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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307657
details
property
value
status
complete
benchmark
5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.543 seconds
cpu usage
302.364
user time
300.667
system time
1.69762
max virtual memory
1.8281984E7
max residence set size
5115220.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
302.26/291.50 WORST_CASE(Omega(n^1), ?) 302.26/291.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 302.26/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 302.26/291.50 302.26/291.50 302.26/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 302.26/291.50 302.26/291.50 (0) CpxTRS 302.26/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 302.26/291.50 (2) TRS for Loop Detection 302.26/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 302.26/291.50 (4) BEST 302.26/291.50 (5) proven lower bound 302.26/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 302.26/291.50 (7) BOUNDS(n^1, INF) 302.26/291.50 (8) TRS for Loop Detection 302.26/291.50 302.26/291.50 302.26/291.50 ---------------------------------------- 302.26/291.50 302.26/291.50 (0) 302.26/291.50 Obligation: 302.26/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 302.26/291.50 302.26/291.50 302.26/291.50 The TRS R consists of the following rules: 302.26/291.50 302.26/291.50 cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x)) 302.26/291.50 and(x, false) -> false 302.26/291.50 and(false, x) -> false 302.26/291.50 and(true, true) -> true 302.26/291.50 even(0) -> true 302.26/291.50 even(s(0)) -> false 302.26/291.50 even(s(s(x))) -> even(x) 302.26/291.50 gr(0, x) -> false 302.26/291.50 gr(s(x), 0) -> true 302.26/291.50 gr(s(x), s(y)) -> gr(x, y) 302.26/291.50 p(0) -> 0 302.26/291.50 p(s(x)) -> x 302.26/291.50 302.26/291.50 S is empty. 302.26/291.50 Rewrite Strategy: FULL 302.26/291.50 ---------------------------------------- 302.26/291.50 302.26/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 302.26/291.50 Transformed a relative TRS into a decreasing-loop problem. 302.26/291.50 ---------------------------------------- 302.26/291.50 302.26/291.50 (2) 302.26/291.50 Obligation: 302.26/291.50 Analyzing the following TRS for decreasing loops: 302.26/291.50 302.26/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 302.26/291.50 302.26/291.50 302.26/291.50 The TRS R consists of the following rules: 302.26/291.50 302.26/291.50 cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x)) 302.26/291.50 and(x, false) -> false 302.26/291.50 and(false, x) -> false 302.26/291.50 and(true, true) -> true 302.26/291.50 even(0) -> true 302.26/291.50 even(s(0)) -> false 302.26/291.50 even(s(s(x))) -> even(x) 302.26/291.50 gr(0, x) -> false 302.26/291.50 gr(s(x), 0) -> true 302.26/291.50 gr(s(x), s(y)) -> gr(x, y) 302.26/291.50 p(0) -> 0 302.26/291.50 p(s(x)) -> x 302.26/291.50 302.26/291.50 S is empty. 302.26/291.50 Rewrite Strategy: FULL 302.26/291.50 ---------------------------------------- 302.26/291.50 302.26/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 302.26/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 302.26/291.50 302.26/291.50 The rewrite sequence 302.26/291.50 302.26/291.50 even(s(s(x))) ->^+ even(x) 302.26/291.50 302.26/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 302.26/291.50 302.26/291.50 The pumping substitution is [x / s(s(x))]. 302.26/291.50 302.26/291.50 The result substitution is [ ]. 302.26/291.50 302.26/291.50 302.26/291.50 302.26/291.50 302.26/291.50 ---------------------------------------- 302.26/291.50 302.26/291.50 (4) 302.26/291.50 Complex Obligation (BEST) 302.26/291.50 302.26/291.50 ---------------------------------------- 302.26/291.50 302.26/291.50 (5) 302.26/291.50 Obligation: 302.26/291.50 Proved the lower bound n^1 for the following obligation:
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