Runti Compl Inner Rewri 22807 pair #381904324

details

property	value
status	complete
benchmark	7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.452149153 seconds
cpu usage	578.640482683
max memory	7.88291584E9

stage attributes

key	value
output-size	22801
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxWeightedTrs
    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTypedWeightedTrs
    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
    (6) CpxTypedWeightedCompleteTrs
    (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (10) CpxRNTS
    (11) InliningProof [UPPER BOUND(ID), 220 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), 221 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 76 ms]
    (22) CpxRNTS
    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 139 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 45 ms]
    (28) CpxRNTS
    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 626 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 269 ms]
    (34) CpxRNTS
    (35) FinalProof [FINISHED, 0 ms]
    (36) BOUNDS(1, n^2)
(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), 237 ms]
    (44) BEST
        (45) proven lower bound
            (46) LowerBoundPropagationProof [FINISHED, 0 ms]
            (47) BOUNDS(n^1, INF)
        (48) typed CpxTrs


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   cond(true, x) -> cond(odd(x), p(p(p(x))))
   odd(0) -> false
   odd(s(0)) -> true
   odd(s(s(x))) -> odd(x)
   p(0) -> 0
   p(s(x)) -> x

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

(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   cond(true, x) -> cond(odd(x), p(p(p(x)))) [1]
   odd(0) -> false [1]
   odd(s(0)) -> true [1]
   odd(s(s(x))) -> odd(x) [1]
   p(0) -> 0 [1]

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