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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308446
details
property
value
status
complete
benchmark
2.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.567 seconds
cpu usage
952.0
user time
945.309
system time
6.6908
max virtual memory
1.9544836E7
max residence set size
7849716.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
951.64/291.51 WORST_CASE(Omega(n^3), ?) 951.64/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 951.64/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 951.64/291.52 951.64/291.52 951.64/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 951.64/291.52 951.64/291.52 (0) CpxTRS 951.64/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 951.64/291.52 (2) CpxTRS 951.64/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 951.64/291.52 (4) typed CpxTrs 951.64/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 951.64/291.52 (6) typed CpxTrs 951.64/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 295 ms] 951.64/291.52 (8) BEST 951.64/291.52 (9) proven lower bound 951.64/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 951.64/291.52 (11) BOUNDS(n^1, INF) 951.64/291.52 (12) typed CpxTrs 951.64/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 32 ms] 951.64/291.52 (14) BEST 951.64/291.52 (15) proven lower bound 951.64/291.52 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 951.64/291.52 (17) BOUNDS(n^2, INF) 951.64/291.52 (18) typed CpxTrs 951.64/291.52 (19) RewriteLemmaProof [LOWER BOUND(ID), 728 ms] 951.64/291.52 (20) typed CpxTrs 951.64/291.52 (21) RewriteLemmaProof [LOWER BOUND(ID), 5854 ms] 951.64/291.52 (22) proven lower bound 951.64/291.52 (23) LowerBoundPropagationProof [FINISHED, 0 ms] 951.64/291.52 (24) BOUNDS(n^3, INF) 951.64/291.52 951.64/291.52 951.64/291.52 ---------------------------------------- 951.64/291.52 951.64/291.52 (0) 951.64/291.52 Obligation: 951.64/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 951.64/291.52 951.64/291.52 951.64/291.52 The TRS R consists of the following rules: 951.64/291.52 951.64/291.52 fac(0) -> 1 951.64/291.52 fac(s(x)) -> *(s(x), fac(x)) 951.64/291.52 floop(0, y) -> y 951.64/291.52 floop(s(x), y) -> floop(x, *(s(x), y)) 951.64/291.52 *(x, 0) -> 0 951.64/291.52 *(x, s(y)) -> +(*(x, y), x) 951.64/291.52 +(x, 0) -> x 951.64/291.52 +(x, s(y)) -> s(+(x, y)) 951.64/291.52 1 -> s(0) 951.64/291.52 fac(0) -> s(0) 951.64/291.52 951.64/291.52 S is empty. 951.64/291.52 Rewrite Strategy: FULL 951.64/291.52 ---------------------------------------- 951.64/291.52 951.64/291.52 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 951.64/291.52 Renamed function symbols to avoid clashes with predefined symbol. 951.64/291.52 ---------------------------------------- 951.64/291.52 951.64/291.52 (2) 951.64/291.52 Obligation: 951.64/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 951.64/291.52 951.64/291.52 951.64/291.52 The TRS R consists of the following rules: 951.64/291.52 951.64/291.52 fac(0') -> 1' 951.64/291.52 fac(s(x)) -> *'(s(x), fac(x)) 951.64/291.52 floop(0', y) -> y 951.64/291.52 floop(s(x), y) -> floop(x, *'(s(x), y)) 951.64/291.52 *'(x, 0') -> 0' 951.64/291.52 *'(x, s(y)) -> +'(*'(x, y), x) 951.64/291.52 +'(x, 0') -> x 951.64/291.52 +'(x, s(y)) -> s(+'(x, y)) 951.64/291.52 1' -> s(0') 951.64/291.52 fac(0') -> s(0') 951.64/291.52 951.64/291.52 S is empty. 951.64/291.52 Rewrite Strategy: FULL 951.64/291.52 ---------------------------------------- 951.64/291.52 951.64/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 951.64/291.52 Infered types. 951.64/291.52 ---------------------------------------- 951.64/291.52 951.64/291.52 (4) 951.64/291.52 Obligation: 951.64/291.52 TRS: 951.64/291.52 Rules: 951.64/291.52 fac(0') -> 1' 951.64/291.52 fac(s(x)) -> *'(s(x), fac(x)) 951.64/291.52 floop(0', y) -> y 951.64/291.52 floop(s(x), y) -> floop(x, *'(s(x), y)) 951.64/291.52 *'(x, 0') -> 0' 951.64/291.52 *'(x, s(y)) -> +'(*'(x, y), x) 951.64/291.52 +'(x, 0') -> x 951.64/291.52 +'(x, s(y)) -> s(+'(x, y))
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