Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313869
details
property
value
status
complete
benchmark
ocall-safe.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.0792 seconds
cpu usage
3.66514
user time
3.5165
system time
0.148632
max virtual memory
1.8277336E7
max residence set size
230712.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
3.51/2.03 WORST_CASE(Omega(n^1), O(n^1)) 3.51/2.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.51/2.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.51/2.05 3.51/2.05 3.51/2.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 3.51/2.05 3.51/2.05 (0) CpxTRS 3.51/2.05 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 3.51/2.05 (2) CpxTRS 3.51/2.05 (3) CpxTrsMatchBoundsTAProof [FINISHED, 35 ms] 3.51/2.05 (4) BOUNDS(1, n^1) 3.51/2.05 (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 3.51/2.05 (6) TRS for Loop Detection 3.51/2.05 (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 3.51/2.05 (8) BEST 3.51/2.05 (9) proven lower bound 3.51/2.05 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 3.51/2.05 (11) BOUNDS(n^1, INF) 3.51/2.05 (12) TRS for Loop Detection 3.51/2.05 3.51/2.05 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (0) 3.51/2.05 Obligation: 3.51/2.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 3.51/2.05 3.51/2.05 3.51/2.05 The TRS R consists of the following rules: 3.51/2.05 3.51/2.05 dbl(S(0), S(0)) -> S(S(S(S(0)))) 3.51/2.05 save(S(x)) -> dbl(0, save(x)) 3.51/2.05 save(0) -> 0 3.51/2.05 dbl(0, y) -> y 3.51/2.05 3.51/2.05 S is empty. 3.51/2.05 Rewrite Strategy: INNERMOST 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 3.51/2.05 transformed relative TRS to TRS 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (2) 3.51/2.05 Obligation: 3.51/2.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 3.51/2.05 3.51/2.05 3.51/2.05 The TRS R consists of the following rules: 3.51/2.05 3.51/2.05 dbl(S(0), S(0)) -> S(S(S(S(0)))) 3.51/2.05 save(S(x)) -> dbl(0, save(x)) 3.51/2.05 save(0) -> 0 3.51/2.05 dbl(0, y) -> y 3.51/2.05 3.51/2.05 S is empty. 3.51/2.05 Rewrite Strategy: INNERMOST 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (3) CpxTrsMatchBoundsTAProof (FINISHED) 3.51/2.05 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1. 3.51/2.05 3.51/2.05 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 3.51/2.05 final states : [1, 2] 3.51/2.05 transitions: 3.51/2.05 S0(0) -> 0 3.51/2.05 00() -> 0 3.51/2.05 dbl0(0, 0) -> 1 3.51/2.05 save0(0) -> 2 3.51/2.05 01() -> 5 3.51/2.05 S1(5) -> 4 3.51/2.05 S1(4) -> 3 3.51/2.05 S1(3) -> 3 3.51/2.05 S1(3) -> 1 3.51/2.05 01() -> 6 3.51/2.05 save1(0) -> 7 3.51/2.05 dbl1(6, 7) -> 2 3.51/2.05 01() -> 2 3.51/2.05 dbl1(6, 7) -> 7 3.51/2.05 01() -> 7 3.51/2.05 0 -> 1 3.51/2.05 7 -> 2 3.51/2.05 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (4) 3.51/2.05 BOUNDS(1, n^1) 3.51/2.05 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 3.51/2.05 Transformed a relative TRS into a decreasing-loop problem. 3.51/2.05 ---------------------------------------- 3.51/2.05 3.51/2.05 (6) 3.51/2.05 Obligation: 3.51/2.05 Analyzing the following TRS for decreasing loops: 3.51/2.05 3.51/2.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40