TRS Standard pair #487071908

details

property	value
status	complete
benchmark	LISTUTILITIES_complete_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.40435 seconds
cpu usage	14.0118
user time	13.4668
system time	0.545021
max virtual memory	1.847958E7
max residence set size	1349084.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSToCSRProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 437 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (9) QCSDP
        (10) QCSDPMuMonotonicPoloProof [EQUIVALENT, 55 ms]
        (11) QCSDP
        (12) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (13) QCSDP
        (14) PIsEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QCSDP
        (17) QCSUsableRulesProof [EQUIVALENT, 42 ms]
        (18) QCSDP
        (19) QCSDPMuMonotonicPoloProof [EQUIVALENT, 316 ms]
        (20) QCSDP
        (21) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (22) TRUE
    (23) QCSDP
        (24) QCSDPSubtermProof [EQUIVALENT, 1 ms]
        (25) QCSDP
        (26) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (27) TRUE
    (28) QCSDP
        (29) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (30) QCSDP
        (31) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (32) TRUE


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2))
   active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2))
   active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2))
   active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2))
   active(U105(tt, V2)) -> mark(U106(isLNat(V2)))
   active(U106(tt)) -> mark(tt)
   active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS))
   active(U111(tt, V2)) -> mark(U112(isLNatKind(V2)))
   active(U112(tt)) -> mark(tt)
   active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS))
   active(U121(tt, V2)) -> mark(U122(isLNatKind(V2)))
   active(U122(tt)) -> mark(tt)
   active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS))
   active(U131(tt)) -> mark(tt)
   active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS)))
   active(U141(tt)) -> mark(tt)
   active(U151(tt)) -> mark(tt)
   active(U161(tt)) -> mark(tt)
   active(U171(tt, V2)) -> mark(U172(isLNatKind(V2)))
   active(U172(tt)) -> mark(tt)
   active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1))
   active(U182(tt, V1)) -> mark(U183(isLNat(V1)))
   active(U183(tt)) -> mark(tt)
   active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1))
   active(U192(tt, V1)) -> mark(U193(isNatural(V1)))
   active(U193(tt)) -> mark(tt)
   active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2))
   active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2))
   active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2))
   active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2))
   active(U205(tt, V2)) -> mark(U206(isLNat(V2)))
   active(U206(tt)) -> mark(tt)
   active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y))
   active(U211(tt)) -> mark(tt)
   active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y))
   active(U221(tt)) -> mark(tt)
   active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X))
   active(U231(tt, V2)) -> mark(U232(isLNatKind(V2)))
   active(U232(tt)) -> mark(tt)
   active(U24(tt, X)) -> mark(X)
   active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2))
   active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2))
   active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2))
   active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2))
   active(U245(tt, V2)) -> mark(U246(isLNat(V2)))
   active(U246(tt)) -> mark(tt)
   active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2))
   active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2))
   active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2))
   active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2))
   active(U255(tt, V2)) -> mark(U256(isLNat(V2)))

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