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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313674
details
property
value
status
complete
benchmark
factorial2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.597 seconds
cpu usage
1127.16
user time
1114.41
system time
12.749
max virtual memory
5.749576E7
max residence set size
1.3999604E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
1126.85/291.50 WORST_CASE(Omega(n^3), ?) 1126.85/291.52 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1126.85/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1126.85/291.52 1126.85/291.52 1126.85/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 1126.85/291.52 1126.85/291.52 (0) CpxTRS 1126.85/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1126.85/291.52 (2) CpxTRS 1126.85/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1126.85/291.52 (4) typed CpxTrs 1126.85/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1126.85/291.52 (6) typed CpxTrs 1126.85/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 311 ms] 1126.85/291.52 (8) BEST 1126.85/291.52 (9) proven lower bound 1126.85/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1126.85/291.52 (11) BOUNDS(n^1, INF) 1126.85/291.52 (12) typed CpxTrs 1126.85/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 85 ms] 1126.85/291.52 (14) BEST 1126.85/291.52 (15) proven lower bound 1126.85/291.52 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1126.85/291.52 (17) BOUNDS(n^2, INF) 1126.85/291.52 (18) typed CpxTrs 1126.85/291.52 (19) RewriteLemmaProof [LOWER BOUND(ID), 609 ms] 1126.85/291.52 (20) typed CpxTrs 1126.85/291.52 (21) RewriteLemmaProof [LOWER BOUND(ID), 266 ms] 1126.85/291.52 (22) proven lower bound 1126.85/291.52 (23) LowerBoundPropagationProof [FINISHED, 0 ms] 1126.85/291.52 (24) BOUNDS(n^3, INF) 1126.85/291.52 1126.85/291.52 1126.85/291.52 ---------------------------------------- 1126.85/291.52 1126.85/291.52 (0) 1126.85/291.52 Obligation: 1126.85/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 1126.85/291.52 1126.85/291.52 1126.85/291.52 The TRS R consists of the following rules: 1126.85/291.52 1126.85/291.52 plus(0, x) -> x 1126.85/291.52 plus(s(x), y) -> s(plus(x, y)) 1126.85/291.52 times(0, y) -> 0 1126.85/291.52 times(s(x), y) -> plus(y, times(x, y)) 1126.85/291.52 p(s(x)) -> x 1126.85/291.52 p(0) -> 0 1126.85/291.52 minus(x, 0) -> x 1126.85/291.52 minus(0, x) -> 0 1126.85/291.52 minus(x, s(y)) -> p(minus(x, y)) 1126.85/291.52 isZero(0) -> true 1126.85/291.52 isZero(s(x)) -> false 1126.85/291.52 facIter(x, y) -> if(isZero(x), minus(x, s(0)), y, times(y, x)) 1126.85/291.52 if(true, x, y, z) -> y 1126.85/291.52 if(false, x, y, z) -> facIter(x, z) 1126.85/291.52 factorial(x) -> facIter(x, s(0)) 1126.85/291.52 1126.85/291.52 S is empty. 1126.85/291.52 Rewrite Strategy: INNERMOST 1126.85/291.52 ---------------------------------------- 1126.85/291.52 1126.85/291.52 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1126.85/291.52 Renamed function symbols to avoid clashes with predefined symbol. 1126.85/291.52 ---------------------------------------- 1126.85/291.52 1126.85/291.52 (2) 1126.85/291.52 Obligation: 1126.85/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 1126.85/291.52 1126.85/291.52 1126.85/291.52 The TRS R consists of the following rules: 1126.85/291.52 1126.85/291.52 plus(0', x) -> x 1126.85/291.52 plus(s(x), y) -> s(plus(x, y)) 1126.85/291.52 times(0', y) -> 0' 1126.85/291.52 times(s(x), y) -> plus(y, times(x, y)) 1126.85/291.52 p(s(x)) -> x 1126.85/291.52 p(0') -> 0' 1126.85/291.52 minus(x, 0') -> x 1126.85/291.52 minus(0', x) -> 0' 1126.85/291.52 minus(x, s(y)) -> p(minus(x, y)) 1126.85/291.52 isZero(0') -> true 1126.85/291.52 isZero(s(x)) -> false 1126.85/291.52 facIter(x, y) -> if(isZero(x), minus(x, s(0')), y, times(y, x)) 1126.85/291.52 if(true, x, y, z) -> y 1126.85/291.52 if(false, x, y, z) -> facIter(x, z) 1126.85/291.52 factorial(x) -> facIter(x, s(0')) 1126.85/291.52 1126.85/291.52 S is empty. 1126.85/291.52 Rewrite Strategy: INNERMOST 1126.85/291.52 ---------------------------------------- 1126.85/291.52 1126.85/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1126.85/291.52 Infered types. 1126.85/291.52 ---------------------------------------- 1126.85/291.52 1126.85/291.52 (4) 1126.85/291.52 Obligation:
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