Runtime Complexity: TRS Innermost pair #487112480

details

property	value
status	complete
benchmark	#3.16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.547 seconds
cpu usage	322.83
user time	319.804
system time	3.02561
max virtual memory	5.6009008E7
max residence set size	5692868.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), O(n^3))

output

WORST_CASE(Omega(n^2), O(n^3))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3).

(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) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxRNTS
    (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxRNTS
    (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (16) CpxRNTS
    (17) IntTrsBoundProof [UPPER BOUND(ID), 436 ms]
    (18) CpxRNTS
    (19) IntTrsBoundProof [UPPER BOUND(ID), 179 ms]
    (20) CpxRNTS
    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 493 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) FinalProof [FINISHED, 0 ms]
    (28) BOUNDS(1, n^3)
(29) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(30) CpxTRS
    (31) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) typed CpxTrs
    (33) OrderProof [LOWER BOUND(ID), 0 ms]
    (34) typed CpxTrs
    (35) RewriteLemmaProof [LOWER BOUND(ID), 265 ms]
    (36) BEST
        (37) proven lower bound
            (38) LowerBoundPropagationProof [FINISHED, 0 ms]
            (39) BOUNDS(n^1, INF)
        (40) typed CpxTrs
            (41) RewriteLemmaProof [LOWER BOUND(ID), 62 ms]
            (42) proven lower bound
            (43) LowerBoundPropagationProof [FINISHED, 0 ms]
            (44) BOUNDS(n^2, INF)


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

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3).


The TRS R consists of the following rules:

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

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^3).


The TRS R consists of the following rules:

   times(x, 0) -> 0 [1]
   times(x, s(y)) -> plus(times(x, y), x) [1]
   plus(x, 0) -> x [1]
   plus(0, x) -> x [1]
   plus(x, s(y)) -> s(plus(x, y)) [1]
   plus(s(x), y) -> s(plus(x, y)) [1]

Rewrite Strategy: INNERMOST
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(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(4)

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