TRS Innermost pair #487093185

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)	3.99398 seconds
cpu usage	10.0861
user time	9.6887
system time	0.397359
max virtual memory	1.881198E7
max residence set size	859648.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) CSRRRRProof [EQUIVALENT, 142 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 50 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 39 ms]
(8) CSR
(9) CSDependencyPairsProof [EQUIVALENT, 115 ms]
(10) QCSDP
(11) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (13) QCSDP
        (14) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (15) QCSDP
        (16) QCSDPMuMonotonicPoloProof [EQUIVALENT, 9 ms]
        (17) QCSDP
        (18) PIsEmptyProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QCSDP
        (21) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (22) QCSDP
        (23) QCSDPMuMonotonicPoloProof [EQUIVALENT, 108 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, 2 ms]
        (33) QCSDP
        (34) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (35) TRUE
    (36) QCSDP
        (37) QCSDPReductionPairProof [EQUIVALENT, 109 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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actions all output return to TRS Innermost