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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307881
details
property
value
status
complete
benchmark
tpa4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.681 seconds
cpu usage
311.874
user time
309.934
system time
1.93998
max virtual memory
1.8279384E7
max residence set size
5408208.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
311.80/291.64 WORST_CASE(Omega(n^2), ?) 311.80/291.65 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 311.80/291.65 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 311.80/291.65 311.80/291.65 311.80/291.65 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 311.80/291.65 311.80/291.65 (0) CpxTRS 311.80/291.65 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 311.80/291.65 (2) CpxTRS 311.80/291.65 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 311.80/291.65 (4) typed CpxTrs 311.80/291.65 (5) OrderProof [LOWER BOUND(ID), 0 ms] 311.80/291.65 (6) typed CpxTrs 311.80/291.65 (7) RewriteLemmaProof [LOWER BOUND(ID), 282 ms] 311.80/291.65 (8) BEST 311.80/291.65 (9) proven lower bound 311.80/291.65 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 311.80/291.65 (11) BOUNDS(n^1, INF) 311.80/291.65 (12) typed CpxTrs 311.80/291.65 (13) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] 311.80/291.65 (14) typed CpxTrs 311.80/291.65 (15) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] 311.80/291.65 (16) BEST 311.80/291.65 (17) proven lower bound 311.80/291.65 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 311.80/291.65 (19) BOUNDS(n^2, INF) 311.80/291.65 (20) typed CpxTrs 311.80/291.65 311.80/291.65 311.80/291.65 ---------------------------------------- 311.80/291.65 311.80/291.65 (0) 311.80/291.65 Obligation: 311.80/291.65 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 311.80/291.65 311.80/291.65 311.80/291.65 The TRS R consists of the following rules: 311.80/291.65 311.80/291.65 -(x, 0) -> x 311.80/291.65 -(s(x), s(y)) -> -(x, y) 311.80/291.65 +(0, y) -> y 311.80/291.65 +(s(x), y) -> s(+(x, y)) 311.80/291.65 *(x, 0) -> 0 311.80/291.65 *(x, s(y)) -> +(x, *(x, y)) 311.80/291.65 p(s(x)) -> x 311.80/291.65 f(s(x)) -> f(-(p(*(s(x), s(x))), *(s(x), s(x)))) 311.80/291.65 311.80/291.65 S is empty. 311.80/291.65 Rewrite Strategy: FULL 311.80/291.65 ---------------------------------------- 311.80/291.65 311.80/291.65 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 311.80/291.65 Renamed function symbols to avoid clashes with predefined symbol. 311.80/291.65 ---------------------------------------- 311.80/291.65 311.80/291.65 (2) 311.80/291.65 Obligation: 311.80/291.65 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 311.80/291.65 311.80/291.65 311.80/291.65 The TRS R consists of the following rules: 311.80/291.65 311.80/291.65 -(x, 0') -> x 311.80/291.65 -(s(x), s(y)) -> -(x, y) 311.80/291.65 +'(0', y) -> y 311.80/291.65 +'(s(x), y) -> s(+'(x, y)) 311.80/291.65 *'(x, 0') -> 0' 311.80/291.65 *'(x, s(y)) -> +'(x, *'(x, y)) 311.80/291.65 p(s(x)) -> x 311.80/291.65 f(s(x)) -> f(-(p(*'(s(x), s(x))), *'(s(x), s(x)))) 311.80/291.65 311.80/291.65 S is empty. 311.80/291.65 Rewrite Strategy: FULL 311.80/291.65 ---------------------------------------- 311.80/291.65 311.80/291.65 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 311.80/291.65 Infered types. 311.80/291.65 ---------------------------------------- 311.80/291.65 311.80/291.65 (4) 311.80/291.65 Obligation: 311.80/291.65 TRS: 311.80/291.65 Rules: 311.80/291.65 -(x, 0') -> x 311.80/291.65 -(s(x), s(y)) -> -(x, y) 311.80/291.65 +'(0', y) -> y 311.80/291.65 +'(s(x), y) -> s(+'(x, y)) 311.80/291.65 *'(x, 0') -> 0' 311.80/291.65 *'(x, s(y)) -> +'(x, *'(x, y)) 311.80/291.65 p(s(x)) -> x 311.80/291.65 f(s(x)) -> f(-(p(*'(s(x), s(x))), *'(s(x), s(x)))) 311.80/291.65 311.80/291.65 Types: 311.80/291.65 - :: 0':s -> 0':s -> 0':s 311.80/291.65 0' :: 0':s 311.80/291.65 s :: 0':s -> 0':s 311.80/291.65 +' :: 0':s -> 0':s -> 0':s 311.80/291.65 *' :: 0':s -> 0':s -> 0':s 311.80/291.65 p :: 0':s -> 0':s
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