s: [1] p: 3 take s: [2] p: 5 #u21 s: [2] p: 0 u122 s: 1 and s: 2 u103 s: [] p: 6 pair s: [1,2] p: 5 fst s: 1 u131 s: 1 natsFrom s: [] p: 6 #u102 s: [] p: 0 #head s: [] p: 0 #u61 s: [] p: 0 splitAt s: [] p: 5 isNaturalKind s: [] p: 5 u52 s: [] p: 4 #u151 s: [1,3] p: 0 #fst s: [] p: 0 #u11 s: [1,3,2] p: 0 u61 s: 2 u92 s: [] p: 3 #u81 s: [2] p: 0 #u143 s: [] p: 0 u221 s: [3,2,1] p: 3 _ s: [] p: 0 #isPLNatKind s: [] p: 0 #u91 s: [2] p: 0 u151 s: 2 u202 s: 1 isNatural s: [1] p: 5 u41 s: [] p: 9 #u72 s: [] p: 0 u211 s: [1,2] p: 2 #u112 s: [] p: 0 u51 s: [] p: 4 tail s: [] p: 1 #mark s: [1] p: 5 0 s: [] p: 8 #sel s: [1,2] p: 0 #u171 s: [2] p: 0 u11 s: [2,1,3] p: 6 #isLNat s: [] p: 0 sel s: [2] p: 5 #s s: [] p: 0 afterNth s: [1] p: 0 #u211 s: [] p: 0 #isPLNat s: [] p: 0 nil s: [] p: 3 isLNat s: [] p: 4 #isNaturalKind s: [] p: 0 #tail s: [] p: 0 #splitAt s: [2,1] p: 0 mark s: [1] p: 3 u101 s: [1,2,3] p: 5 #afterNth s: [2] p: 0 #u122 s: [] p: 0 u72 s: [] p: 3 u21 s: [1,2] p: 4 u201 s: [] p: 5 u143 s: [] p: 3 #u41 s: [3,1,2] p: 0 isLNatKind s: [] p: 5 u43 s: 1 #u221 s: [3] p: 0 u82 s: [] p: 8 #_ s: [2,1] p: 0 u161 s: [1] p: 5 #u202 s: [2] p: 0 #u142 s: [1] p: 0 #u133 s: [] p: 0 u171 s: [2] p: 1 active s: [1] p: 9 head s: [] p: 2 #u42 s: [1] p: 0 #snd s: [] p: 0 cons s: [2] p: 5 u142 s: [1] p: 3 #natsFrom s: [] p: 0 #active s: [1] p: 5 #u31 s: [] p: 0 snd s: [] p: 6 u112 s: [1] p: 7 u42 s: [] p: 0 tt s: [] p: 7 #u53 s: [] p: 0 #u131 s: [] p: 0 u152 s: 1 #isNatural s: [] p: 0 #pair s: [] p: 0 u71 s: [1] p: 9 #u181 s: [1,2] p: 0 #u153 s: [] p: 0 #u43 s: [] p: 0 #u62 s: [] p: 0 u31 s: [] p: 1 #and s: [] p: 0 u141 s: [1,3] p: 3 #u121 s: [] p: 0 #u111 s: [1,2] p: 0 #u71 s: [] p: 0 #u132 s: [1,2] p: 0 #u92 s: [] p: 0 USABLE RULES: { 154 155 158..175 178..181 184..189 202..205 208..217 230..237 240..271 284..297 300..309 320..323 326..329 332..335 338..341 344..347 350..357 } Removed DPs: #405 Number of SCCs: 1, DPs: 19 SCC { #4 #5 #36 #50 #94 #128 #260 #300 #316 #321 #371 #376 #383 #391 #403 #447 #504 #516 #588 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #isLNatKind s: [] p: 0 u81 s: 1 #u101 s: [2,3] p: 0 #u191 s: [2] p: 0 u62 s: [] p: 3 #u152 s: [2] p: 0 #u103 s: [] p: 0 #u82 s: [] p: 0 #u201 s: [2,3,4,1] p: 0 u133 s: 1 #cons s: [1] p: 0 s s: [1] p: 5 u132 s: [] p: 9 u91 s: [2] p: 2 #u52 s: [] p: 0 #take s: [] p: 0 u111 s: [1,2] p: 9 u53 s: 1 isPLNatKind s: [] p: 9 u191 s: 2 isPLNat s: [] p: 9 #u141 s: [2,3,1] p: 0 #u161 s: [1] p: 0 u102 s: [2] p: 3 u121 s: [2] p: 5 #u51 s: [2,1,3] p: 0 u181 s: 1 u153 s: [1] p: 3 take s: [2] p: 6 #u21 s: [2] p: 0 u122 s: 1 and s: 2 u103 s: [] p: 6 pair s: [2,1] p: 5 fst s: 1 u131 s: 1 natsFrom s: [] p: 6 #u102 s: [] p: 0 #head s: [] p: 0 #u61 s: [] p: 0 splitAt s: [] p: 5 isNaturalKind s: [] p: 5 u52 s: [] p: 4 #u151 s: [1,3] p: 0 #fst s: [] p: 0 #u11 s: [1,3,2] p: 0 u61 s: 2 u92 s: [] p: 3 #u81 s: [2] p: 0 #u143 s: [] p: 0 u221 s: [3,2,1] p: 3 _ s: [] p: 0 #isPLNatKind s: [] p: 0 #u91 s: [2] p: 0 u151 s: 2 u202 s: 1 isNatural s: [1] p: 5 u41 s: [2,1] p: 5 #u72 s: [] p: 0 u211 s: [1,2] p: 2 #u112 s: [] p: 0 u51 s: [] p: 4 tail s: [] p: 1 #mark s: [1] p: 5 0 s: [] p: 8 #sel s: [1,2] p: 0 #u171 s: [2] p: 0 u11 s: [2,1,3] p: 6 #isLNat s: [] p: 0 sel s: [2] p: 5 #s s: [] p: 0 afterNth s: [1] p: 0 #u211 s: [] p: 0 #isPLNat s: [] p: 0 nil s: [] p: 8 isLNat s: [] p: 4 #isNaturalKind s: [] p: 0 #tail s: [] p: 0 #splitAt s: [2,1] p: 0 mark s: [1] p: 3 u101 s: [1,2,3] p: 5 #afterNth s: [2] p: 0 #u122 s: [] p: 0 u72 s: [] p: 3 u21 s: [2] p: 4 u201 s: [] p: 5 u143 s: [] p: 3 #u41 s: [3,1,2] p: 0 isLNatKind s: [1] p: 5 u43 s: 1 #u221 s: [3] p: 0 u82 s: [] p: 8 #_ s: [2,1] p: 0 u161 s: [1] p: 5 #u202 s: [2] p: 0 #u142 s: [1] p: 0 #u133 s: [] p: 0 u171 s: [2] p: 1 active s: [1] p: 9 head s: [] p: 2 #u42 s: [1] p: 0 #snd s: [] p: 0 cons s: [2,1] p: 5 u142 s: [1] p: 3 #natsFrom s: [] p: 0 #active s: [1] p: 5 #u31 s: [] p: 0 snd s: [1] p: 6 u112 s: [1] p: 7 u42 s: [] p: 0 tt s: [] p: 7 #u53 s: [] p: 0 #u131 s: [] p: 0 u152 s: 1 #isNatural s: [] p: 0 #pair s: [] p: 0 u71 s: [1] p: 9 #u181 s: [1,2] p: 0 #u153 s: [] p: 0 #u43 s: [] p: 0 #u62 s: [] p: 0 u31 s: [] p: 1 #and s: [] p: 0 u141 s: [1,3] p: 3 #u121 s: [] p: 0 #u111 s: [1,2] p: 0 #u71 s: [] p: 0 #u132 s: [1,2] p: 0 #u92 s: [] p: 0 USABLE RULES: { 154 155 158..175 178..181 184..189 202..205 208..217 230..237 240..267 284..287 294..297 300..309 320..323 326..329 332..335 338..341 344..347 350..357 } Removed DPs: #316 Number of SCCs: 1, DPs: 17 SCC { #4 #5 #36 #50 #94 #260 #300 #321 #371 #376 #383 #391 #403 #447 #504 #516 #588 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #isLNatKind s: [] p: 0 u81 s: [2] p: 14 #u101 s: [2,3] p: 0 #u191 s: [] p: 0 u62 s: [] p: 1 #u152 s: [2] p: 0 #u103 s: [] p: 0 #u82 s: [] p: 0 #u201 s: [2,3,4,1] p: 0 u133 s: [1] p: 14 #cons s: [1] p: 0 s s: [1] p: 12 u132 s: [2] p: 14 u91 s: [2] p: 2 #u52 s: [] p: 0 #take s: [] p: 0 u111 s: 1 u53 s: 1 isPLNatKind s: [1] p: 14 u191 s: [] p: 7 isPLNat s: [1] p: 14 #u141 s: [2,3,1] p: 0 #u161 s: [1] p: 0 u102 s: [2] p: 0 u121 s: [2] p: 6 #u51 s: [2] p: 0 u181 s: [2] p: 16 u153 s: 1 take s: [1] p: 1 #u21 s: [2] p: 0 u122 s: [1] p: 5 and s: 2 u103 s: [] p: 7 pair s: [1] p: 15 fst s: [] p: 14 u131 s: 1 natsFrom s: [] p: 3 #u102 s: [] p: 0 #head s: [] p: 0 #u61 s: [] p: 0 splitAt s: [] p: 12 isNaturalKind s: [] p: 8 u52 s: [] p: 7 #u151 s: [1,3] p: 0 #fst s: [] p: 0 #u11 s: [1,3,2] p: 0 u61 s: [2,1] p: 14 u92 s: [] p: 3 #u81 s: [2] p: 0 #u143 s: [] p: 0 u221 s: [3,2,1] p: 13 _ s: [] p: 0 #isPLNatKind s: [] p: 0 #u91 s: [2] p: 0 u151 s: 2 u202 s: 1 isNatural s: [] p: 6 u41 s: [1,2] p: 11 #u72 s: [] p: 0 u211 s: 1 #u112 s: [] p: 0 u51 s: [] p: 7 tail s: [] p: 1 #mark s: [1] p: 9 0 s: [] p: 4 #sel s: [1,2] p: 0 #u171 s: [] p: 0 u11 s: [2,1,3] p: 11 #isLNat s: [] p: 0 sel s: [1] p: 2 #s s: [] p: 0 afterNth s: [] p: 10 #u211 s: [] p: 0 #isPLNat s: [] p: 0 nil s: [] p: 7 isLNat s: [] p: 7 #isNaturalKind s: [] p: 0 #tail s: [] p: 0 #splitAt s: [2,1] p: 0 mark s: [1] p: 6 u101 s: [2] p: 1 #afterNth s: [2] p: 0 #u122 s: [] p: 0 u72 s: [] p: 3 u21 s: [] p: 6 u201 s: [] p: 12 u143 s: [] p: 6 #u41 s: [3,1,2] p: 0 isLNatKind s: 1 u43 s: 1 #u221 s: [] p: 0 u82 s: 1 #_ s: [2,1] p: 0 u161 s: 2 #u202 s: [2] p: 0 #u142 s: [1] p: 0 #u133 s: [] p: 0 u171 s: [] p: 0 active s: [1] p: 14 head s: [1] p: 1 #u42 s: [1] p: 0 #snd s: [] p: 0 cons s: [2] p: 3 u142 s: 1 #natsFrom s: [] p: 0 #active s: [1] p: 9 #u31 s: [] p: 0 snd s: [1] p: 15 u112 s: [] p: 14 u42 s: [] p: 1 tt s: [] p: 4 #u53 s: [] p: 0 #u131 s: [] p: 0 u152 s: [1] p: 14 #isNatural s: [] p: 0 #pair s: [] p: 0 u71 s: [] p: 8 #u181 s: [1,2] p: 0 #u153 s: [] p: 0 #u43 s: [] p: 0 #u62 s: [] p: 0 u31 s: 1 #and s: [] p: 0 u141 s: [1,3] p: 8 #u121 s: [] p: 0 #u111 s: [1,2] p: 0 #u71 s: [] p: 0 #u132 s: [1,2] p: 0 #u92 s: [] p: 0 USABLE RULES: { 144..155 158..165 168..171 178..181 190..193 208..217 220..223 228..231 240..243 256..267 272..297 300..309 312..317 320..323 338..347 } Removed DPs: #376 #403 Number of SCCs: 1, DPs: 14 SCC { #4 #5 #36 #50 #94 #260 #300 #321 #371 #383 #447 #504 #516 #588 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #isLNatKind s: [] p: 0 u81 s: [2] p: 15 #u101 s: [2,3] p: 0 #u191 s: [] p: 0 u62 s: [] p: 2 #u152 s: [2] p: 0 #u103 s: [] p: 0 #u82 s: [] p: 0 #u201 s: [2,3,4,1] p: 0 u133 s: [1] p: 15 #cons s: [1] p: 0 s s: [1] p: 13 u132 s: [2] p: 15 u91 s: [2] p: 3 #u52 s: [] p: 0 #take s: [] p: 0 u111 s: 1 u53 s: 1 isPLNatKind s: [1] p: 15 u191 s: [] p: 8 isPLNat s: [1] p: 15 #u141 s: [2,3,1] p: 0 #u161 s: [1] p: 0 u102 s: [2] p: 0 u121 s: [2] p: 7 #u51 s: [2] p: 0 u181 s: [2] p: 17 u153 s: 1 take s: [1] p: 1 #u21 s: [2] p: 0 u122 s: [1] p: 6 and s: [2] p: 2 u103 s: [] p: 8 pair s: [1] p: 16 fst s: [] p: 15 u131 s: 1 natsFrom s: [] p: 1 #u102 s: [] p: 0 #head s: [] p: 0 #u61 s: [] p: 0 splitAt s: [] p: 12 isNaturalKind s: [] p: 12 u52 s: [] p: 8 #u151 s: [1,3] p: 0 #fst s: [] p: 0 #u11 s: [1,3,2] p: 0 u61 s: [2,1] p: 15 u92 s: [] p: 4 #u81 s: [2] p: 0 #u143 s: [] p: 0 u221 s: [3,2,1] p: 14 _ s: [] p: 0 #isPLNatKind s: [] p: 0 #u91 s: [2] p: 0 u151 s: 2 u202 s: 1 isNatural s: [] p: 7 u41 s: [1,2] p: 14 #u72 s: [] p: 0 u211 s: 1 #u112 s: [] p: 0 u51 s: [] p: 8 tail s: [] p: 1 #mark s: [1] p: 14 0 s: [] p: 5 #sel s: [1,2] p: 0 #u171 s: [] p: 0 u11 s: [2,1,3] p: 11 #isLNat s: [] p: 0 sel s: [1] p: 3 #s s: [] p: 0 afterNth s: [] p: 13 #u211 s: [] p: 0 #isPLNat s: [] p: 0 nil s: [] p: 8 isLNat s: [] p: 8 #isNaturalKind s: [] p: 0 #tail s: [] p: 0 #splitAt s: [2,1] p: 0 mark s: [1] p: 7 u101 s: [2] p: 1 #afterNth s: [2] p: 0 #u122 s: [] p: 0 u72 s: [] p: 4 u21 s: [] p: 7 u201 s: [] p: 12 u143 s: [] p: 7 #u41 s: [3,1,2] p: 0 isLNatKind s: 1 u43 s: 1 #u221 s: [] p: 0 u82 s: 1 #_ s: [2,1] p: 0 u161 s: 2 #u202 s: [2] p: 0 #u142 s: [1] p: 0 #u133 s: [] p: 0 u171 s: [] p: 0 active s: [1] p: 15 head s: [1] p: 2 #u42 s: [1] p: 0 #snd s: [] p: 0 cons s: [2] p: 4 u142 s: 1 #natsFrom s: [] p: 0 #active s: [1] p: 14 #u31 s: [] p: 0 snd s: [1] p: 16 u112 s: [] p: 15 u42 s: [] p: 2 tt s: [] p: 5 #u53 s: [] p: 0 #u131 s: [] p: 0 u152 s: [1] p: 15 #isNatural s: [] p: 0 #pair s: [] p: 0 u71 s: [] p: 9 #u181 s: [1,2] p: 0 #u153 s: [] p: 0 #u43 s: [] p: 0 #u62 s: [] p: 0 u31 s: 1 #and s: [] p: 0 u141 s: [1,3] p: 9 #u121 s: [] p: 0 #u111 s: [1,2] p: 0 #u71 s: [] p: 0 #u132 s: [1,2] p: 0 #u92 s: [] p: 0 USABLE RULES: { 144..155 158..165 168..171 178..181 190..193 208..217 220..223 228..231 240..243 256..267 272..297 300..309 312..317 320..323 338..347 } Removed DPs: #5 Number of SCCs: 1, DPs: 12 SCC { #4 #36 #50 #94 #260 #300 #321 #371 #447 #504 #516 #588 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #isLNatKind s: [] p: 0 u81 s: [2] p: 10 #u101 s: [2,3] p: 0 #u191 s: [] p: 0 u62 s: 1 #u152 s: [2] p: 0 #u103 s: [] p: 0 #u82 s: [] p: 0 #u201 s: [2,3,4,1] p: 0 u133 s: [1] p: 14 #cons s: [1] p: 0 s s: [] p: 7 u132 s: [2] p: 14 u91 s: [2] p: 3 #u52 s: [] p: 0 #take s: [] p: 0 u111 s: [] p: 14 u53 s: 1 isPLNatKind s: [] p: 3 u191 s: [1] p: 10 isPLNat s: [1] p: 9 #u141 s: [2,3,1] p: 0 #u161 s: [1] p: 0 u102 s: [1] p: 1 u121 s: [2] p: 13 #u51 s: [2] p: 0 u181 s: [] p: 16 u153 s: [] p: 2 take s: [1] p: 1 #u21 s: [2] p: 0 u122 s: [] p: 13 and s: 2 u103 s: [] p: 8 pair s: [] p: 10 fst s: [] p: 3 u131 s: 1 natsFrom s: [1] p: 6 #u102 s: [] p: 0 #head s: [] p: 0 #u61 s: [] p: 0 splitAt s: [] p: 15 isNaturalKind s: [] p: 6 u52 s: [2] p: 4 #u151 s: [1,3] p: 0 #fst s: [] p: 0 #u11 s: [1,3,2] p: 0 u61 s: 1 u92 s: [] p: 8 #u81 s: [2] p: 0 #u143 s: [] p: 0 u221 s: [1,2] p: 2 _ s: [] p: 0 #isPLNatKind s: [] p: 0 #u91 s: [2] p: 0 u151 s: 2 u202 s: 1 isNatural s: [] p: 1 u41 s: [1,2] p: 8 #u72 s: [] p: 0 u211 s: [2] p: 3 #u112 s: [] p: 0 u51 s: [3,2] p: 4 tail s: 1 #mark s: [1] p: 16 0 s: [] p: 11 #sel s: [1,2] p: 0 #u171 s: [] p: 0 u11 s: [1,2,3] p: 14 #isLNat s: [] p: 0 sel s: [1,2] p: 3 #s s: [] p: 0 afterNth s: [] p: 7 #u211 s: [] p: 0 #isPLNat s: [] p: 0 nil s: [] p: 14 isLNat s: [1] p: 4 #isNaturalKind s: [] p: 0 #tail s: [] p: 0 #splitAt s: [2,1] p: 0 mark s: 1 u101 s: [2] p: 1 #afterNth s: [2] p: 0 #u122 s: [] p: 0 u72 s: [] p: 7 u21 s: [] p: 2 u201 s: [] p: 15 u143 s: [] p: 13 #u41 s: [3,1,2] p: 0 isLNatKind s: 1 u43 s: [] p: 14 #u221 s: [] p: 0 u82 s: 1 #_ s: [2,1] p: 0 u161 s: [1,2] p: 5 #u202 s: [2] p: 0 #u142 s: [1] p: 0 #u133 s: [] p: 0 u171 s: [] p: 3 active s: 1 head s: [1] p: 4 #u42 s: [1] p: 0 #snd s: [] p: 0 cons s: [2,1] p: 4 u142 s: [] p: 3 #natsFrom s: [] p: 0 #active s: [1] p: 16 #u31 s: [] p: 0 snd s: [1] p: 15 u112 s: [1] p: 9 u42 s: [] p: 14 tt s: [] p: 12 #u53 s: [] p: 0 #u131 s: [] p: 0 u152 s: [1] p: 15 #isNatural s: [] p: 0 #pair s: [] p: 0 u71 s: [] p: 8 #u181 s: [1,2] p: 0 #u153 s: [] p: 0 #u43 s: [] p: 0 #u62 s: [] p: 0 u31 s: [1,2] p: 4 #and s: [] p: 0 u141 s: [1,3] p: 6 #u121 s: [] p: 0 #u111 s: [1,2] p: 0 #u71 s: [] p: 0 #u132 s: [1,2] p: 0 #u92 s: [] p: 0 USABLE RULES: { 6 8 11 14 21 29 30 35 39 46 82 99 106 112 113 122 123 142 154..195 202..213 218..283 288..325 330..353 } Removed DPs: #94 Number of SCCs: 1, DPs: 10 SCC { #36 #50 #260 #300 #321 #371 #447 #504 #516 #588 } POLO(Sum)... succeeded. #isLNatKind w: 0 u81 w: x1 + 6323 #u101 w: 0 #u191 w: 0 u62 w: 0 #u152 w: 0 #u103 w: 0 #u82 w: 0 #u201 w: 0 u133 w: x1 + 15214 #cons w: 0 s w: x1 u132 w: x1 + x2 + 1800 u91 w: x1 + x2 + 3065 #u52 w: 0 #take w: 0 u111 w: x1 + x2 + 4862 u53 w: x1 + 15611 isPLNatKind w: x1 + 2953 u191 w: x1 + x2 + 3613 isPLNat w: 0 #u141 w: 0 #u161 w: 0 u102 w: x1 + x2 + 10410 u121 w: x2 + 6856 #u51 w: 0 u181 w: x2 + 23408 u153 w: 673 take w: x1 + 5857 #u21 w: 0 u122 w: 1643 and w: x1 + x2 + 14269 u103 w: 848 pair w: 11315 fst w: x1 + 3762 u131 w: x2 natsFrom w: 97 #u102 w: 0 #head w: 0 #u61 w: 0 splitAt w: 15615 isNaturalKind w: x1 u52 w: 15615 #u151 w: 0 #fst w: 0 #u11 w: 0 u61 w: 0 u92 w: 11322 #u81 w: 0 #u143 w: 0 u221 w: x2 + x3 + 15693 _ w: 0 #isPLNatKind w: 0 #u91 w: 0 u151 w: x1 + 1247 u202 w: x1 isNatural w: x1 u41 w: x1 + x2 + x3 + 8260 #u72 w: 0 u211 w: x2 + 12748 #u112 w: 0 u51 w: x2 + 15616 tail w: 7420 #mark w: x1 0 w: 0 #sel w: 0 #u171 w: 0 u11 w: x1 + x3 + 8539 #isLNat w: 0 sel w: x1 + x2 + 8500 #s w: 0 afterNth w: x1 + 8202 #u211 w: 0 #isPLNat w: 0 nil w: 1778 isLNat w: 0 #isNaturalKind w: 0 #tail w: 0 #splitAt w: 0 mark w: x1 + 4008 u101 w: x1 + 397 #afterNth w: 0 #u122 w: 0 u72 w: 1266 u21 w: x2 + 24405 u201 w: 15615 u143 w: x1 + 8529 #u41 w: 0 isLNatKind w: x1 u43 w: x1 + 6844 #u221 w: 0 u82 w: x1 + 1838 #_ w: 0 u161 w: 8417 #u202 w: 0 #u142 w: 0 #u133 w: 0 u171 w: x1 + x2 + 5679 active w: x1 + 4008 head w: 0 #u42 w: 0 #snd w: 0 cons w: x1 + 22257 u142 w: 3494 #natsFrom w: 0 #active w: 15615 #u31 w: 0 snd w: x1 + 2952 u112 w: 11693 u42 w: 20590 tt w: 3943 #u53 w: 0 #u131 w: 0 u152 w: x2 + 5191 #isNatural w: 0 #pair w: 0 u71 w: x1 + 74 #u181 w: 0 #u153 w: 0 #u43 w: 0 #u62 w: 0 u31 w: x2 + 1666 #and w: 0 u141 w: x3 #u121 w: 0 #u111 w: 0 #u71 w: 0 #u132 w: 0 #u92 w: 0 USABLE RULES: { 6 41 82 91 135 144..155 158..165 168..181 184..193 196..205 208..217 220..229 232..237 244..281 284..297 300..309 312..315 318..323 326..329 332..349 } Removed DPs: #371 #504 #588 Number of SCCs: 1, DPs: 5 SCC { #36 #50 #260 #321 #447 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #isLNatKind s: [] p: 0 w: 1 u81 s: [] p: 11 w: max(x1 + 1) #u101 s: [3,2,1] p: 0 w: max(x1, x2, x3) #u191 s: [] p: 0 w: max(x1) u62 s: [] p: 11 w: 4358 #u152 s: [1,2] p: 0 w: max(x1, x2) #u103 s: [] p: 0 w: 0 #u82 s: [] p: 0 w: 0 #u201 s: [3,4] p: 0 w: max(x1 + 1, x3, x4) u133 s: [] p: 11 w: 0 #cons s: [2,1] p: 0 w: max(x1, x2) s s: [1] p: 4 w: x1 u132 s: [] p: 12 w: 0 u91 s: [] p: 11 w: max(x1) #u52 s: [] p: 0 w: max(x1) #take s: [2,1] p: 0 w: x1 + x2 + 1 u111 s: [1] p: 11 w: max(x1 + 18) u53 s: [] p: 11 w: 0 isPLNatKind s: [] p: 9 w: 16 u191 s: [] p: 2 w: max(x1 + 9, x2 + 14) isPLNat s: [] p: 12 w: 19665 #u141 s: [2,1,3] p: 0 w: max(x1 + 1, x2, x3) #u161 s: [] p: 0 w: max(x1 + 1) u102 s: [2] p: 11 w: max(x1 + 10, x2 + 9) u121 s: [] p: 12 w: max(x1 + 31) #u51 s: [] p: 0 w: max(x2 + 1) u181 s: [2] p: 12 w: max(x2) u153 s: [] p: 11 w: 1870 take s: [] p: 13 w: x1 + x2 + 19700 #u21 s: [2] p: 0 w: max(x2) u122 s: [] p: 11 w: 24 and s: 2 u103 s: [] p: 11 w: 10 pair s: [] p: 1 w: max(x1, x2 + 3) fst s: [] p: 12 w: x1 + 19683 u131 s: [] p: 10 w: max(x1 + 43) natsFrom s: [] p: 10 w: x1 + 8622 #u102 s: [1] p: 0 w: max(x1 + 1) #head s: [] p: 0 w: 0 #u61 s: [1,2] p: 0 w: max(x1 + 1, x2 + 1) splitAt s: [1,2] p: 3 w: max(x1 + 13, x2 + 15) isNaturalKind s: [] p: 9 w: 16 u52 s: [] p: 12 w: 0 #u151 s: [3] p: 0 w: max(x3) #fst s: [] p: 0 w: 0 #u11 s: [2] p: 0 w: max(x2) u61 s: [] p: 5 w: max(x1 + 19666) u92 s: [] p: 11 w: 0 #u81 s: [1,2] p: 0 w: max(x1 + 1, x2 + 1) #u143 s: [] p: 0 w: 0 u221 s: [2] p: 14 w: max(x1 + 8236, x2 + 19697, x3 + 19699) _ s: [] p: 0 w: x2 #isPLNatKind s: [] p: 0 w: 0 #u91 s: [] p: 0 w: max(x1) u151 s: [] p: 11 w: max(x1 + 18326) u202 s: [2,1] p: 1 w: max(x1, x2 + 1) isNatural s: [] p: 10 w: 59 u41 s: [3] p: 11 w: max(x2 + 52, x3 + 63) #u72 s: [] p: 0 w: 0 u211 s: [2,1] p: 5 w: max(x1 + 2, x2 + 1) #u112 s: [] p: 0 w: 0 u51 s: [3] p: 10 w: max(x3 + 12) tail s: [] p: 9 w: x1 + 19 #mark s: [1] p: 2 w: x1 + 47 0 s: [] p: 1 w: 13 #sel s: [2,1] p: 0 w: x1 + x2 + 1 #u171 s: [1,2,3] p: 0 w: max(x1, x2, x3 + 1) u11 s: [] p: 12 w: max(x1 + 25, x2 + 25, x3 + 24) #isLNat s: [] p: 0 w: 0 sel s: [2,1] p: 15 w: x1 + x2 + 59 #s s: [] p: 0 w: 0 afterNth s: [1,2] p: 13 w: max(x1 + 41, x2 + 51) #u211 s: [2,1] p: 0 w: max(x1, x2 + 1) #isPLNat s: [] p: 0 w: 1 nil s: [] p: 6 w: 8 isLNat s: [1] p: 11 w: x1 + 12 #isNaturalKind s: [] p: 0 w: 1 #tail s: [] p: 0 w: 1 #splitAt s: [1,2] p: 0 w: max(x1 + 1, x2) mark s: 1 u101 s: [2] p: 12 w: max(x1 + 63, x2 + 19707, x3 + 19683) #afterNth s: [] p: 0 w: max(x1) #u122 s: [] p: 0 w: 0 u72 s: [] p: 11 w: 0 u21 s: [] p: 12 w: max(x2 + 19683) u201 s: [2,4,3] p: 3 w: max(x2 + 13, x3 + 4, x4 + 15) u143 s: [] p: 11 w: 0 #u41 s: [2,3,1] p: 0 w: max(x1, x2, x3 + 1) isLNatKind s: [] p: 9 w: 16 u43 s: [] p: 11 w: 2 #u221 s: [] p: 0 w: max(x2) u82 s: [] p: 11 w: 1 #_ s: [] p: 0 w: x2 u161 s: [] p: 10 w: max(x2 + 8622) #u202 s: [] p: 0 w: 0 #u142 s: [] p: 0 w: max(x2) #u133 s: [] p: 0 w: 0 u171 s: [] p: 14 w: max(x1 + 42, x2 + 42, x3 + 52) active s: 1 head s: [] p: 14 w: x1 + 1 #u42 s: [] p: 0 w: max(x2) #snd s: [] p: 0 w: 0 cons s: [] p: 10 w: max(x1, x2) u142 s: [] p: 12 w: 0 #natsFrom s: [] p: 0 w: 1 #active s: [1] p: 2 w: x1 + 47 #u31 s: [2] p: 0 w: max(x2 + 1) snd s: [] p: 12 w: x1 + 8 u112 s: [] p: 11 w: 0 u42 s: [1] p: 10 w: max(x1 + 3) tt s: [] p: 11 w: 0 #u53 s: [] p: 0 w: 1 #u131 s: [2] p: 0 w: max(x2, x3 + 1) u152 s: [1] p: 12 w: max(x1 + 10739) #isNatural s: [] p: 0 w: 0 #pair s: [2] p: 0 w: max(x2) u71 s: [1] p: 11 w: max(x1 + 8606) #u181 s: [2] p: 0 w: max(x2) #u153 s: [] p: 0 w: 1 #u43 s: [] p: 0 w: 0 #u62 s: [] p: 0 w: 0 u31 s: [2] p: 5 w: max(x2 + 1) #and s: [1,2] p: 0 w: max(x1, x2) u141 s: [] p: 5 w: max(x1 + 7) #u121 s: [1,2] p: 0 w: max(x1, x2 + 1) #u111 s: [] p: 0 w: 0 #u71 s: [] p: 0 w: max(x2) #u132 s: [2] p: 0 w: max(x2) #u92 s: [] p: 0 w: 0 USABLE RULES: { 1..357 } Removed DPs: #36 #447 Number of SCCs: 0, DPs: 0 >>YES ******** Signature ******** map : ((A -> A),A) -> A nil : A cons : (A,A) -> A app : ((A -> A),A) -> A foldr : (((A,A) -> A),A,A) -> A ******** Computation rules ******** (358) map(%X.Z109[%X],nil) => nil (359) map(%Y.G109[%Y],cons(V109,W109)) => cons(G109[V109],map(%Z.G109[%Z],W109)) (360) %U.J109[%U]@X110 => J109[X110] (361) foldr(%W.%V.Z110[%W,%V],U110,nil) => U110 (362) foldr(%G.%F.H110[%G,%F],W110,cons(P110,X111)) => H110[P110,foldr(%I.%H.H110[%I,%H],W110,X111)] ******** General Schema criterion ******** Found constructors: 0, nil, tt Checking type order >>OK Checking positivity of constructors >>OK Checking function dependency >>Regared as equal: mark, active Checking (1) active(u101(tt,X,Y)) => mark(u102(isNatural(X),Y)) (fun active=mark) subterm comparison of args w. LR LR >>False Try again using status RL Checking (1) active(u101(tt,X,Y)) => mark(u102(isNatural(X),Y)) (fun active=mark) subterm comparison of args w. RL RL >>False Try again using status Mul Checking (1) active(u101(tt,X,Y)) => mark(u102(isNatural(X),Y)) (fun active=mark) subterm comparison of args w. Mul Mul >>False Found constructors: nil, cons Checking type order >>OK Checking positivity of constructors >>OK Checking function dependency >>OK Checking (358) map(%X.Z109[%X],nil) => nil (fun map>nil) >>True Checking (359) map(%Y.G109[%Y],cons(V109,W109)) => cons(G109[V109],map(%Z.G109[%Z],W109)) (fun map>cons) (meta G109)[is acc in %Y.G109[%Y],cons(V109,W109)] [is acc in G109[%Y]] (meta V109)[is acc in %Y.G109[%Y],cons(V109,W109)] [is positive in cons(V109,W109)] [is acc in V109] (fun map=map) subterm comparison of args w. LR LR (meta G109)[is acc in %Y.G109[%Y],cons(V109,W109)] [is acc in G109[%Y]] (meta W109)[is acc in %Y.G109[%Y],cons(V109,W109)] [is positive in cons(V109,W109)] [is acc in W109] >>True Checking (360) %U.J109[%U]@X110 => J109[X110] (meta J109)[is acc in %U.J109[%U],X110] [is acc in J109[%U]] (meta X110)[is acc in %U.J109[%U],X110] [is acc in X110] >>True Checking (361) foldr(%W.%V.Z110[%W,%V],U110,nil) => U110 (meta U110)[is acc in %W.%V.Z110[%W,%V],U110,nil] [is acc in U110] >>True Checking (362) foldr(%G.%F.H110[%G,%F],W110,cons(P110,X111)) => H110[P110,foldr(%I.%H.H110[%I,%H],W110,X111)] (meta H110)[is acc in %G.%F.H110[%G,%F],W110,cons(P110,X111)] [is acc in H110[%G,%F]] (meta P110)[is acc in %G.%F.H110[%G,%F],W110,cons(P110,X111)] [is positive in cons(P110,X111)] [is acc in P110] (fun foldr=foldr) subterm comparison of args w. LR LR (meta H110)[is acc in %G.%F.H110[%G,%F],W110,cons(P110,X111)] [is acc in H110[%G,%F]] (meta W110)[is acc in %G.%F.H110[%G,%F],W110,cons(P110,X111)] [is acc in W110] (meta X111)[is acc in %G.%F.H110[%G,%F],W110,cons(P110,X111)] [is positive in cons(P110,X111)] [is acc in X111] >>True #SN! ******** Signature ******** 0 : A active : A -> A afterNth : (A,A) -> A and : (A,A) -> A app : ((A -> A),A) -> A cons : (A,A) -> A foldr : (((A,A) -> A),A,A) -> A fst : A -> A head : A -> A isLNat : A -> A isLNatKind : A -> A isNatural : A -> A isNaturalKind : A -> A isPLNat : A -> A isPLNatKind : A -> A map : ((A -> A),A) -> A mark : A -> A natsFrom : A -> A nil : A pair : (A,A) -> A s : A -> A sel : (A,A) -> A snd : A -> A splitAt : (A,A) -> A tail : A -> A take : (A,A) -> A tt : A u101 : (A,A,A) -> A u102 : (A,A) -> A u103 : A -> A u11 : (A,A,A) -> A u111 : (A,A) -> A u112 : A -> A u121 : (A,A) -> A u122 : A -> A u131 : (A,A,A) -> A u132 : (A,A) -> A u133 : A -> A u141 : (A,A,A) -> A u142 : (A,A) -> A u143 : A -> A u151 : (A,A,A) -> A u152 : (A,A) -> A u153 : A -> A u161 : (A,A) -> A u171 : (A,A,A) -> A u181 : (A,A) -> A u191 : (A,A) -> A u201 : (A,A,A,A) -> A u202 : (A,A) -> A u21 : (A,A) -> A u211 : (A,A) -> A u221 : (A,A,A) -> A u31 : (A,A) -> A u41 : (A,A,A) -> A u42 : (A,A) -> A u43 : A -> A u51 : (A,A,A) -> A u52 : (A,A) -> A u53 : A -> A u61 : (A,A) -> A u62 : A -> A u71 : (A,A) -> A u72 : A -> A u81 : (A,A) -> A u82 : A -> A u91 : (A,A) -> A u92 : A -> A ******** Computation Rules ******** (1) active(u101(tt,X,Y)) => mark(u102(isNatural(X),Y)) (2) active(u102(tt,U)) => mark(u103(isLNat(U))) (3) active(u103(tt)) => mark(tt) (4) active(u11(tt,V,W)) => mark(snd(splitAt(V,W))) (5) active(u111(tt,P)) => mark(u112(isLNat(P))) (6) active(u112(tt)) => mark(tt) (7) active(u121(tt,X1)) => mark(u122(isNatural(X1))) (8) active(u122(tt)) => mark(tt) (9) active(u131(tt,Y1,U1)) => mark(u132(isNatural(Y1),U1)) (10) active(u132(tt,V1)) => mark(u133(isLNat(V1))) (11) active(u133(tt)) => mark(tt) (12) active(u141(tt,W1,P1)) => mark(u142(isLNat(W1),P1)) (13) active(u142(tt,X2)) => mark(u143(isLNat(X2))) (14) active(u143(tt)) => mark(tt) (15) active(u151(tt,Y2,U2)) => mark(u152(isNatural(Y2),U2)) (16) active(u152(tt,V2)) => mark(u153(isLNat(V2))) (17) active(u153(tt)) => mark(tt) (18) active(u161(tt,W2)) => mark(cons(W2,natsFrom(s(W2)))) (19) active(u171(tt,P2,X3)) => mark(head(afterNth(P2,X3))) (20) active(u181(tt,Y3)) => mark(Y3) (21) active(u191(tt,U3)) => mark(pair(nil,U3)) (22) active(u201(tt,V3,W3,P3)) => mark(u202(splitAt(V3,P3),W3)) (23) active(u202(pair(X4,Y4),U4)) => mark(pair(cons(U4,X4),Y4)) (24) active(u21(tt,V4)) => mark(V4) (25) active(u211(tt,W4)) => mark(W4) (26) active(u221(tt,P4,X5)) => mark(fst(splitAt(P4,X5))) (27) active(u31(tt,Y5)) => mark(Y5) (28) active(u41(tt,U5,V5)) => mark(u42(isNatural(U5),V5)) (29) active(u42(tt,W5)) => mark(u43(isLNat(W5))) (30) active(u43(tt)) => mark(tt) (31) active(u51(tt,P5,X6)) => mark(u52(isNatural(P5),X6)) (32) active(u52(tt,Y6)) => mark(u53(isLNat(Y6))) (33) active(u53(tt)) => mark(tt) (34) active(u61(tt,U6)) => mark(u62(isPLNat(U6))) (35) active(u62(tt)) => mark(tt) (36) active(u71(tt,V6)) => mark(u72(isNatural(V6))) (37) active(u72(tt)) => mark(tt) (38) active(u81(tt,W6)) => mark(u82(isPLNat(W6))) (39) active(u82(tt)) => mark(tt) (40) active(u91(tt,P6)) => mark(u92(isLNat(P6))) (41) active(u92(tt)) => mark(tt) (42) active(afterNth(X7,Y7)) => mark(u11(and(and(isNatural(X7),isNaturalKind(X7)),and(isLNat(Y7),isLNatKind(Y7))),X7,Y7)) (43) active(and(tt,U7)) => mark(U7) (44) active(fst(pair(V7,W7))) => mark(u21(and(and(isLNat(V7),isLNatKind(V7)),and(isLNat(W7),isLNatKind(W7))),V7)) (45) active(head(cons(P7,X8))) => mark(u31(and(and(isNatural(P7),isNaturalKind(P7)),and(isLNat(X8),isLNatKind(X8))),P7)) (46) active(isLNat(nil)) => mark(tt) (47) active(isLNat(afterNth(Y8,U8))) => mark(u41(and(isNaturalKind(Y8),isLNatKind(U8)),Y8,U8)) (48) active(isLNat(cons(V8,W8))) => mark(u51(and(isNaturalKind(V8),isLNatKind(W8)),V8,W8)) (49) active(isLNat(fst(P8))) => mark(u61(isPLNatKind(P8),P8)) (50) active(isLNat(natsFrom(X9))) => mark(u71(isNaturalKind(X9),X9)) (51) active(isLNat(snd(Y9))) => mark(u81(isPLNatKind(Y9),Y9)) (52) active(isLNat(tail(U9))) => mark(u91(isLNatKind(U9),U9)) (53) active(isLNat(take(V9,W9))) => mark(u101(and(isNaturalKind(V9),isLNatKind(W9)),V9,W9)) (54) active(isLNatKind(nil)) => mark(tt) (55) active(isLNatKind(afterNth(P9,X10))) => mark(and(isNaturalKind(P9),isLNatKind(X10))) (56) active(isLNatKind(cons(Y10,U10))) => mark(and(isNaturalKind(Y10),isLNatKind(U10))) (57) active(isLNatKind(fst(V10))) => mark(isPLNatKind(V10)) (58) active(isLNatKind(natsFrom(W10))) => mark(isNaturalKind(W10)) (59) active(isLNatKind(snd(P10))) => mark(isPLNatKind(P10)) (60) active(isLNatKind(tail(X11))) => mark(isLNatKind(X11)) (61) active(isLNatKind(take(Y11,U11))) => mark(and(isNaturalKind(Y11),isLNatKind(U11))) (62) active(isNatural(0)) => mark(tt) (63) active(isNatural(head(V11))) => mark(u111(isLNatKind(V11),V11)) (64) active(isNatural(s(W11))) => mark(u121(isNaturalKind(W11),W11)) (65) active(isNatural(sel(P11,X12))) => mark(u131(and(isNaturalKind(P11),isLNatKind(X12)),P11,X12)) (66) active(isNaturalKind(0)) => mark(tt) (67) active(isNaturalKind(head(Y12))) => mark(isLNatKind(Y12)) (68) active(isNaturalKind(s(U12))) => mark(isNaturalKind(U12)) (69) active(isNaturalKind(sel(V12,W12))) => mark(and(isNaturalKind(V12),isLNatKind(W12))) (70) active(isPLNat(pair(P12,X13))) => mark(u141(and(isLNatKind(P12),isLNatKind(X13)),P12,X13)) (71) active(isPLNat(splitAt(Y13,U13))) => mark(u151(and(isNaturalKind(Y13),isLNatKind(U13)),Y13,U13)) (72) active(isPLNatKind(pair(V13,W13))) => mark(and(isLNatKind(V13),isLNatKind(W13))) (73) active(isPLNatKind(splitAt(P13,X14))) => mark(and(isNaturalKind(P13),isLNatKind(X14))) (74) active(natsFrom(Y14)) => mark(u161(and(isNatural(Y14),isNaturalKind(Y14)),Y14)) (75) active(sel(U14,V14)) => mark(u171(and(and(isNatural(U14),isNaturalKind(U14)),and(isLNat(V14),isLNatKind(V14))),U14,V14)) (76) active(snd(pair(W14,P14))) => mark(u181(and(and(isLNat(W14),isLNatKind(W14)),and(isLNat(P14),isLNatKind(P14))),P14)) (77) active(splitAt(0,X15)) => mark(u191(and(isLNat(X15),isLNatKind(X15)),X15)) (78) active(splitAt(s(Y15),cons(U15,V15))) => mark(u201(and(and(isNatural(Y15),isNaturalKind(Y15)),and(and(isNatural(U15),isNaturalKind(U15)),and(isLNat(V15),isLNatKind(V15)))),Y15,U15,V15)) (79) active(tail(cons(W15,P15))) => mark(u211(and(and(isNatural(W15),isNaturalKind(W15)),and(isLNat(P15),isLNatKind(P15))),P15)) (80) active(take(X16,Y16)) => mark(u221(and(and(isNatural(X16),isNaturalKind(X16)),and(isLNat(Y16),isLNatKind(Y16))),X16,Y16)) (81) mark(u101(U16,V16,W16)) => active(u101(mark(U16),V16,W16)) (82) mark(tt) => active(tt) (83) mark(u102(P16,X17)) => active(u102(mark(P16),X17)) (84) mark(isNatural(Y17)) => active(isNatural(Y17)) (85) mark(u103(U17)) => active(u103(mark(U17))) (86) mark(isLNat(V17)) => active(isLNat(V17)) (87) mark(u11(W17,P17,X18)) => active(u11(mark(W17),P17,X18)) (88) mark(snd(Y18)) => active(snd(mark(Y18))) (89) mark(splitAt(U18,V18)) => active(splitAt(mark(U18),mark(V18))) (90) mark(u111(W18,P18)) => active(u111(mark(W18),P18)) (91) mark(u112(X19)) => active(u112(mark(X19))) (92) mark(u121(Y19,U19)) => active(u121(mark(Y19),U19)) (93) mark(u122(V19)) => active(u122(mark(V19))) (94) mark(u131(W19,P19,X20)) => active(u131(mark(W19),P19,X20)) (95) mark(u132(Y20,U20)) => active(u132(mark(Y20),U20)) (96) mark(u133(V20)) => active(u133(mark(V20))) (97) mark(u141(W20,P20,X21)) => active(u141(mark(W20),P20,X21)) (98) mark(u142(Y21,U21)) => active(u142(mark(Y21),U21)) (99) mark(u143(V21)) => active(u143(mark(V21))) (100) mark(u151(W21,P21,X22)) => active(u151(mark(W21),P21,X22)) (101) mark(u152(Y22,U22)) => active(u152(mark(Y22),U22)) (102) mark(u153(V22)) => active(u153(mark(V22))) (103) mark(u161(W22,P22)) => active(u161(mark(W22),P22)) (104) mark(cons(X23,Y23)) => active(cons(mark(X23),Y23)) (105) mark(natsFrom(U23)) => active(natsFrom(mark(U23))) (106) mark(s(V23)) => active(s(mark(V23))) (107) mark(u171(W23,P23,X24)) => active(u171(mark(W23),P23,X24)) (108) mark(head(Y24)) => active(head(mark(Y24))) (109) mark(afterNth(U24,V24)) => active(afterNth(mark(U24),mark(V24))) (110) mark(u181(W24,P24)) => active(u181(mark(W24),P24)) (111) mark(u191(X25,Y25)) => active(u191(mark(X25),Y25)) (112) mark(pair(U25,V25)) => active(pair(mark(U25),mark(V25))) (113) mark(nil) => active(nil) (114) mark(u201(W25,P25,X26,Y26)) => active(u201(mark(W25),P25,X26,Y26)) (115) mark(u202(U26,V26)) => active(u202(mark(U26),V26)) (116) mark(u21(W26,P26)) => active(u21(mark(W26),P26)) (117) mark(u211(X27,Y27)) => active(u211(mark(X27),Y27)) (118) mark(u221(U27,V27,W27)) => active(u221(mark(U27),V27,W27)) (119) mark(fst(P27)) => active(fst(mark(P27))) (120) mark(u31(X28,Y28)) => active(u31(mark(X28),Y28)) (121) mark(u41(U28,V28,W28)) => active(u41(mark(U28),V28,W28)) (122) mark(u42(P28,X29)) => active(u42(mark(P28),X29)) (123) mark(u43(Y29)) => active(u43(mark(Y29))) (124) mark(u51(U29,V29,W29)) => active(u51(mark(U29),V29,W29)) (125) mark(u52(P29,X30)) => active(u52(mark(P29),X30)) (126) mark(u53(Y30)) => active(u53(mark(Y30))) (127) mark(u61(U30,V30)) => active(u61(mark(U30),V30)) (128) mark(u62(W30)) => active(u62(mark(W30))) (129) mark(isPLNat(P30)) => active(isPLNat(P30)) (130) mark(u71(X31,Y31)) => active(u71(mark(X31),Y31)) (131) mark(u72(U31)) => active(u72(mark(U31))) (132) mark(u81(V31,W31)) => active(u81(mark(V31),W31)) (133) mark(u82(P31)) => active(u82(mark(P31))) (134) mark(u91(X32,Y32)) => active(u91(mark(X32),Y32)) (135) mark(u92(U32)) => active(u92(mark(U32))) (136) mark(and(V32,W32)) => active(and(mark(V32),W32)) (137) mark(isNaturalKind(P32)) => active(isNaturalKind(P32)) (138) mark(isLNatKind(X33)) => active(isLNatKind(X33)) (139) mark(isPLNatKind(Y33)) => active(isPLNatKind(Y33)) (140) mark(tail(U33)) => active(tail(mark(U33))) (141) mark(take(V33,W33)) => active(take(mark(V33),mark(W33))) (142) mark(0) => active(0) (143) mark(sel(P33,X34)) => active(sel(mark(P33),mark(X34))) (144) u101(mark(Y34),U34,V34) => u101(Y34,U34,V34) (145) u101(W34,mark(P34),X35) => u101(W34,P34,X35) (146) u101(Y35,U35,mark(V35)) => u101(Y35,U35,V35) (147) u101(active(W35),P35,X36) => u101(W35,P35,X36) (148) u101(Y36,active(U36),V36) => u101(Y36,U36,V36) (149) u101(W36,P36,active(X37)) => u101(W36,P36,X37) (150) u102(mark(Y37),U37) => u102(Y37,U37) (151) u102(V37,mark(W37)) => u102(V37,W37) (152) u102(active(P37),X38) => u102(P37,X38) (153) u102(Y38,active(U38)) => u102(Y38,U38) (154) isNatural(mark(V38)) => isNatural(V38) (155) isNatural(active(W38)) => isNatural(W38) (156) u103(mark(P38)) => u103(P38) (157) u103(active(X39)) => u103(X39) (158) isLNat(mark(Y39)) => isLNat(Y39) (159) isLNat(active(U39)) => isLNat(U39) (160) u11(mark(V39),W39,P39) => u11(V39,W39,P39) (161) u11(X40,mark(Y40),U40) => u11(X40,Y40,U40) (162) u11(V40,W40,mark(P40)) => u11(V40,W40,P40) (163) u11(active(X41),Y41,U41) => u11(X41,Y41,U41) (164) u11(V41,active(W41),P41) => u11(V41,W41,P41) (165) u11(X42,Y42,active(U42)) => u11(X42,Y42,U42) (166) snd(mark(V42)) => snd(V42) (167) snd(active(W42)) => snd(W42) (168) splitAt(mark(P42),X43) => splitAt(P42,X43) (169) splitAt(Y43,mark(U43)) => splitAt(Y43,U43) (170) splitAt(active(V43),W43) => splitAt(V43,W43) (171) splitAt(P43,active(X44)) => splitAt(P43,X44) (172) u111(mark(Y44),U44) => u111(Y44,U44) (173) u111(V44,mark(W44)) => u111(V44,W44) (174) u111(active(P44),X45) => u111(P44,X45) (175) u111(Y45,active(U45)) => u111(Y45,U45) (176) u112(mark(V45)) => u112(V45) (177) u112(active(W45)) => u112(W45) (178) u121(mark(P45),X46) => u121(P45,X46) (179) u121(Y46,mark(U46)) => u121(Y46,U46) (180) u121(active(V46),W46) => u121(V46,W46) (181) u121(P46,active(X47)) => u121(P46,X47) (182) u122(mark(Y47)) => u122(Y47) (183) u122(active(U47)) => u122(U47) (184) u131(mark(V47),W47,P47) => u131(V47,W47,P47) (185) u131(X48,mark(Y48),U48) => u131(X48,Y48,U48) (186) u131(V48,W48,mark(P48)) => u131(V48,W48,P48) (187) u131(active(X49),Y49,U49) => u131(X49,Y49,U49) (188) u131(V49,active(W49),P49) => u131(V49,W49,P49) (189) u131(X50,Y50,active(U50)) => u131(X50,Y50,U50) (190) u132(mark(V50),W50) => u132(V50,W50) (191) u132(P50,mark(X51)) => u132(P50,X51) (192) u132(active(Y51),U51) => u132(Y51,U51) (193) u132(V51,active(W51)) => u132(V51,W51) (194) u133(mark(P51)) => u133(P51) (195) u133(active(X52)) => u133(X52) (196) u141(mark(Y52),U52,V52) => u141(Y52,U52,V52) (197) u141(W52,mark(P52),X53) => u141(W52,P52,X53) (198) u141(Y53,U53,mark(V53)) => u141(Y53,U53,V53) (199) u141(active(W53),P53,X54) => u141(W53,P53,X54) (200) u141(Y54,active(U54),V54) => u141(Y54,U54,V54) (201) u141(W54,P54,active(X55)) => u141(W54,P54,X55) (202) u142(mark(Y55),U55) => u142(Y55,U55) (203) u142(V55,mark(W55)) => u142(V55,W55) (204) u142(active(P55),X56) => u142(P55,X56) (205) u142(Y56,active(U56)) => u142(Y56,U56) (206) u143(mark(V56)) => u143(V56) (207) u143(active(W56)) => u143(W56) (208) u151(mark(P56),X57,Y57) => u151(P56,X57,Y57) (209) u151(U57,mark(V57),W57) => u151(U57,V57,W57) (210) u151(P57,X58,mark(Y58)) => u151(P57,X58,Y58) (211) u151(active(U58),V58,W58) => u151(U58,V58,W58) (212) u151(P58,active(X59),Y59) => u151(P58,X59,Y59) (213) u151(U59,V59,active(W59)) => u151(U59,V59,W59) (214) u152(mark(P59),X60) => u152(P59,X60) (215) u152(Y60,mark(U60)) => u152(Y60,U60) (216) u152(active(V60),W60) => u152(V60,W60) (217) u152(P60,active(X61)) => u152(P60,X61) (218) u153(mark(Y61)) => u153(Y61) (219) u153(active(U61)) => u153(U61) (220) u161(mark(V61),W61) => u161(V61,W61) (221) u161(P61,mark(X62)) => u161(P61,X62) (222) u161(active(Y62),U62) => u161(Y62,U62) (223) u161(V62,active(W62)) => u161(V62,W62) (224) cons(mark(P62),X63) => cons(P62,X63) (225) cons(Y63,mark(U63)) => cons(Y63,U63) (226) cons(active(V63),W63) => cons(V63,W63) (227) cons(P63,active(X64)) => cons(P63,X64) (228) natsFrom(mark(Y64)) => natsFrom(Y64) (229) natsFrom(active(U64)) => natsFrom(U64) (230) s(mark(V64)) => s(V64) (231) s(active(W64)) => s(W64) (232) u171(mark(P64),X65,Y65) => u171(P64,X65,Y65) (233) u171(U65,mark(V65),W65) => u171(U65,V65,W65) (234) u171(P65,X66,mark(Y66)) => u171(P65,X66,Y66) (235) u171(active(U66),V66,W66) => u171(U66,V66,W66) (236) u171(P66,active(X67),Y67) => u171(P66,X67,Y67) (237) u171(U67,V67,active(W67)) => u171(U67,V67,W67) (238) head(mark(P67)) => head(P67) (239) head(active(X68)) => head(X68) (240) afterNth(mark(Y68),U68) => afterNth(Y68,U68) (241) afterNth(V68,mark(W68)) => afterNth(V68,W68) (242) afterNth(active(P68),X69) => afterNth(P68,X69) (243) afterNth(Y69,active(U69)) => afterNth(Y69,U69) (244) u181(mark(V69),W69) => u181(V69,W69) (245) u181(P69,mark(X70)) => u181(P69,X70) (246) u181(active(Y70),U70) => u181(Y70,U70) (247) u181(V70,active(W70)) => u181(V70,W70) (248) u191(mark(P70),X71) => u191(P70,X71) (249) u191(Y71,mark(U71)) => u191(Y71,U71) (250) u191(active(V71),W71) => u191(V71,W71) (251) u191(P71,active(X72)) => u191(P71,X72) (252) pair(mark(Y72),U72) => pair(Y72,U72) (253) pair(V72,mark(W72)) => pair(V72,W72) (254) pair(active(P72),X73) => pair(P72,X73) (255) pair(Y73,active(U73)) => pair(Y73,U73) (256) u201(mark(V73),W73,P73,X74) => u201(V73,W73,P73,X74) (257) u201(Y74,mark(U74),V74,W74) => u201(Y74,U74,V74,W74) (258) u201(P74,X75,mark(Y75),U75) => u201(P74,X75,Y75,U75) (259) u201(V75,W75,P75,mark(X76)) => u201(V75,W75,P75,X76) (260) u201(active(Y76),U76,V76,W76) => u201(Y76,U76,V76,W76) (261) u201(P76,active(X77),Y77,U77) => u201(P76,X77,Y77,U77) (262) u201(V77,W77,active(P77),X78) => u201(V77,W77,P77,X78) (263) u201(Y78,U78,V78,active(W78)) => u201(Y78,U78,V78,W78) (264) u202(mark(P78),X79) => u202(P78,X79) (265) u202(Y79,mark(U79)) => u202(Y79,U79) (266) u202(active(V79),W79) => u202(V79,W79) (267) u202(P79,active(X80)) => u202(P79,X80) (268) u21(mark(Y80),U80) => u21(Y80,U80) (269) u21(V80,mark(W80)) => u21(V80,W80) (270) u21(active(P80),X81) => u21(P80,X81) (271) u21(Y81,active(U81)) => u21(Y81,U81) (272) u211(mark(V81),W81) => u211(V81,W81) (273) u211(P81,mark(X82)) => u211(P81,X82) (274) u211(active(Y82),U82) => u211(Y82,U82) (275) u211(V82,active(W82)) => u211(V82,W82) (276) u221(mark(P82),X83,Y83) => u221(P82,X83,Y83) (277) u221(U83,mark(V83),W83) => u221(U83,V83,W83) (278) u221(P83,X84,mark(Y84)) => u221(P83,X84,Y84) (279) u221(active(U84),V84,W84) => u221(U84,V84,W84) (280) u221(P84,active(X85),Y85) => u221(P84,X85,Y85) (281) u221(U85,V85,active(W85)) => u221(U85,V85,W85) (282) fst(mark(P85)) => fst(P85) (283) fst(active(X86)) => fst(X86) (284) u31(mark(Y86),U86) => u31(Y86,U86) (285) u31(V86,mark(W86)) => u31(V86,W86) (286) u31(active(P86),X87) => u31(P86,X87) (287) u31(Y87,active(U87)) => u31(Y87,U87) (288) u41(mark(V87),W87,P87) => u41(V87,W87,P87) (289) u41(X88,mark(Y88),U88) => u41(X88,Y88,U88) (290) u41(V88,W88,mark(P88)) => u41(V88,W88,P88) (291) u41(active(X89),Y89,U89) => u41(X89,Y89,U89) (292) u41(V89,active(W89),P89) => u41(V89,W89,P89) (293) u41(X90,Y90,active(U90)) => u41(X90,Y90,U90) (294) u42(mark(V90),W90) => u42(V90,W90) (295) u42(P90,mark(X91)) => u42(P90,X91) (296) u42(active(Y91),U91) => u42(Y91,U91) (297) u42(V91,active(W91)) => u42(V91,W91) (298) u43(mark(P91)) => u43(P91) (299) u43(active(X92)) => u43(X92) (300) u51(mark(Y92),U92,V92) => u51(Y92,U92,V92) (301) u51(W92,mark(P92),X93) => u51(W92,P92,X93) (302) u51(Y93,U93,mark(V93)) => u51(Y93,U93,V93) (303) u51(active(W93),P93,X94) => u51(W93,P93,X94) (304) u51(Y94,active(U94),V94) => u51(Y94,U94,V94) (305) u51(W94,P94,active(X95)) => u51(W94,P94,X95) (306) u52(mark(Y95),U95) => u52(Y95,U95) (307) u52(V95,mark(W95)) => u52(V95,W95) (308) u52(active(P95),X96) => u52(P95,X96) (309) u52(Y96,active(U96)) => u52(Y96,U96) (310) u53(mark(V96)) => u53(V96) (311) u53(active(W96)) => u53(W96) (312) u61(mark(P96),X97) => u61(P96,X97) (313) u61(Y97,mark(U97)) => u61(Y97,U97) (314) u61(active(V97),W97) => u61(V97,W97) (315) u61(P97,active(X98)) => u61(P97,X98) (316) u62(mark(Y98)) => u62(Y98) (317) u62(active(U98)) => u62(U98) (318) isPLNat(mark(V98)) => isPLNat(V98) (319) isPLNat(active(W98)) => isPLNat(W98) (320) u71(mark(P98),X99) => u71(P98,X99) (321) u71(Y99,mark(U99)) => u71(Y99,U99) (322) u71(active(V99),W99) => u71(V99,W99) (323) u71(P99,active(X100)) => u71(P99,X100) (324) u72(mark(Y100)) => u72(Y100) (325) u72(active(U100)) => u72(U100) (326) u81(mark(V100),W100) => u81(V100,W100) (327) u81(P100,mark(X101)) => u81(P100,X101) (328) u81(active(Y101),U101) => u81(Y101,U101) (329) u81(V101,active(W101)) => u81(V101,W101) (330) u82(mark(P101)) => u82(P101) (331) u82(active(X102)) => u82(X102) (332) u91(mark(Y102),U102) => u91(Y102,U102) (333) u91(V102,mark(W102)) => u91(V102,W102) (334) u91(active(P102),X103) => u91(P102,X103) (335) u91(Y103,active(U103)) => u91(Y103,U103) (336) u92(mark(V103)) => u92(V103) (337) u92(active(W103)) => u92(W103) (338) and(mark(P103),X104) => and(P103,X104) (339) and(Y104,mark(U104)) => and(Y104,U104) (340) and(active(V104),W104) => and(V104,W104) (341) and(P104,active(X105)) => and(P104,X105) (342) isNaturalKind(mark(Y105)) => isNaturalKind(Y105) (343) isNaturalKind(active(U105)) => isNaturalKind(U105) (344) isLNatKind(mark(V105)) => isLNatKind(V105) (345) isLNatKind(active(W105)) => isLNatKind(W105) (346) isPLNatKind(mark(P105)) => isPLNatKind(P105) (347) isPLNatKind(active(X106)) => isPLNatKind(X106) (348) tail(mark(Y106)) => tail(Y106) (349) tail(active(U106)) => tail(U106) (350) take(mark(V106),W106) => take(V106,W106) (351) take(P106,mark(X107)) => take(P106,X107) (352) take(active(Y107),U107) => take(Y107,U107) (353) take(V107,active(W107)) => take(V107,W107) (354) sel(mark(P107),X108) => sel(P107,X108) (355) sel(Y108,mark(U108)) => sel(Y108,U108) (356) sel(active(V108),W108) => sel(V108,W108) (357) sel(P108,active(X109)) => sel(P108,X109) (358) map(%X.Z109[%X],nil) => nil (359) map(%Y.G109[%Y],cons(V109,W109)) => cons(G109[V109],map(%Z.G109[%Z],W109)) (360) %U.J109[%U]@X110 => J109[X110] (361) foldr(%W.%V.Z110[%W,%V],U110,nil) => U110 (362) foldr(%G.%F.H110[%G,%F],W110,cons(P110,X111)) => H110[P110,foldr(%I.%H.H110[%I,%H],W110,X111)] YES