Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308012
details
property
value
status
complete
benchmark
Ex15_Luc06_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.0983 seconds
cpu usage
19.4112
user time
18.0469
system time
1.36429
max virtual memory
1.87141E7
max residence set size
3192860.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
19.19/6.66 WORST_CASE(Omega(n^1), O(n^1)) 19.19/6.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.19/6.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.19/6.67 19.19/6.67 19.19/6.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.19/6.67 19.19/6.67 (0) CpxTRS 19.19/6.67 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 19.19/6.67 (2) CpxTRS 19.19/6.67 (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 19.19/6.67 (4) BOUNDS(1, n^1) 19.19/6.67 (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 19.19/6.67 (6) TRS for Loop Detection 19.19/6.67 (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 19.19/6.67 (8) BEST 19.19/6.67 (9) proven lower bound 19.19/6.67 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 19.19/6.67 (11) BOUNDS(n^1, INF) 19.19/6.67 (12) TRS for Loop Detection 19.19/6.67 19.19/6.67 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (0) 19.19/6.67 Obligation: 19.19/6.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.19/6.67 19.19/6.67 19.19/6.67 The TRS R consists of the following rules: 19.19/6.67 19.19/6.67 f(n__f(n__a)) -> f(n__g(n__f(n__a))) 19.19/6.67 f(X) -> n__f(X) 19.19/6.67 a -> n__a 19.19/6.67 g(X) -> n__g(X) 19.19/6.67 activate(n__f(X)) -> f(X) 19.19/6.67 activate(n__a) -> a 19.19/6.67 activate(n__g(X)) -> g(activate(X)) 19.19/6.67 activate(X) -> X 19.19/6.67 19.19/6.67 S is empty. 19.19/6.67 Rewrite Strategy: FULL 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 19.19/6.67 transformed relative TRS to TRS 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (2) 19.19/6.67 Obligation: 19.19/6.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 19.19/6.67 19.19/6.67 19.19/6.67 The TRS R consists of the following rules: 19.19/6.67 19.19/6.67 f(n__f(n__a)) -> f(n__g(n__f(n__a))) 19.19/6.67 f(X) -> n__f(X) 19.19/6.67 a -> n__a 19.19/6.67 g(X) -> n__g(X) 19.19/6.67 activate(n__f(X)) -> f(X) 19.19/6.67 activate(n__a) -> a 19.19/6.67 activate(n__g(X)) -> g(activate(X)) 19.19/6.67 activate(X) -> X 19.19/6.67 19.19/6.67 S is empty. 19.19/6.67 Rewrite Strategy: FULL 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (3) CpxTrsMatchBoundsProof (FINISHED) 19.19/6.67 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. 19.19/6.67 The certificate found is represented by the following graph. 19.19/6.67 19.19/6.67 "[1, 2, 7, 8, 9, 10] 19.19/6.67 {(1,2,[f_1|0, a|0, g_1|0, activate_1|0, n__f_1|1, n__a|1, n__g_1|1, f_1|1, a|1, n__f_1|2, n__a|2]), (1,7,[f_1|1, n__f_1|2]), (1,10,[g_1|1, n__g_1|2]), (2,2,[n__f_1|0, n__a|0, n__g_1|0]), (7,8,[n__g_1|1]), (8,9,[n__f_1|1]), (9,2,[n__a|1]), (10,2,[activate_1|1, f_1|1, n__f_1|1, a|1, n__a|1, n__g_1|1, n__f_1|2, n__a|2]), (10,10,[g_1|1, n__g_1|2]), (10,7,[f_1|1, n__f_1|2])}" 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (4) 19.19/6.67 BOUNDS(1, n^1) 19.19/6.67 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 19.19/6.67 Transformed a relative TRS into a decreasing-loop problem. 19.19/6.67 ---------------------------------------- 19.19/6.67 19.19/6.67 (6) 19.19/6.67 Obligation: 19.19/6.67 Analyzing the following TRS for decreasing loops: 19.19/6.67 19.19/6.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.19/6.67 19.19/6.67 19.19/6.67 The TRS R consists of the following rules: 19.19/6.67 19.19/6.67 f(n__f(n__a)) -> f(n__g(n__f(n__a))) 19.19/6.67 f(X) -> n__f(X) 19.19/6.67 a -> n__a 19.19/6.67 g(X) -> n__g(X) 19.19/6.67 activate(n__f(X)) -> f(X) 19.19/6.67 activate(n__a) -> a
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11