TRS Innermost pair #487524225

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	n151.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.57899212837 seconds
cpu usage	10.840087299
max memory	9.50829056E8

stage attributes

key	value
output-size	142947
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) CSRRRRProof [EQUIVALENT, 121 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 95 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 0 ms]
(8) CSR
(9) CSRRRRProof [EQUIVALENT, 0 ms]
(10) CSR
(11) CSDependencyPairsProof [EQUIVALENT, 102 ms]
(12) QCSDP
(13) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(14) AND
    (15) QCSDP
        (16) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (17) QCSDP
        (18) QCSDPMuMonotonicPoloProof [EQUIVALENT, 0 ms]
        (19) QCSDP
        (20) PIsEmptyProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QCSDP
        (23) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (24) QCSDP
        (25) QCSDPMuMonotonicPoloProof [EQUIVALENT, 87 ms]
        (26) QCSDP
        (27) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (28) QCSDP
        (29) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (30) QCSDP
        (31) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (32) TRUE
    (33) QCSDP
        (34) QCSDPSubtermProof [EQUIVALENT, 7 ms]
        (35) QCSDP
        (36) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (37) TRUE
    (38) QCSDP
        (39) QCSDPReductionPairProof [EQUIVALENT, 80 ms]
        (40) QCSDP
        (41) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (42) 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)))

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actions all output return to TRS Innermost