Runti Compl Full Rewri 10127 pair #381902672

details

property	value
status	complete
benchmark	#3.22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.25120782852 seconds
cpu usage	19.420840674
max memory	3.398713344E9

stage attributes

key	value
output-size	19360
starexec-result	WORST_CASE(Omega(n^2), 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^2), O(n^2))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) CpxTRS
(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
(2) CpxTRS
    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTRS
    (5) RelTrsToWeightedTrsProof [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), 273 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 87 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 615 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 158 ms]
    (30) CpxRNTS
    (31) FinalProof [FINISHED, 0 ms]
    (32) BOUNDS(1, n^2)
(33) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(34) CpxTRS
    (35) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) typed CpxTrs
    (37) OrderProof [LOWER BOUND(ID), 0 ms]
    (38) typed CpxTrs
    (39) RewriteLemmaProof [LOWER BOUND(ID), 278 ms]
    (40) BEST
        (41) proven lower bound
            (42) LowerBoundPropagationProof [FINISHED, 0 ms]
            (43) BOUNDS(n^1, INF)
        (44) typed CpxTrs
            (45) RewriteLemmaProof [LOWER BOUND(ID), 9 ms]
            (46) proven lower bound
            (47) LowerBoundPropagationProof [FINISHED, 0 ms]
            (48) BOUNDS(n^2, INF)


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


The TRS R consists of the following rules:

   times(x, plus(y, s(z))) -> plus(times(x, plus(y, times(s(z), 0))), times(x, s(z)))
   times(x, 0) -> 0
   times(x, s(y)) -> plus(times(x, y), x)
   plus(x, 0) -> x
   plus(x, s(y)) -> s(plus(x, y))

S is empty.
Rewrite Strategy: FULL
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(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
The following defined symbols can occur below the 0th argument of plus: plus, times

Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
times(x, plus(y, s(z))) -> plus(times(x, plus(y, times(s(z), 0))), times(x, s(z)))

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


The TRS R consists of the following rules:

   times(x, 0) -> 0
   times(x, s(y)) -> plus(times(x, y), x)

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