TRS Innermost pair #516979131

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	n069.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	4.73389601707 seconds
cpu usage	15.472163294
max memory	1.303785472E9

stage attributes

key	value
output-size	218004
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRSToCSRProof [SOUND, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 512 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (9) QCSDP
        (10) QCSDPMuMonotonicPoloProof [EQUIVALENT, 76 ms]
        (11) QCSDP
        (12) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (13) QCSDP
        (14) PIsEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QCSDP
        (17) QCSUsableRulesProof [EQUIVALENT, 34 ms]
        (18) QCSDP
        (19) QCSDPMuMonotonicPoloProof [EQUIVALENT, 339 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, 11 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)))

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actions all output return to TRS Innermost