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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313750
details
property
value
status
complete
benchmark
#3.55.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.257 seconds
cpu usage
1132.68
user time
1118.47
system time
14.2057
max virtual memory
5.699992E7
max residence set size
1.499714E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1117.84/291.50 WORST_CASE(Omega(n^2), ?) 1132.45/295.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1132.45/295.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1132.45/295.17 1132.45/295.17 1132.45/295.17 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1132.45/295.17 1132.45/295.17 (0) CpxTRS 1132.45/295.17 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1132.45/295.17 (2) CpxTRS 1132.45/295.17 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1132.45/295.17 (4) typed CpxTrs 1132.45/295.17 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1132.45/295.17 (6) typed CpxTrs 1132.45/295.17 (7) RewriteLemmaProof [LOWER BOUND(ID), 285 ms] 1132.45/295.17 (8) BEST 1132.45/295.17 (9) proven lower bound 1132.45/295.17 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1132.45/295.17 (11) BOUNDS(n^1, INF) 1132.45/295.17 (12) typed CpxTrs 1132.45/295.17 (13) RewriteLemmaProof [LOWER BOUND(ID), 73 ms] 1132.45/295.17 (14) typed CpxTrs 1132.45/295.17 (15) RewriteLemmaProof [LOWER BOUND(ID), 77 ms] 1132.45/295.17 (16) typed CpxTrs 1132.45/295.17 (17) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 1132.45/295.17 (18) typed CpxTrs 1132.45/295.17 (19) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 1132.45/295.17 (20) typed CpxTrs 1132.45/295.17 (21) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] 1132.45/295.17 (22) proven lower bound 1132.45/295.17 (23) LowerBoundPropagationProof [FINISHED, 0 ms] 1132.45/295.17 (24) BOUNDS(n^2, INF) 1132.45/295.17 1132.45/295.17 1132.45/295.17 ---------------------------------------- 1132.45/295.17 1132.45/295.17 (0) 1132.45/295.17 Obligation: 1132.45/295.17 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1132.45/295.17 1132.45/295.17 1132.45/295.17 The TRS R consists of the following rules: 1132.45/295.17 1132.45/295.17 minus(x, 0) -> x 1132.45/295.17 minus(s(x), s(y)) -> minus(x, y) 1132.45/295.17 quot(0, s(y)) -> 0 1132.45/295.17 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1132.45/295.17 le(0, y) -> true 1132.45/295.17 le(s(x), 0) -> false 1132.45/295.17 le(s(x), s(y)) -> le(x, y) 1132.45/295.17 app(nil, y) -> y 1132.45/295.17 app(add(n, x), y) -> add(n, app(x, y)) 1132.45/295.17 low(n, nil) -> nil 1132.45/295.17 low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) 1132.45/295.17 if_low(true, n, add(m, x)) -> add(m, low(n, x)) 1132.45/295.17 if_low(false, n, add(m, x)) -> low(n, x) 1132.45/295.17 high(n, nil) -> nil 1132.45/295.17 high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) 1132.45/295.17 if_high(true, n, add(m, x)) -> high(n, x) 1132.45/295.17 if_high(false, n, add(m, x)) -> add(m, high(n, x)) 1132.45/295.17 quicksort(nil) -> nil 1132.45/295.17 quicksort(add(n, x)) -> app(quicksort(low(n, x)), add(n, quicksort(high(n, x)))) 1132.45/295.17 1132.45/295.17 S is empty. 1132.45/295.17 Rewrite Strategy: INNERMOST 1132.45/295.17 ---------------------------------------- 1132.45/295.17 1132.45/295.17 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1132.45/295.17 Renamed function symbols to avoid clashes with predefined symbol. 1132.45/295.17 ---------------------------------------- 1132.45/295.17 1132.45/295.17 (2) 1132.45/295.17 Obligation: 1132.45/295.17 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1132.45/295.17 1132.45/295.17 1132.45/295.17 The TRS R consists of the following rules: 1132.45/295.17 1132.45/295.17 minus(x, 0') -> x 1132.45/295.17 minus(s(x), s(y)) -> minus(x, y) 1132.45/295.17 quot(0', s(y)) -> 0' 1132.45/295.17 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1132.45/295.17 le(0', y) -> true 1132.45/295.17 le(s(x), 0') -> false 1132.45/295.17 le(s(x), s(y)) -> le(x, y) 1132.45/295.17 app(nil, y) -> y 1132.45/295.17 app(add(n, x), y) -> add(n, app(x, y)) 1132.45/295.17 low(n, nil) -> nil 1132.45/295.17 low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) 1132.45/295.17 if_low(true, n, add(m, x)) -> add(m, low(n, x)) 1132.45/295.17 if_low(false, n, add(m, x)) -> low(n, x) 1132.45/295.17 high(n, nil) -> nil 1132.45/295.17 high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) 1132.45/295.17 if_high(true, n, add(m, x)) -> high(n, x) 1132.45/295.17 if_high(false, n, add(m, x)) -> add(m, high(n, x)) 1132.45/295.17 quicksort(nil) -> nil 1132.45/295.17 quicksort(add(n, x)) -> app(quicksort(low(n, x)), add(n, quicksort(high(n, x)))) 1132.45/295.17 1132.45/295.17 S is empty. 1132.45/295.17 Rewrite Strategy: INNERMOST
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