HRS union beta 16688 pair #381734612

details
property	value
status	complete
benchmark	h33.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n012.star.cs.uiowa.edu
space	Hamana_Kikuchi_18
run statistics
property	value
solver	sol 37957
configuration	default
runtime (wallclock)	12.8902180195 seconds
cpu usage	14.266645265
max memory	1.77373184E8
stage attributes
key	value
output-size	92805
starexec-result	YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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(fst(splitAt(X,Y)))
    2: active(u11(tt(),U,V)) -> mark(snd(splitAt(U,V)))
    3: active(u21(tt(),W)) -> mark(W)
    4: active(u31(tt(),P)) -> mark(P)
    5: active(u41(tt(),X1)) -> mark(cons(X1,natsFrom(s(X1))))
    6: active(u51(tt(),Y1,U1)) -> mark(head(afterNth(Y1,U1)))
    7: active(u61(tt(),V1)) -> mark(V1)
    8: active(u71(tt(),W1)) -> mark(pair(nil(),W1))
    9: active(u81(tt(),P1,X2,Y2)) -> mark(u82(splitAt(P1,Y2),X2))
    10: active(u82(pair(U2,V2),W2)) -> mark(pair(cons(W2,U2),V2))
    11: active(u91(tt(),P2)) -> mark(P2)
    12: active(afterNth(X3,Y3)) -> mark(u11(and(isNatural(X3),isLNat(Y3)),X3,Y3))
    13: active(and(tt(),U3)) -> mark(U3)
    14: active(fst(pair(V3,W3))) -> mark(u21(and(isLNat(V3),isLNat(W3)),V3))
    15: active(head(cons(P3,X4))) -> mark(u31(and(isNatural(P3),isLNat(X4)),P3))
    16: active(isLNat(nil())) -> mark(tt())
    17: active(isLNat(afterNth(Y4,U4))) -> mark(and(isNatural(Y4),isLNat(U4)))
    18: active(isLNat(cons(V4,W4))) -> mark(and(isNatural(V4),isLNat(W4)))
    19: active(isLNat(fst(P4))) -> mark(isPLNat(P4))
    20: active(isLNat(natsFrom(X5))) -> mark(isNatural(X5))
    21: active(isLNat(snd(Y5))) -> mark(isPLNat(Y5))
    22: active(isLNat(tail(U5))) -> mark(isLNat(U5))
    23: active(isLNat(take(V5,W5))) -> mark(and(isNatural(V5),isLNat(W5)))
    24: active(isNatural(0())) -> mark(tt())
    25: active(isNatural(head(P5))) -> mark(isLNat(P5))
    26: active(isNatural(s(X6))) -> mark(isNatural(X6))
    27: active(isNatural(sel(Y6,U6))) -> mark(and(isNatural(Y6),isLNat(U6)))
    28: active(isPLNat(pair(V6,W6))) -> mark(and(isLNat(V6),isLNat(W6)))
    29: active(isPLNat(splitAt(P6,X7))) -> mark(and(isNatural(P6),isLNat(X7)))
    30: active(natsFrom(Y7)) -> mark(u41(isNatural(Y7),Y7))
    31: active(sel(U7,V7)) -> mark(u51(and(isNatural(U7),isLNat(V7)),U7,V7))
    32: active(snd(pair(W7,P7))) -> mark(u61(and(isLNat(W7),isLNat(P7)),P7))
    33: active(splitAt(0(),X8)) -> mark(u71(isLNat(X8),X8))
    34: active(splitAt(s(Y8),cons(U8,V8))) -> mark(u81(and(isNatural(Y8),and(isNatural(U8),isLNat(V8))),Y8,U8,V8))
    35: active(tail(cons(W8,P8))) -> mark(u91(and(isNatural(W8),isLNat(P8)),P8))
    36: active(take(X9,Y9)) -> mark(u101(and(isNatural(X9),isLNat(Y9)),X9,Y9))
    37: mark(u101(U9,V9,W9)) -> active(u101(mark(U9),V9,W9))
    38: mark(tt()) -> active(tt())
    39: mark(fst(P9)) -> active(fst(mark(P9)))
    40: mark(splitAt(X10,Y10)) -> active(splitAt(mark(X10),mark(Y10)))
    41: mark(u11(U10,V10,W10)) -> active(u11(mark(U10),V10,W10))
    42: mark(snd(P10)) -> active(snd(mark(P10)))
    43: mark(u21(X11,Y11)) -> active(u21(mark(X11),Y11))
    44: mark(u31(U11,V11)) -> active(u31(mark(U11),V11))
    45: mark(u41(W11,P11)) -> active(u41(mark(W11),P11))
    46: mark(cons(X12,Y12)) -> active(cons(mark(X12),Y12))
    47: mark(natsFrom(U12)) -> active(natsFrom(mark(U12)))
    48: mark(s(V12)) -> active(s(mark(V12)))
    49: mark(u51(W12,P12,X13)) -> active(u51(mark(W12),P12,X13))
    50: mark(head(Y13)) -> active(head(mark(Y13)))
    51: mark(afterNth(U13,V13)) -> active(afterNth(mark(U13),mark(V13)))
    52: mark(u61(W13,P13)) -> active(u61(mark(W13),P13))
    53: mark(u71(X14,Y14)) -> active(u71(mark(X14),Y14))
    54: mark(pair(U14,V14)) -> active(pair(mark(U14),mark(V14)))
    55: mark(nil()) -> active(nil())
    56: mark(u81(W14,P14,X15,Y15)) -> active(u81(mark(W14),P14,X15,Y15))
    57: mark(u82(U15,V15)) -> active(u82(mark(U15),V15))
    58: mark(u91(W15,P15)) -> active(u91(mark(W15),P15))
    59: mark(and(X16,Y16)) -> active(and(mark(X16),Y16))
    60: mark(isNatural(U16)) -> active(isNatural(U16))
    61: mark(isLNat(V16)) -> active(isLNat(V16))
    62: mark(isPLNat(W16)) -> active(isPLNat(W16))
    63: mark(tail(P16)) -> active(tail(mark(P16)))
    64: mark(take(X17,Y17)) -> active(take(mark(X17),mark(Y17)))
    65: mark(0()) -> active(0())
    66: mark(sel(U17,V17)) -> active(sel(mark(U17),mark(V17)))
    67: u101(mark(W17),P17,X18) -> u101(W17,P17,X18)
    68: u101(Y18,mark(U18),V18) -> u101(Y18,U18,V18)
    69: u101(W18,P18,mark(X19)) -> u101(W18,P18,X19)
    70: u101(active(Y19),U19,V19) -> u101(Y19,U19,V19)
    71: u101(W19,active(P19),X20) -> u101(W19,P19,X20)
    72: u101(Y20,U20,active(V20)) -> u101(Y20,U20,V20)
    73: fst(mark(W20)) -> fst(W20)
    74: fst(active(P20)) -> fst(P20)
    75: splitAt(mark(X21),Y21) -> splitAt(X21,Y21)
    76: splitAt(U21,mark(V21)) -> splitAt(U21,V21)
    77: splitAt(active(W21),P21) -> splitAt(W21,P21)
    78: splitAt(X22,active(Y22)) -> splitAt(X22,Y22)
    79: u11(mark(U22),V22,W22) -> u11(U22,V22,W22)
    80: u11(P22,mark(X23),Y23) -> u11(P22,X23,Y23)
    81: u11(U23,V23,mark(W23)) -> u11(U23,V23,W23)
    82: u11(active(P23),X24,Y24) -> u11(P23,X24,Y24)
    83: u11(U24,active(V24),W24) -> u11(U24,V24,W24)
    84: u11(P24,X25,active(Y25)) -> u11(P24,X25,Y25)
    85: snd(mark(U25)) -> snd(U25)
    86: snd(active(V25)) -> snd(V25)
    87: u21(mark(W25),P25) -> u21(W25,P25)
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