TRS Inner 89993 pair #381733705

details

property	value
status	complete
benchmark	OvConsOS_complete_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	13.4924581051 seconds
cpu usage	43.379488176
max memory	3.899113472E9

stage attributes

key	value
output-size	212618
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 306 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) QDPOrderProof [EQUIVALENT, 963 ms]
        (21) QDP
        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPOrderProof [EQUIVALENT, 487 ms]
        (25) QDP
        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
        (27) AND
            (28) QDP
                (29) UsableRulesProof [EQUIVALENT, 0 ms]
                (30) QDP
                (31) QReductionProof [EQUIVALENT, 14 ms]
                (32) QDP
                (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (34) YES
            (35) QDP
                (36) QDPOrderProof [EQUIVALENT, 869 ms]
                (37) QDP
                (38) DependencyGraphProof [EQUIVALENT, 0 ms]
                (39) TRUE


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

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

   a__zeros -> cons(0, zeros)
   a__U101(tt, V1, V2) -> a__U102(a__isNatKind(V1), V1, V2)
   a__U102(tt, V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2)
   a__U103(tt, V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2)
   a__U104(tt, V1, V2) -> a__U105(a__isNat(V1), V2)
   a__U105(tt, V2) -> a__U106(a__isNatIList(V2))
   a__U106(tt) -> tt
   a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1)
   a__U111(tt, L, N) -> a__U112(a__isNatIListKind(L), L, N)
   a__U112(tt, L, N) -> a__U113(a__isNat(N), L, N)
   a__U113(tt, L, N) -> a__U114(a__isNatKind(N), L)
   a__U114(tt, L) -> s(a__length(mark(L)))
   a__U12(tt, V1) -> a__U13(a__isNatList(V1))
   a__U121(tt, IL) -> a__U122(a__isNatIListKind(IL))
   a__U122(tt) -> nil
   a__U13(tt) -> tt
   a__U131(tt, IL, M, N) -> a__U132(a__isNatIListKind(IL), IL, M, N)
   a__U132(tt, IL, M, N) -> a__U133(a__isNat(M), IL, M, N)
   a__U133(tt, IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N)
   a__U134(tt, IL, M, N) -> a__U135(a__isNat(N), IL, M, N)
   a__U135(tt, IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N)
   a__U136(tt, IL, M, N) -> cons(mark(N), take(M, IL))
   a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1)
   a__U22(tt, V1) -> a__U23(a__isNat(V1))
   a__U23(tt) -> tt
   a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V)
   a__U32(tt, V) -> a__U33(a__isNatList(V))
   a__U33(tt) -> tt
   a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
   a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
   a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
   a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2)
   a__U45(tt, V2) -> a__U46(a__isNatIList(V2))
   a__U46(tt) -> tt
   a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2))
   a__U52(tt) -> tt
   a__U61(tt, V2) -> a__U62(a__isNatIListKind(V2))
   a__U62(tt) -> tt

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