Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308524
details
property
value
status
complete
benchmark
#4.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.44204 seconds
cpu usage
18.5684
user time
16.7025
system time
1.86591
max virtual memory
1.8813492E7
max residence set size
4663252.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
18.35/6.40 WORST_CASE(Omega(n^1), O(n^1)) 18.35/6.41 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 18.35/6.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.35/6.41 18.35/6.41 18.35/6.41 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.35/6.41 18.35/6.41 (0) CpxTRS 18.35/6.41 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 18.35/6.41 (2) CpxTRS 18.35/6.41 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 18.35/6.41 (4) CpxTRS 18.35/6.41 (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 18.35/6.41 (6) BOUNDS(1, n^1) 18.35/6.41 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 18.35/6.41 (8) TRS for Loop Detection 18.35/6.41 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 18.35/6.41 (10) BEST 18.35/6.41 (11) proven lower bound 18.35/6.41 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 18.35/6.41 (13) BOUNDS(n^1, INF) 18.35/6.41 (14) TRS for Loop Detection 18.35/6.41 18.35/6.41 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (0) 18.35/6.41 Obligation: 18.35/6.41 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.35/6.41 18.35/6.41 18.35/6.41 The TRS R consists of the following rules: 18.35/6.41 18.35/6.41 f(s(0), g(x)) -> f(x, g(x)) 18.35/6.41 g(s(x)) -> g(x) 18.35/6.41 18.35/6.41 S is empty. 18.35/6.41 Rewrite Strategy: FULL 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (1) DependencyGraphProof (UPPER BOUND(ID)) 18.35/6.41 The following rules are not reachable from basic terms in the dependency graph and can be removed: 18.35/6.41 18.35/6.41 f(s(0), g(x)) -> f(x, g(x)) 18.35/6.41 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (2) 18.35/6.41 Obligation: 18.35/6.41 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 18.35/6.41 18.35/6.41 18.35/6.41 The TRS R consists of the following rules: 18.35/6.41 18.35/6.41 g(s(x)) -> g(x) 18.35/6.41 18.35/6.41 S is empty. 18.35/6.41 Rewrite Strategy: FULL 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 18.35/6.41 transformed relative TRS to TRS 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (4) 18.35/6.41 Obligation: 18.35/6.41 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 18.35/6.41 18.35/6.41 18.35/6.41 The TRS R consists of the following rules: 18.35/6.41 18.35/6.41 g(s(x)) -> g(x) 18.35/6.41 18.35/6.41 S is empty. 18.35/6.41 Rewrite Strategy: FULL 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (5) CpxTrsMatchBoundsProof (FINISHED) 18.35/6.41 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. 18.35/6.41 The certificate found is represented by the following graph. 18.35/6.41 18.35/6.41 "[1, 2] 18.35/6.41 {(1,2,[g_1|0, g_1|1]), (2,2,[s_1|0])}" 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (6) 18.35/6.41 BOUNDS(1, n^1) 18.35/6.41 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (7) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 18.35/6.41 Transformed a relative TRS into a decreasing-loop problem. 18.35/6.41 ---------------------------------------- 18.35/6.41 18.35/6.41 (8) 18.35/6.41 Obligation: 18.35/6.41 Analyzing the following TRS for decreasing loops: 18.35/6.41 18.35/6.41 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.35/6.41
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
