HRS union beta 16688 pair #381734576

details
property	value
status	complete
benchmark	h29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Hamana_Kikuchi_18
run statistics
property	value
solver	sol 37957
configuration	default
runtime (wallclock)	46.4882130623 seconds
cpu usage	50.672720883
max memory	4.48151552E8
stage attributes
key	value
output-size	105831
starexec-result	YES
output
/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))
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job log
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actions all output return to HRS union beta 16688