Runtime Complexity: TRS pair #487110688

details

property	value
status	complete
benchmark	divExp.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	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.641 seconds
cpu usage	984.987
user time	973.047
system time	11.9401
max virtual memory	5.5806616E7
max residence set size	1.0770132E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

WORST_CASE(Omega(n^1), O(n^3))
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^1, n^3).

(0) CpxTRS
(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxWeightedTrs
    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxTypedWeightedTrs
    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (12) CpxRNTS
    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxRNTS
    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (18) CpxRNTS
    (19) IntTrsBoundProof [UPPER BOUND(ID), 354 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 178 ms]
    (22) CpxRNTS
    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 587 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 349 ms]
    (28) CpxRNTS
    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 182 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 35 ms]
    (34) CpxRNTS
    (35) FinalProof [FINISHED, 0 ms]
    (36) BOUNDS(1, n^3)
(37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(38) CpxTRS
    (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) typed CpxTrs
    (41) OrderProof [LOWER BOUND(ID), 0 ms]
    (42) typed CpxTrs
    (43) RewriteLemmaProof [LOWER BOUND(ID), 239 ms]
    (44) BEST
        (45) proven lower bound
            (46) LowerBoundPropagationProof [FINISHED, 0 ms]
            (47) BOUNDS(n^1, INF)
        (48) typed CpxTrs


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

(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3).


The TRS R consists of the following rules:

   minus(x, x) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   minus(0, x) -> 0
   minus(x, 0) -> x
   div(s(x), s(y)) -> s(div(minus(x, y), s(y)))
   div(0, s(y)) -> 0
   f(x, 0, b) -> x
   f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b)

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

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

The duplicating contexts are:
div(s(x), s([]))
f(x, s(y), [])


The defined contexts are:
div([], x1)
f(x0, [], x2)
div([], s(x1))
minus([], x1)
minus(s([]), s(0))


[] just represents basic- or constructor-terms in the following defined contexts:
f(x0, [], x2)
div([], s(x1))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Runtime Complexity: TRS