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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307631
details
property
value
status
complete
benchmark
list-sum-prod-assoc-append.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n081.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.548 seconds
cpu usage
370.595
user time
365.924
system time
4.67054
max virtual memory
1.8279384E7
max residence set size
7887904.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
370.41/291.50 WORST_CASE(Omega(n^2), ?) 370.51/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 370.51/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 370.51/291.51 370.51/291.51 370.51/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 370.51/291.51 370.51/291.51 (0) CpxTRS 370.51/291.51 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 370.51/291.51 (2) CpxTRS 370.51/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 370.51/291.51 (4) typed CpxTrs 370.51/291.51 (5) OrderProof [LOWER BOUND(ID), 0 ms] 370.51/291.51 (6) typed CpxTrs 370.51/291.51 (7) RewriteLemmaProof [LOWER BOUND(ID), 334 ms] 370.51/291.51 (8) BEST 370.51/291.51 (9) proven lower bound 370.51/291.51 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 370.51/291.51 (11) BOUNDS(n^1, INF) 370.51/291.51 (12) typed CpxTrs 370.51/291.51 (13) RewriteLemmaProof [LOWER BOUND(ID), 4191 ms] 370.51/291.51 (14) BEST 370.51/291.51 (15) proven lower bound 370.51/291.51 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 370.51/291.51 (17) BOUNDS(n^2, INF) 370.51/291.51 (18) typed CpxTrs 370.51/291.51 (19) RewriteLemmaProof [LOWER BOUND(ID), 27 ms] 370.51/291.51 (20) typed CpxTrs 370.51/291.51 (21) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 370.51/291.51 (22) typed CpxTrs 370.51/291.51 (23) RewriteLemmaProof [LOWER BOUND(ID), 396 ms] 370.51/291.51 (24) BOUNDS(1, INF) 370.51/291.51 370.51/291.51 370.51/291.51 ---------------------------------------- 370.51/291.51 370.51/291.51 (0) 370.51/291.51 Obligation: 370.51/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 370.51/291.51 370.51/291.51 370.51/291.51 The TRS R consists of the following rules: 370.51/291.51 370.51/291.51 +(x, 0) -> x 370.51/291.51 +(0, x) -> x 370.51/291.51 +(s(x), s(y)) -> s(s(+(x, y))) 370.51/291.51 +(+(x, y), z) -> +(x, +(y, z)) 370.51/291.51 *(x, 0) -> 0 370.51/291.51 *(0, x) -> 0 370.51/291.51 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) 370.51/291.51 *(*(x, y), z) -> *(x, *(y, z)) 370.51/291.51 app(nil, l) -> l 370.51/291.51 app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 370.51/291.51 sum(nil) -> 0 370.51/291.51 sum(cons(x, l)) -> +(x, sum(l)) 370.51/291.51 sum(app(l1, l2)) -> +(sum(l1), sum(l2)) 370.51/291.51 prod(nil) -> s(0) 370.51/291.51 prod(cons(x, l)) -> *(x, prod(l)) 370.51/291.51 prod(app(l1, l2)) -> *(prod(l1), prod(l2)) 370.51/291.51 370.51/291.51 S is empty. 370.51/291.51 Rewrite Strategy: FULL 370.51/291.51 ---------------------------------------- 370.51/291.51 370.51/291.51 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 370.51/291.51 Renamed function symbols to avoid clashes with predefined symbol. 370.51/291.51 ---------------------------------------- 370.51/291.51 370.51/291.51 (2) 370.51/291.51 Obligation: 370.51/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 370.51/291.51 370.51/291.51 370.51/291.51 The TRS R consists of the following rules: 370.51/291.51 370.51/291.51 +'(x, 0') -> x 370.51/291.51 +'(0', x) -> x 370.51/291.51 +'(s(x), s(y)) -> s(s(+'(x, y))) 370.51/291.51 +'(+'(x, y), z) -> +'(x, +'(y, z)) 370.51/291.51 *'(x, 0') -> 0' 370.51/291.51 *'(0', x) -> 0' 370.51/291.51 *'(s(x), s(y)) -> s(+'(*'(x, y), +'(x, y))) 370.51/291.51 *'(*'(x, y), z) -> *'(x, *'(y, z)) 370.51/291.51 app(nil, l) -> l 370.51/291.51 app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 370.51/291.51 sum(nil) -> 0' 370.51/291.51 sum(cons(x, l)) -> +'(x, sum(l)) 370.51/291.51 sum(app(l1, l2)) -> +'(sum(l1), sum(l2)) 370.51/291.51 prod(nil) -> s(0') 370.51/291.51 prod(cons(x, l)) -> *'(x, prod(l)) 370.51/291.51 prod(app(l1, l2)) -> *'(prod(l1), prod(l2)) 370.51/291.51 370.51/291.51 S is empty. 370.51/291.51 Rewrite Strategy: FULL 370.51/291.51 ---------------------------------------- 370.51/291.51 370.51/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 370.51/291.51 Infered types. 370.51/291.51 ---------------------------------------- 370.51/291.51
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