Runtime Complexity: TRS pair #487111422

details

property	value
status	complete
benchmark	2.12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.39409 seconds
cpu usage	27.6694
user time	26.0859
system time	1.58354
max virtual memory	1.9013892E7
max residence set size	3984376.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^3), O(n^3))

output

WORST_CASE(Omega(n^3), O(n^3))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3).

(0) CpxTRS
(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 11 ms]
(2) CpxTRS
    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxWeightedTrs
    (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 130 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 48 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 130 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 54 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 1265 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 151 ms]
    (36) CpxRNTS
    (37) FinalProof [FINISHED, 0 ms]
    (38) BOUNDS(1, n^3)
(39) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(40) CpxTRS
    (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) typed CpxTrs
    (43) OrderProof [LOWER BOUND(ID), 0 ms]
    (44) typed CpxTrs
    (45) RewriteLemmaProof [LOWER BOUND(ID), 284 ms]
    (46) BEST
        (47) proven lower bound
            (48) LowerBoundPropagationProof [FINISHED, 0 ms]
            (49) BOUNDS(n^1, INF)
        (50) typed CpxTrs
            (51) RewriteLemmaProof [LOWER BOUND(ID), 1743 ms]
            (52) typed CpxTrs
            (53) RewriteLemmaProof [LOWER BOUND(ID), 64 ms]
            (54) proven lower bound
            (55) LowerBoundPropagationProof [FINISHED, 0 ms]
            (56) BOUNDS(n^3, INF)


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

(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3).


The TRS R consists of the following rules:

   +(0, y) -> y
   +(s(x), y) -> s(+(x, y))
   +(p(x), y) -> p(+(x, y))
   minus(0) -> 0
   minus(s(x)) -> p(minus(x))
   minus(p(x)) -> s(minus(x))
   *(0, y) -> 0
   *(s(x), y) -> +(*(x, y), y)
   *(p(x), y) -> +(*(x, y), minus(y))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

The duplicating contexts are:
*(s(x), [])
*(p(x), [])


The defined contexts are:
+([], x1)
+(x0, [])

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