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Runti Compl Full Rewri 10127 pair #381902422
details
property
value
status
complete
benchmark
#4.30b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
15.7778019905 seconds
cpu usage
47.176024047
max memory
3.993677824E9
stage attributes
key
value
output-size
21055
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 497 ms] (12) BOUNDS(1, n^1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) if_mod(true, x, y) -> mod(minus(x, y), y) if_mod(false, s(x), s(y)) -> s(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: mod(s(x), s([])) mod(s([]), s(y)) if_mod(true, x, []) The defined contexts are: if_mod([], s(x1), s(x2)) mod([], x1) le(x0, []) if_mod(x0, s([]), s(x2)) minus([], x1) [] just represents basic- or constructor-terms in the following defined contexts: if_mod([], s(x1), s(x2)) mod([], x1) 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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
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