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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307616
details
property
value
status
complete
benchmark
thiemann40_modified.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n066.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.563 seconds
cpu usage
307.956
user time
305.669
system time
2.28708
max virtual memory
1.8283404E7
max residence set size
5589520.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
307.80/291.52 WORST_CASE(Omega(n^2), ?) 307.80/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 307.80/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 307.80/291.53 307.80/291.53 307.80/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 307.80/291.53 307.80/291.53 (0) CpxTRS 307.80/291.53 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 307.80/291.53 (2) CpxTRS 307.80/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 307.80/291.53 (4) typed CpxTrs 307.80/291.53 (5) OrderProof [LOWER BOUND(ID), 0 ms] 307.80/291.53 (6) typed CpxTrs 307.80/291.53 (7) RewriteLemmaProof [LOWER BOUND(ID), 284 ms] 307.80/291.53 (8) BEST 307.80/291.53 (9) proven lower bound 307.80/291.53 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 307.80/291.53 (11) BOUNDS(n^1, INF) 307.80/291.53 (12) typed CpxTrs 307.80/291.53 (13) RewriteLemmaProof [LOWER BOUND(ID), 41 ms] 307.80/291.53 (14) proven lower bound 307.80/291.53 (15) LowerBoundPropagationProof [FINISHED, 0 ms] 307.80/291.53 (16) BOUNDS(n^2, INF) 307.80/291.53 307.80/291.53 307.80/291.53 ---------------------------------------- 307.80/291.53 307.80/291.53 (0) 307.80/291.53 Obligation: 307.80/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 307.80/291.53 307.80/291.53 307.80/291.53 The TRS R consists of the following rules: 307.80/291.53 307.80/291.53 nonZero(0) -> false 307.80/291.53 nonZero(s(x)) -> true 307.80/291.53 p(s(0)) -> 0 307.80/291.53 p(s(s(x))) -> s(p(s(x))) 307.80/291.53 id_inc(x) -> x 307.80/291.53 id_inc(x) -> s(x) 307.80/291.53 random(x) -> rand(x, 0) 307.80/291.53 rand(x, y) -> if(nonZero(x), x, y) 307.80/291.53 if(false, x, y) -> y 307.80/291.53 if(true, x, y) -> rand(p(x), id_inc(y)) 307.80/291.53 307.80/291.53 S is empty. 307.80/291.53 Rewrite Strategy: FULL 307.80/291.53 ---------------------------------------- 307.80/291.53 307.80/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 307.80/291.53 Renamed function symbols to avoid clashes with predefined symbol. 307.80/291.53 ---------------------------------------- 307.80/291.53 307.80/291.53 (2) 307.80/291.53 Obligation: 307.80/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 307.80/291.53 307.80/291.53 307.80/291.53 The TRS R consists of the following rules: 307.80/291.53 307.80/291.53 nonZero(0') -> false 307.80/291.53 nonZero(s(x)) -> true 307.80/291.53 p(s(0')) -> 0' 307.80/291.53 p(s(s(x))) -> s(p(s(x))) 307.80/291.53 id_inc(x) -> x 307.80/291.53 id_inc(x) -> s(x) 307.80/291.53 random(x) -> rand(x, 0') 307.80/291.53 rand(x, y) -> if(nonZero(x), x, y) 307.80/291.53 if(false, x, y) -> y 307.80/291.53 if(true, x, y) -> rand(p(x), id_inc(y)) 307.80/291.53 307.80/291.53 S is empty. 307.80/291.53 Rewrite Strategy: FULL 307.80/291.53 ---------------------------------------- 307.80/291.53 307.80/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 307.80/291.53 Infered types. 307.80/291.53 ---------------------------------------- 307.80/291.53 307.80/291.53 (4) 307.80/291.53 Obligation: 307.80/291.53 TRS: 307.80/291.53 Rules: 307.80/291.53 nonZero(0') -> false 307.80/291.53 nonZero(s(x)) -> true 307.80/291.53 p(s(0')) -> 0' 307.80/291.53 p(s(s(x))) -> s(p(s(x))) 307.80/291.53 id_inc(x) -> x 307.80/291.53 id_inc(x) -> s(x) 307.80/291.53 random(x) -> rand(x, 0') 307.80/291.53 rand(x, y) -> if(nonZero(x), x, y) 307.80/291.53 if(false, x, y) -> y 307.80/291.53 if(true, x, y) -> rand(p(x), id_inc(y)) 307.80/291.53 307.80/291.53 Types: 307.80/291.53 nonZero :: 0':s -> false:true 307.80/291.53 0' :: 0':s 307.80/291.53 false :: false:true 307.80/291.53 s :: 0':s -> 0':s
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