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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307727
details
property
value
status
complete
benchmark
#3.5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n017.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.4093 seconds
cpu usage
30.4109
user time
28.5752
system time
1.83567
max virtual memory
1.9147756E7
max residence set size
3919160.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
30.27/10.37 WORST_CASE(Omega(n^1), O(n^1)) 30.27/10.38 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.27/10.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.27/10.38 30.27/10.38 30.27/10.38 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 30.27/10.38 30.27/10.38 (0) CpxTRS 30.27/10.38 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 30.27/10.38 (2) CpxTRS 30.27/10.38 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 30.27/10.38 (4) CpxWeightedTrs 30.27/10.38 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] 30.27/10.38 (6) CpxTypedWeightedTrs 30.27/10.38 (7) CompletionProof [UPPER BOUND(ID), 4 ms] 30.27/10.38 (8) CpxTypedWeightedCompleteTrs 30.27/10.38 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 30.27/10.38 (10) CpxRNTS 30.27/10.38 (11) CompleteCoflocoProof [FINISHED, 486 ms] 30.27/10.38 (12) BOUNDS(1, n^1) 30.27/10.38 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 30.27/10.38 (14) CpxTRS 30.27/10.38 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 30.27/10.38 (16) typed CpxTrs 30.27/10.38 (17) OrderProof [LOWER BOUND(ID), 0 ms] 30.27/10.38 (18) typed CpxTrs 30.27/10.38 (19) RewriteLemmaProof [LOWER BOUND(ID), 248 ms] 30.27/10.38 (20) BEST 30.27/10.38 (21) proven lower bound 30.27/10.38 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 30.27/10.38 (23) BOUNDS(n^1, INF) 30.27/10.38 (24) typed CpxTrs 30.27/10.38 (25) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] 30.27/10.38 (26) typed CpxTrs 30.27/10.38 30.27/10.38 30.27/10.38 ---------------------------------------- 30.27/10.38 30.27/10.38 (0) 30.27/10.38 Obligation: 30.27/10.38 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 30.27/10.38 30.27/10.38 30.27/10.38 The TRS R consists of the following rules: 30.27/10.38 30.27/10.38 le(0, y) -> true 30.27/10.38 le(s(x), 0) -> false 30.27/10.38 le(s(x), s(y)) -> le(x, y) 30.27/10.38 minus(x, 0) -> x 30.27/10.38 minus(s(x), s(y)) -> minus(x, y) 30.27/10.38 mod(0, y) -> 0 30.27/10.38 mod(s(x), 0) -> 0 30.27/10.38 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) 30.27/10.38 if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y)) 30.27/10.38 if_mod(false, s(x), s(y)) -> s(x) 30.27/10.38 30.27/10.38 S is empty. 30.27/10.38 Rewrite Strategy: FULL 30.27/10.38 ---------------------------------------- 30.27/10.38 30.27/10.38 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 30.27/10.38 Converted rc-obligation to irc-obligation. 30.27/10.38 30.27/10.38 The duplicating contexts are: 30.27/10.38 mod(s(x), s([])) 30.27/10.38 mod(s([]), s(y)) 30.27/10.38 if_mod(true, s(x), s([])) 30.27/10.38 30.27/10.38 30.27/10.38 The defined contexts are: 30.27/10.38 if_mod([], s(x1), s(x2)) 30.27/10.38 mod([], s(x1)) 30.27/10.38 le(x0, []) 30.27/10.38 if_mod(x0, s([]), s(x2)) 30.27/10.38 minus([], x1) 30.27/10.38 30.27/10.38 30.27/10.38 [] just represents basic- or constructor-terms in the following defined contexts: 30.27/10.38 if_mod([], s(x1), s(x2)) 30.27/10.38 mod([], s(x1)) 30.27/10.38 30.27/10.38 30.27/10.38 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 30.27/10.38 ---------------------------------------- 30.27/10.38 30.27/10.38 (2) 30.27/10.38 Obligation: 30.27/10.38 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 30.27/10.38 30.27/10.38 30.27/10.38 The TRS R consists of the following rules: 30.27/10.38 30.27/10.38 le(0, y) -> true 30.27/10.38 le(s(x), 0) -> false 30.27/10.38 le(s(x), s(y)) -> le(x, y) 30.27/10.38 minus(x, 0) -> x 30.27/10.38 minus(s(x), s(y)) -> minus(x, y) 30.27/10.38 mod(0, y) -> 0 30.27/10.38 mod(s(x), 0) -> 0 30.27/10.38 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
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