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Runti Compl Full Rewri 10127 pair #381903597
details
property
value
status
complete
benchmark
Ex25_Luc06_FR.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
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.55954694748 seconds
cpu usage
3.446093074
max memory
2.16956928E8
stage attributes
key
value
output-size
5767
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) 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(X)) -> c(n__f(n__g(n__f(X)))) c(X) -> d(activate(X)) h(X) -> c(n__d(X)) f(X) -> n__f(X) g(X) -> n__g(X) d(X) -> n__d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) activate(n__d(X)) -> d(X) 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(X)) -> c(n__f(n__g(n__f(X)))) c(X) -> d(activate(X)) h(X) -> c(n__d(X)) f(X) -> n__f(X) g(X) -> n__g(X) d(X) -> n__d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) activate(n__d(X)) -> d(X) 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 4. The certificate found is represented by the following graph. "[31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41] {(31,32,[f_1|0, c_1|0, h_1|0, g_1|0, d_1|0, activate_1|0, n__f_1|1, n__g_1|1, n__d_1|1, g_1|1, d_1|1, n__g_1|2, n__d_1|2]), (31,33,[d_1|1, n__d_1|2]), (31,34,[c_1|1]), (31,35,[f_1|1, n__f_1|2]), (31,36,[d_1|2, n__d_1|3]), (31,37,[c_1|2]), (31,40,[d_1|3, n__d_1|4]), (32,32,[n__f_1|0, n__g_1|0, n__d_1|0]), (33,32,[activate_1|1, n__f_1|1, g_1|1, n__g_1|1, d_1|1, n__d_1|1, n__g_1|2, n__d_1|2]), (33,35,[f_1|1, n__f_1|2]), (33,37,[c_1|2]), (33,40,[d_1|3, n__d_1|4]), (34,32,[n__d_1|1]), (35,32,[activate_1|1, n__f_1|1, g_1|1, n__g_1|1, d_1|1, n__d_1|1, n__g_1|2, n__d_1|2]), (35,35,[f_1|1, n__f_1|2]), (35,37,[c_1|2]), (35,40,[d_1|3, n__d_1|4]), (36,34,[activate_1|2]), (36,32,[d_1|2, n__d_1|2, n__d_1|3]), (37,38,[n__f_1|2]), (38,39,[n__g_1|2]), (39,35,[n__f_1|2]), (40,37,[activate_1|3]), (40,41,[f_1|3, n__f_1|4]), (40,38,[n__f_1|3]), (41,38,[activate_1|3]), (41,39,[g_1|3, n__g_1|3, n__g_1|4])}" ---------------------------------------- (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).
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