Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307605
details
property
value
status
complete
benchmark
maxsortcondition.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n044.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.557 seconds
cpu usage
309.351
user time
307.663
system time
1.68823
max virtual memory
1.8281444E7
max residence set size
5223396.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
309.22/291.50 WORST_CASE(Omega(n^2), ?) 309.22/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 309.22/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 309.22/291.52 309.22/291.52 309.22/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 309.22/291.52 309.22/291.52 (0) CpxTRS 309.22/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 309.22/291.52 (2) CpxTRS 309.22/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 309.22/291.52 (4) typed CpxTrs 309.22/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 309.22/291.52 (6) typed CpxTrs 309.22/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 300 ms] 309.22/291.52 (8) BEST 309.22/291.52 (9) proven lower bound 309.22/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 309.22/291.52 (11) BOUNDS(n^1, INF) 309.22/291.52 (12) typed CpxTrs 309.22/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 41 ms] 309.22/291.52 (14) typed CpxTrs 309.22/291.52 (15) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] 309.22/291.52 (16) typed CpxTrs 309.22/291.52 (17) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] 309.22/291.52 (18) proven lower bound 309.22/291.52 (19) LowerBoundPropagationProof [FINISHED, 0 ms] 309.22/291.52 (20) BOUNDS(n^2, INF) 309.22/291.52 309.22/291.52 309.22/291.52 ---------------------------------------- 309.22/291.52 309.22/291.52 (0) 309.22/291.52 Obligation: 309.22/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 309.22/291.52 309.22/291.52 309.22/291.52 The TRS R consists of the following rules: 309.22/291.52 309.22/291.52 max(nil) -> 0 309.22/291.52 max(cons(x, nil)) -> x 309.22/291.52 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 309.22/291.52 if1(true, x, y, xs) -> max(cons(x, xs)) 309.22/291.52 if1(false, x, y, xs) -> max(cons(y, xs)) 309.22/291.52 del(x, nil) -> nil 309.22/291.52 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 309.22/291.52 if2(true, x, y, xs) -> xs 309.22/291.52 if2(false, x, y, xs) -> cons(y, del(x, xs)) 309.22/291.52 eq(0, 0) -> true 309.22/291.52 eq(0, s(y)) -> false 309.22/291.52 eq(s(x), 0) -> false 309.22/291.52 eq(s(x), s(y)) -> eq(x, y) 309.22/291.52 sort(xs) -> if3(empty(xs), xs) 309.22/291.52 if3(true, xs) -> nil 309.22/291.52 if3(false, xs) -> sort(del(max(xs), xs)) 309.22/291.52 empty(nil) -> true 309.22/291.52 empty(cons(x, xs)) -> false 309.22/291.52 ge(x, 0) -> true 309.22/291.52 ge(0, s(x)) -> false 309.22/291.52 ge(s(x), s(y)) -> ge(x, y) 309.22/291.52 309.22/291.52 S is empty. 309.22/291.52 Rewrite Strategy: FULL 309.22/291.52 ---------------------------------------- 309.22/291.52 309.22/291.52 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 309.22/291.52 Renamed function symbols to avoid clashes with predefined symbol. 309.22/291.52 ---------------------------------------- 309.22/291.52 309.22/291.52 (2) 309.22/291.52 Obligation: 309.22/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 309.22/291.52 309.22/291.52 309.22/291.52 The TRS R consists of the following rules: 309.22/291.52 309.22/291.52 max(nil) -> 0' 309.22/291.52 max(cons(x, nil)) -> x 309.22/291.52 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 309.22/291.52 if1(true, x, y, xs) -> max(cons(x, xs)) 309.22/291.52 if1(false, x, y, xs) -> max(cons(y, xs)) 309.22/291.52 del(x, nil) -> nil 309.22/291.52 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 309.22/291.52 if2(true, x, y, xs) -> xs 309.22/291.52 if2(false, x, y, xs) -> cons(y, del(x, xs)) 309.22/291.52 eq(0', 0') -> true 309.22/291.52 eq(0', s(y)) -> false 309.22/291.52 eq(s(x), 0') -> false 309.22/291.52 eq(s(x), s(y)) -> eq(x, y) 309.22/291.52 sort(xs) -> if3(empty(xs), xs) 309.22/291.52 if3(true, xs) -> nil 309.22/291.52 if3(false, xs) -> sort(del(max(xs), xs)) 309.22/291.52 empty(nil) -> true 309.22/291.52 empty(cons(x, xs)) -> false 309.22/291.52 ge(x, 0') -> true 309.22/291.52 ge(0', s(x)) -> false 309.22/291.52 ge(s(x), s(y)) -> ge(x, y) 309.22/291.52 309.22/291.52 S is empty. 309.22/291.52 Rewrite Strategy: FULL
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
