Runtime Complexity: TRS pair #487111188

details

property	value
status	complete
benchmark	test76.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Strategy_removed_mixed_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.37779 seconds
cpu usage	18.7991
user time	17.4068
system time	1.39231
max virtual memory	1.9275864E7
max residence set size	3863072.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^1).

(0) CpxTRS
(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxWeightedTrs
    (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 3 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), 151 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 15 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 290 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 105 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 200 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 116 ms]
    (36) CpxRNTS
    (37) FinalProof [FINISHED, 0 ms]
    (38) BOUNDS(1, n^1)
(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), 241 ms]
    (46) BEST
        (47) proven lower bound
            (48) LowerBoundPropagationProof [FINISHED, 0 ms]
            (49) BOUNDS(n^1, INF)
        (50) typed CpxTrs


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


The TRS R consists of the following rules:

   +(X, 0) -> X
   +(X, s(Y)) -> s(+(X, Y))
   f(0, s(0), X) -> f(X, +(X, X), X)
   g(X, Y) -> X
   g(X, Y) -> Y

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

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

The duplicating contexts are:
f(0, s(0), [])


The defined contexts are:
f(x0, [], x2)


As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
----------------------------------------

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


The TRS R consists of the following rules:

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job log

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actions all output return to Runtime Complexity: TRS