Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313921
details
property
value
status
complete
benchmark
27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n107.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.84315 seconds
cpu usage
11.9673
user time
11.1964
system time
0.77092
max virtual memory
1.8279384E7
max residence set size
2182528.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
11.62/3.78 WORST_CASE(Omega(n^1), O(n^1)) 11.62/3.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.62/3.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.62/3.78 11.62/3.78 11.62/3.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 11.62/3.78 11.62/3.78 (0) CpxTRS 11.62/3.78 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 11.62/3.78 (2) CpxTRS 11.62/3.78 (3) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms] 11.62/3.78 (4) BOUNDS(1, n^1) 11.62/3.78 (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 11.62/3.78 (6) CpxTRS 11.62/3.78 (7) SlicingProof [LOWER BOUND(ID), 0 ms] 11.62/3.78 (8) CpxTRS 11.62/3.78 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 11.62/3.78 (10) typed CpxTrs 11.62/3.78 (11) OrderProof [LOWER BOUND(ID), 0 ms] 11.62/3.78 (12) typed CpxTrs 11.62/3.78 (13) RewriteLemmaProof [LOWER BOUND(ID), 487 ms] 11.62/3.78 (14) BEST 11.62/3.78 (15) proven lower bound 11.62/3.78 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 11.62/3.78 (17) BOUNDS(n^1, INF) 11.62/3.78 (18) typed CpxTrs 11.62/3.78 (19) RewriteLemmaProof [LOWER BOUND(ID), 93 ms] 11.62/3.78 (20) typed CpxTrs 11.62/3.78 (21) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] 11.62/3.78 (22) BOUNDS(1, INF) 11.62/3.78 11.62/3.78 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (0) 11.62/3.78 Obligation: 11.62/3.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 11.62/3.78 11.62/3.78 11.62/3.78 The TRS R consists of the following rules: 11.62/3.78 11.62/3.78 h(f(x), y) -> f(g(x, y)) 11.62/3.78 g(x, y) -> h(x, y) 11.62/3.78 11.62/3.78 S is empty. 11.62/3.78 Rewrite Strategy: INNERMOST 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 11.62/3.78 transformed relative TRS to TRS 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (2) 11.62/3.78 Obligation: 11.62/3.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 11.62/3.78 11.62/3.78 11.62/3.78 The TRS R consists of the following rules: 11.62/3.78 11.62/3.78 h(f(x), y) -> f(g(x, y)) 11.62/3.78 g(x, y) -> h(x, y) 11.62/3.78 11.62/3.78 S is empty. 11.62/3.78 Rewrite Strategy: INNERMOST 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (3) CpxTrsMatchBoundsTAProof (FINISHED) 11.62/3.78 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 2. 11.62/3.78 11.62/3.78 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 11.62/3.78 final states : [1, 2] 11.62/3.78 transitions: 11.62/3.78 f0(0) -> 0 11.62/3.78 h0(0, 0) -> 1 11.62/3.78 g0(0, 0) -> 2 11.62/3.78 g1(0, 0) -> 3 11.62/3.78 f1(3) -> 1 11.62/3.78 h1(0, 0) -> 2 11.62/3.78 f1(3) -> 2 11.62/3.78 h2(0, 0) -> 3 11.62/3.78 f1(3) -> 3 11.62/3.78 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (4) 11.62/3.78 BOUNDS(1, n^1) 11.62/3.78 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (5) RenamingProof (BOTH BOUNDS(ID, ID)) 11.62/3.78 Renamed function symbols to avoid clashes with predefined symbol. 11.62/3.78 ---------------------------------------- 11.62/3.78 11.62/3.78 (6) 11.62/3.78 Obligation: 11.62/3.78 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 11.62/3.78 11.62/3.78 11.62/3.78 The TRS R consists of the following rules: 11.62/3.78
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