TRS Context Sensitive pair #487523855

details

property	value
status	complete
benchmark	LISTUTILITIES_complete-noand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n022.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.88030385971 seconds
cpu usage	11.85645999
max memory	1.417064448E9

stage attributes

key	value
output-size	121816
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given CSR could be proven:

(0) CSR
(1) CSDependencyPairsProof [EQUIVALENT, 636 ms]
(2) QCSDP
(3) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QCSDP
        (6) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (7) QCSDP
        (8) QCSDPMuMonotonicPoloProof [EQUIVALENT, 38 ms]
        (9) QCSDP
        (10) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (11) QCSDP
        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QCSDP
        (15) QCSUsableRulesProof [EQUIVALENT, 44 ms]
        (16) QCSDP
        (17) QCSDPMuMonotonicPoloProof [EQUIVALENT, 293 ms]
        (18) QCSDP
        (19) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (20) TRUE
    (21) QCSDP
        (22) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (23) QCSDP
        (24) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (25) TRUE
    (26) QCSDP
        (27) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (28) QCSDP
        (29) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (30) TRUE


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

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

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actions all output return to TRS Context Sensitive