Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313915
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
n172.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
298.911 seconds
cpu usage
1124.91
user time
1110.61
system time
14.301
max virtual memory
5.5806688E7
max residence set size
1.4937132E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1124.46/298.77 WORST_CASE(Omega(n^2), ?) 1124.46/298.80 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1124.46/298.80 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1124.46/298.80 1124.46/298.80 1124.46/298.80 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1124.46/298.80 1124.46/298.80 (0) CpxTRS 1124.46/298.80 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.46/298.80 (2) CpxTRS 1124.46/298.80 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.46/298.80 (4) typed CpxTrs 1124.46/298.80 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1124.46/298.80 (6) typed CpxTrs 1124.46/298.80 (7) RewriteLemmaProof [LOWER BOUND(ID), 303 ms] 1124.46/298.80 (8) BEST 1124.46/298.80 (9) proven lower bound 1124.46/298.80 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.46/298.80 (11) BOUNDS(n^1, INF) 1124.46/298.80 (12) typed CpxTrs 1124.46/298.80 (13) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 1124.46/298.80 (14) typed CpxTrs 1124.46/298.80 (15) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] 1124.46/298.80 (16) typed CpxTrs 1124.46/298.80 (17) RewriteLemmaProof [LOWER BOUND(ID), 81 ms] 1124.46/298.80 (18) proven lower bound 1124.46/298.80 (19) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.46/298.80 (20) BOUNDS(n^2, INF) 1124.46/298.80 1124.46/298.80 1124.46/298.80 ---------------------------------------- 1124.46/298.80 1124.46/298.80 (0) 1124.46/298.80 Obligation: 1124.46/298.80 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1124.46/298.80 1124.46/298.80 1124.46/298.80 The TRS R consists of the following rules: 1124.46/298.80 1124.46/298.80 max(nil) -> 0 1124.46/298.80 max(cons(x, nil)) -> x 1124.46/298.80 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 1124.46/298.80 if1(true, x, y, xs) -> max(cons(x, xs)) 1124.46/298.80 if1(false, x, y, xs) -> max(cons(y, xs)) 1124.46/298.80 del(x, nil) -> nil 1124.46/298.80 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1124.46/298.80 if2(true, x, y, xs) -> xs 1124.46/298.80 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1124.46/298.80 eq(0, 0) -> true 1124.46/298.80 eq(0, s(y)) -> false 1124.46/298.80 eq(s(x), 0) -> false 1124.46/298.80 eq(s(x), s(y)) -> eq(x, y) 1124.46/298.80 sort(xs) -> if3(empty(xs), xs) 1124.46/298.80 if3(true, xs) -> nil 1124.46/298.80 if3(false, xs) -> sort(del(max(xs), xs)) 1124.46/298.80 empty(nil) -> true 1124.46/298.80 empty(cons(x, xs)) -> false 1124.46/298.80 ge(x, 0) -> true 1124.46/298.80 ge(0, s(x)) -> false 1124.46/298.80 ge(s(x), s(y)) -> ge(x, y) 1124.46/298.80 1124.46/298.80 S is empty. 1124.46/298.80 Rewrite Strategy: INNERMOST 1124.46/298.80 ---------------------------------------- 1124.46/298.80 1124.46/298.80 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1124.46/298.80 Renamed function symbols to avoid clashes with predefined symbol. 1124.46/298.80 ---------------------------------------- 1124.46/298.80 1124.46/298.80 (2) 1124.46/298.80 Obligation: 1124.46/298.80 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1124.46/298.80 1124.46/298.80 1124.46/298.80 The TRS R consists of the following rules: 1124.46/298.80 1124.46/298.80 max(nil) -> 0' 1124.46/298.80 max(cons(x, nil)) -> x 1124.46/298.80 max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 1124.46/298.80 if1(true, x, y, xs) -> max(cons(x, xs)) 1124.46/298.80 if1(false, x, y, xs) -> max(cons(y, xs)) 1124.46/298.80 del(x, nil) -> nil 1124.46/298.80 del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 1124.46/298.80 if2(true, x, y, xs) -> xs 1124.46/298.80 if2(false, x, y, xs) -> cons(y, del(x, xs)) 1124.46/298.80 eq(0', 0') -> true 1124.46/298.80 eq(0', s(y)) -> false 1124.46/298.80 eq(s(x), 0') -> false 1124.46/298.80 eq(s(x), s(y)) -> eq(x, y) 1124.46/298.80 sort(xs) -> if3(empty(xs), xs) 1124.46/298.80 if3(true, xs) -> nil 1124.46/298.80 if3(false, xs) -> sort(del(max(xs), xs)) 1124.46/298.80 empty(nil) -> true 1124.46/298.80 empty(cons(x, xs)) -> false 1124.46/298.80 ge(x, 0') -> true 1124.46/298.80 ge(0', s(x)) -> false 1124.46/298.80 ge(s(x), s(y)) -> ge(x, y) 1124.46/298.80 1124.46/298.80 S is empty. 1124.46/298.80 Rewrite Strategy: INNERMOST
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