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Runti Compl Inner Rewri 22807 pair #381905145
details
property
value
status
complete
benchmark
Ex15_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.14277720451 seconds
cpu usage
12.549305793
max memory
4.121317376E9
stage attributes
key
value
output-size
4433
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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 (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(X) mark(a) -> a mark(g(X)) -> g(mark(X)) a__f(X) -> f(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (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: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(X) mark(a) -> a mark(g(X)) -> g(mark(X)) a__f(X) -> f(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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 2. The certificate found is represented by the following graph. "[1, 2, 3, 4, 5, 6] {(1,2,[a__f_1|0, mark_1|0, f_1|1, a__f_1|1, a|1, f_1|2]), (1,3,[a__f_1|1, f_1|2]), (1,6,[g_1|1]), (2,2,[f_1|0, a|0, g_1|0]), (3,4,[g_1|1]), (4,5,[f_1|1]), (5,2,[a|1]), (6,2,[mark_1|1, a__f_1|1, a|1, f_1|2]), (6,6,[g_1|1]), (6,3,[a__f_1|1, f_1|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 (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(X) mark(a) -> a mark(g(X)) -> g(mark(X)) a__f(X) -> f(X)
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