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Runti Compl Full Rewri 10127 pair #381902813
details
property
value
status
complete
benchmark
Ex49_GM04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.03575611115 seconds
cpu usage
24.340998435
max memory
4.358135808E9
stage attributes
key
value
output-size
17430
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 332 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: minus(0, Y) -> 0 minus(s(X), s(Y)) -> minus(X, Y) geq(X, 0) -> true geq(0, s(Y)) -> false geq(s(X), s(Y)) -> geq(X, Y) div(0, s(Y)) -> 0 div(s(X), s(Y)) -> if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0) if(true, X, Y) -> X if(false, 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: div(s([]), s(Y)) div(s(X), s([])) The defined contexts are: if([], s(x1), 0) if(x0, s([]), 0) div([], s(x1)) geq([], x1) minus([], x1) [] just represents basic- or constructor-terms in the following defined contexts: if([], s(x1), 0) div([], s(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: minus(0, Y) -> 0 minus(s(X), s(Y)) -> minus(X, Y) geq(X, 0) -> true geq(0, s(Y)) -> false geq(s(X), s(Y)) -> geq(X, Y) div(0, s(Y)) -> 0 div(s(X), s(Y)) -> if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0) if(true, X, Y) -> X if(false, X, Y) -> Y
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