TRS Context Sensitive pair #487523911

details

property	value
status	complete
benchmark	OvConsOS_complete-noand.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	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.2245850563 seconds
cpu usage	10.348993457
max memory	1.000448E9

stage attributes

key	value
output-size	93606
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 of the given CSR could be proven:

(0) CSR
(1) CSRRRRProof [EQUIVALENT, 130 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 39 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 7 ms]
(6) CSR
(7) CSDependencyPairsProof [EQUIVALENT, 114 ms]
(8) QCSDP
(9) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QCSDP
        (12) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (13) QCSDP
        (14) QCSDPMuMonotonicPoloProof [EQUIVALENT, 0 ms]
        (15) QCSDP
        (16) PIsEmptyProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QCSDP
        (19) QCSUsableRulesProof [EQUIVALENT, 11 ms]
        (20) QCSDP
        (21) QCSDPMuMonotonicPoloProof [EQUIVALENT, 63 ms]
        (22) QCSDP
        (23) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (24) QCSDP
        (25) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (26) QCSDP
        (27) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (28) TRUE
    (29) QCSDP
        (30) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (31) QCSDP
        (32) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (33) TRUE
    (34) QCSDP
        (35) QCSDPReductionPairProof [EQUIVALENT, 105 ms]
        (36) QCSDP
        (37) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (38) TRUE


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

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

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

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actions all output return to TRS Context Sensitive