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Runtime Complexity: TRS pair #487110234
details
property
value
status
complete
benchmark
Ex18_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.89462 seconds
cpu usage
8.46667
user time
7.98572
system time
0.480957
max virtual memory
1.8279408E7
max residence set size
1338528.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(mark(X)) mark(a) -> a mark(g(X)) -> g(X) a__f(X) -> f(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: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(mark(X)) mark(a) -> a mark(g(X)) -> g(X) a__f(X) -> f(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. "[3, 4, 5, 6, 7, 8, 9, 10, 11] {(3,4,[a__f_1|0, mark_1|0, f_1|1, a|1, g_1|1]), (3,5,[a__f_1|1, f_1|2]), (3,8,[a__f_1|1, f_1|2]), (3,9,[a__f_1|2, f_1|3]), (4,4,[f_1|0, a|0, g_1|0]), (5,6,[g_1|1]), (6,7,[f_1|1]), (7,4,[a|1]), (8,4,[mark_1|1, a|1, g_1|1]), (8,8,[a__f_1|1, f_1|2]), (8,9,[a__f_1|2, f_1|3]), (9,10,[g_1|2]), (10,11,[f_1|2]), (11,4,[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: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(mark(X)) mark(a) -> a mark(g(X)) -> g(X) a__f(X) -> f(X) S is empty. Rewrite Strategy: FULL ---------------------------------------- (7) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1):
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