TRS Innermost pair #487093415

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	n139.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.16162 seconds
cpu usage	12.8175
user time	12.2973
system time	0.5202
max virtual memory	1.8545116E7
max residence set size	1291448.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [SOUND, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 410 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (9) QCSDP
        (10) QCSDPMuMonotonicPoloProof [EQUIVALENT, 54 ms]
        (11) QCSDP
        (12) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (13) QCSDP
        (14) PIsEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QCSDP
        (17) QCSUsableRulesProof [EQUIVALENT, 52 ms]
        (18) QCSDP
        (19) QCSDPMuMonotonicPoloProof [EQUIVALENT, 249 ms]
        (20) QCSDP
        (21) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (22) TRUE
    (23) QCSDP
        (24) QCSDPSubtermProof [EQUIVALENT, 2 ms]
        (25) QCSDP
        (26) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (27) TRUE
    (28) QCSDP
        (29) QCSDPSubtermProof [EQUIVALENT, 7 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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actions all output return to TRS Innermost