TRS Standard pair #487069658

details

property	value
status	complete
benchmark	OvConsOS_complete_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.72644 seconds
cpu usage	10.9521
user time	10.4628
system time	0.489372
max virtual memory	1.8875764E7
max residence set size	799956.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [EQUIVALENT, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 144 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 41 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 37 ms]
(8) CSR
(9) CSDependencyPairsProof [EQUIVALENT, 87 ms]
(10) QCSDP
(11) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (13) QCSDP
        (14) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (15) QCSDP
        (16) QCSDPMuMonotonicPoloProof [EQUIVALENT, 20 ms]
        (17) QCSDP
        (18) PIsEmptyProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QCSDP
        (21) QCSUsableRulesProof [EQUIVALENT, 30 ms]
        (22) QCSDP
        (23) QCSDPMuMonotonicPoloProof [EQUIVALENT, 42 ms]
        (24) QCSDP
        (25) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (26) QCSDP
        (27) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (28) QCSDP
        (29) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (30) TRUE
    (31) QCSDP
        (32) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (33) QCSDP
        (34) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (35) TRUE
    (36) QCSDP
        (37) QCSDPReductionPairProof [EQUIVALENT, 63 ms]
        (38) QCSDP
        (39) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (40) TRUE


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

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

   active(zeros) -> mark(cons(0, zeros))
   active(U101(tt, V1, V2)) -> mark(U102(isNatKind(V1), V1, V2))
   active(U102(tt, V1, V2)) -> mark(U103(isNatIListKind(V2), V1, V2))
   active(U103(tt, V1, V2)) -> mark(U104(isNatIListKind(V2), V1, V2))
   active(U104(tt, V1, V2)) -> mark(U105(isNat(V1), V2))
   active(U105(tt, V2)) -> mark(U106(isNatIList(V2)))
   active(U106(tt)) -> mark(tt)
   active(U11(tt, V1)) -> mark(U12(isNatIListKind(V1), V1))
   active(U111(tt, L, N)) -> mark(U112(isNatIListKind(L), L, N))
   active(U112(tt, L, N)) -> mark(U113(isNat(N), L, N))
   active(U113(tt, L, N)) -> mark(U114(isNatKind(N), L))
   active(U114(tt, L)) -> mark(s(length(L)))
   active(U12(tt, V1)) -> mark(U13(isNatList(V1)))
   active(U121(tt, IL)) -> mark(U122(isNatIListKind(IL)))
   active(U122(tt)) -> mark(nil)
   active(U13(tt)) -> mark(tt)
   active(U131(tt, IL, M, N)) -> mark(U132(isNatIListKind(IL), IL, M, N))
   active(U132(tt, IL, M, N)) -> mark(U133(isNat(M), IL, M, N))
   active(U133(tt, IL, M, N)) -> mark(U134(isNatKind(M), IL, M, N))
   active(U134(tt, IL, M, N)) -> mark(U135(isNat(N), IL, M, N))
   active(U135(tt, IL, M, N)) -> mark(U136(isNatKind(N), IL, M, N))
   active(U136(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
   active(U23(tt)) -> mark(tt)
   active(U31(tt, V)) -> mark(U32(isNatIListKind(V), V))
   active(U32(tt, V)) -> mark(U33(isNatList(V)))
   active(U33(tt)) -> mark(tt)
   active(U41(tt, V1, V2)) -> mark(U42(isNatKind(V1), V1, V2))
   active(U42(tt, V1, V2)) -> mark(U43(isNatIListKind(V2), V1, V2))
   active(U43(tt, V1, V2)) -> mark(U44(isNatIListKind(V2), V1, V2))
   active(U44(tt, V1, V2)) -> mark(U45(isNat(V1), V2))
   active(U45(tt, V2)) -> mark(U46(isNatIList(V2)))
   active(U46(tt)) -> mark(tt)
   active(U51(tt, V2)) -> mark(U52(isNatIListKind(V2)))
   active(U52(tt)) -> mark(tt)
   active(U61(tt, V2)) -> mark(U62(isNatIListKind(V2)))
   active(U62(tt)) -> mark(tt)
   active(U71(tt)) -> mark(tt)
   active(U81(tt)) -> mark(tt)
   active(U91(tt, V1, V2)) -> mark(U92(isNatKind(V1), V1, V2))
   active(U92(tt, V1, V2)) -> mark(U93(isNatIListKind(V2), V1, V2))
   active(U93(tt, V1, V2)) -> mark(U94(isNatIListKind(V2), V1, V2))

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