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Runti Compl Full Rewri 10127 pair #381903775
details
property
value
status
complete
benchmark
Ex18_Luc06_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.50953006744 seconds
cpu usage
3.366429939
max memory
2.15830528E8
stage attributes
key
value
output-size
4611
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] (4) BOUNDS(1, n^1) (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) 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: f(f(a)) -> f(g(n__f(n__a))) f(X) -> n__f(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__a) -> a activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(f(a)) -> f(g(n__f(n__a))) f(X) -> n__f(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__a) -> a activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[13, 14, 15, 16, 17, 18] {(13,14,[f_1|0, a|0, activate_1|0, n__f_1|1, n__a|1, a|1, g_1|1, n__a|2]), (13,15,[f_1|1, n__f_1|2]), (13,16,[f_1|2, n__f_1|3]), (14,14,[g_1|0, n__f_1|0, n__a|0]), (15,14,[activate_1|1, n__f_1|1, a|1, n__a|1, g_1|1, n__a|2]), (15,15,[f_1|1, n__f_1|2]), (15,16,[f_1|2, n__f_1|3]), (16,17,[g_1|2]), (17,18,[n__f_1|2]), (18,14,[n__a|2])}" ---------------------------------------- (4) BOUNDS(1, n^1) ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: 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: f(f(a)) -> f(g(n__f(n__a))) f(X) -> n__f(X) a -> n__a activate(n__f(X)) -> f(activate(X))
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