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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307683
details
property
value
status
complete
benchmark
Liveness6.4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n125.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.747 seconds
cpu usage
1090.76
user time
1072.17
system time
18.59
max virtual memory
3.8050524E7
max residence set size
1.4999148E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1090.35/291.54 WORST_CASE(Omega(n^1), ?) 1090.35/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1090.35/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1090.35/291.57 1090.35/291.57 1090.35/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1090.35/291.57 1090.35/291.57 (0) CpxTRS 1090.35/291.57 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1090.35/291.57 (2) TRS for Loop Detection 1090.35/291.57 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1090.35/291.57 (4) BEST 1090.35/291.57 (5) proven lower bound 1090.35/291.57 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1090.35/291.57 (7) BOUNDS(n^1, INF) 1090.35/291.57 (8) TRS for Loop Detection 1090.35/291.57 1090.35/291.57 1090.35/291.57 ---------------------------------------- 1090.35/291.57 1090.35/291.57 (0) 1090.35/291.57 Obligation: 1090.35/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1090.35/291.57 1090.35/291.57 1090.35/291.57 The TRS R consists of the following rules: 1090.35/291.57 1090.35/291.57 top1(free(x), y) -> top2(check(new(x)), y) 1090.35/291.57 top1(free(x), y) -> top2(new(x), check(y)) 1090.35/291.57 top1(free(x), y) -> top2(check(x), new(y)) 1090.35/291.57 top1(free(x), y) -> top2(x, check(new(y))) 1090.35/291.57 top2(x, free(y)) -> top1(check(new(x)), y) 1090.35/291.57 top2(x, free(y)) -> top1(new(x), check(y)) 1090.35/291.57 top2(x, free(y)) -> top1(check(x), new(y)) 1090.35/291.57 top2(x, free(y)) -> top1(x, check(new(y))) 1090.35/291.57 new(free(x)) -> free(new(x)) 1090.35/291.57 old(free(x)) -> free(old(x)) 1090.35/291.57 new(serve) -> free(serve) 1090.35/291.57 old(serve) -> free(serve) 1090.35/291.57 check(free(x)) -> free(check(x)) 1090.35/291.57 check(new(x)) -> new(check(x)) 1090.35/291.57 check(old(x)) -> old(check(x)) 1090.35/291.57 check(old(x)) -> old(x) 1090.35/291.57 1090.35/291.57 S is empty. 1090.35/291.57 Rewrite Strategy: FULL 1090.35/291.57 ---------------------------------------- 1090.35/291.57 1090.35/291.57 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1090.35/291.57 Transformed a relative TRS into a decreasing-loop problem. 1090.35/291.57 ---------------------------------------- 1090.35/291.57 1090.35/291.57 (2) 1090.35/291.57 Obligation: 1090.35/291.57 Analyzing the following TRS for decreasing loops: 1090.35/291.57 1090.35/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1090.35/291.57 1090.35/291.57 1090.35/291.57 The TRS R consists of the following rules: 1090.35/291.57 1090.35/291.57 top1(free(x), y) -> top2(check(new(x)), y) 1090.35/291.57 top1(free(x), y) -> top2(new(x), check(y)) 1090.35/291.57 top1(free(x), y) -> top2(check(x), new(y)) 1090.35/291.57 top1(free(x), y) -> top2(x, check(new(y))) 1090.35/291.57 top2(x, free(y)) -> top1(check(new(x)), y) 1090.35/291.57 top2(x, free(y)) -> top1(new(x), check(y)) 1090.35/291.57 top2(x, free(y)) -> top1(check(x), new(y)) 1090.35/291.57 top2(x, free(y)) -> top1(x, check(new(y))) 1090.35/291.57 new(free(x)) -> free(new(x)) 1090.35/291.57 old(free(x)) -> free(old(x)) 1090.35/291.57 new(serve) -> free(serve) 1090.35/291.57 old(serve) -> free(serve) 1090.35/291.57 check(free(x)) -> free(check(x)) 1090.35/291.57 check(new(x)) -> new(check(x)) 1090.35/291.57 check(old(x)) -> old(check(x)) 1090.35/291.57 check(old(x)) -> old(x) 1090.35/291.57 1090.35/291.57 S is empty. 1090.35/291.57 Rewrite Strategy: FULL 1090.35/291.57 ---------------------------------------- 1090.35/291.57 1090.35/291.57 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1090.35/291.57 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1090.35/291.57 1090.35/291.57 The rewrite sequence 1090.35/291.57 1090.35/291.57 check(free(x)) ->^+ free(check(x)) 1090.35/291.57 1090.35/291.57 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1090.35/291.57 1090.35/291.57 The pumping substitution is [x / free(x)]. 1090.35/291.57 1090.35/291.57 The result substitution is [ ]. 1090.35/291.57 1090.35/291.57 1090.35/291.57 1090.35/291.57 1090.35/291.57 ---------------------------------------- 1090.35/291.57
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