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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307682
details
property
value
status
complete
benchmark
fac.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.524 seconds
cpu usage
317.398
user time
315.115
system time
2.28268
max virtual memory
1.8279384E7
max residence set size
5695424.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
317.33/291.48 WORST_CASE(Omega(n^2), ?) 317.33/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 317.33/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 317.33/291.49 317.33/291.49 317.33/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 317.33/291.49 317.33/291.49 (0) CpxTRS 317.33/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 317.33/291.49 (2) CpxTRS 317.33/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 317.33/291.49 (4) typed CpxTrs 317.33/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 317.33/291.49 (6) typed CpxTrs 317.33/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 303 ms] 317.33/291.49 (8) BEST 317.33/291.49 (9) proven lower bound 317.33/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 317.33/291.49 (11) BOUNDS(n^1, INF) 317.33/291.49 (12) typed CpxTrs 317.33/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 36 ms] 317.33/291.49 (14) BEST 317.33/291.49 (15) proven lower bound 317.33/291.49 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 317.33/291.49 (17) BOUNDS(n^2, INF) 317.33/291.49 (18) typed CpxTrs 317.33/291.49 (19) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] 317.33/291.49 (20) typed CpxTrs 317.33/291.49 (21) RewriteLemmaProof [LOWER BOUND(ID), 1859 ms] 317.33/291.49 (22) BOUNDS(1, INF) 317.33/291.49 317.33/291.49 317.33/291.49 ---------------------------------------- 317.33/291.49 317.33/291.49 (0) 317.33/291.49 Obligation: 317.33/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 317.33/291.49 317.33/291.49 317.33/291.49 The TRS R consists of the following rules: 317.33/291.49 317.33/291.49 plus(x, 0) -> x 317.33/291.49 plus(x, s(y)) -> s(plus(x, y)) 317.33/291.49 times(0, y) -> 0 317.33/291.49 times(x, 0) -> 0 317.33/291.49 times(s(x), y) -> plus(times(x, y), y) 317.33/291.49 p(s(s(x))) -> s(p(s(x))) 317.33/291.49 p(s(0)) -> 0 317.33/291.49 fac(s(x)) -> times(fac(p(s(x))), s(x)) 317.33/291.49 317.33/291.49 S is empty. 317.33/291.49 Rewrite Strategy: FULL 317.33/291.49 ---------------------------------------- 317.33/291.49 317.33/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 317.33/291.49 Renamed function symbols to avoid clashes with predefined symbol. 317.33/291.49 ---------------------------------------- 317.33/291.49 317.33/291.49 (2) 317.33/291.49 Obligation: 317.33/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 317.33/291.49 317.33/291.49 317.33/291.49 The TRS R consists of the following rules: 317.33/291.49 317.33/291.49 plus(x, 0') -> x 317.33/291.49 plus(x, s(y)) -> s(plus(x, y)) 317.33/291.49 times(0', y) -> 0' 317.33/291.49 times(x, 0') -> 0' 317.33/291.49 times(s(x), y) -> plus(times(x, y), y) 317.33/291.49 p(s(s(x))) -> s(p(s(x))) 317.33/291.49 p(s(0')) -> 0' 317.33/291.49 fac(s(x)) -> times(fac(p(s(x))), s(x)) 317.33/291.49 317.33/291.49 S is empty. 317.33/291.49 Rewrite Strategy: FULL 317.33/291.49 ---------------------------------------- 317.33/291.49 317.33/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 317.33/291.49 Infered types. 317.33/291.49 ---------------------------------------- 317.33/291.49 317.33/291.49 (4) 317.33/291.49 Obligation: 317.33/291.49 TRS: 317.33/291.49 Rules: 317.33/291.49 plus(x, 0') -> x 317.33/291.49 plus(x, s(y)) -> s(plus(x, y)) 317.33/291.49 times(0', y) -> 0' 317.33/291.49 times(x, 0') -> 0' 317.33/291.49 times(s(x), y) -> plus(times(x, y), y) 317.33/291.49 p(s(s(x))) -> s(p(s(x))) 317.33/291.49 p(s(0')) -> 0' 317.33/291.49 fac(s(x)) -> times(fac(p(s(x))), s(x)) 317.33/291.49 317.33/291.49 Types: 317.33/291.49 plus :: 0':s -> 0':s -> 0':s 317.33/291.49 0' :: 0':s 317.33/291.49 s :: 0':s -> 0':s 317.33/291.49 times :: 0':s -> 0':s -> 0':s
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