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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307890
details
property
value
status
complete
benchmark
aprove4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.552 seconds
cpu usage
309.781
user time
307.486
system time
2.295
max virtual memory
1.8281448E7
max residence set size
5574396.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
309.55/291.46 WORST_CASE(Omega(n^1), ?) 309.73/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 309.73/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 309.73/291.51 309.73/291.51 309.73/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.73/291.51 309.73/291.51 (0) CpxTRS 309.73/291.51 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 309.73/291.51 (2) TRS for Loop Detection 309.73/291.51 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 309.73/291.51 (4) BEST 309.73/291.51 (5) proven lower bound 309.73/291.51 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 309.73/291.51 (7) BOUNDS(n^1, INF) 309.73/291.51 (8) TRS for Loop Detection 309.73/291.51 309.73/291.51 309.73/291.51 ---------------------------------------- 309.73/291.51 309.73/291.51 (0) 309.73/291.51 Obligation: 309.73/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.73/291.51 309.73/291.51 309.73/291.51 The TRS R consists of the following rules: 309.73/291.51 309.73/291.51 p(0) -> s(s(0)) 309.73/291.51 p(s(x)) -> x 309.73/291.51 p(p(s(x))) -> p(x) 309.73/291.51 le(p(s(x)), x) -> le(x, x) 309.73/291.51 le(0, y) -> true 309.73/291.51 le(s(x), 0) -> false 309.73/291.51 le(s(x), s(y)) -> le(x, y) 309.73/291.51 minus(x, y) -> if(le(x, y), x, y) 309.73/291.51 if(true, x, y) -> 0 309.73/291.51 if(false, x, y) -> s(minus(p(x), y)) 309.73/291.51 309.73/291.51 S is empty. 309.73/291.51 Rewrite Strategy: FULL 309.73/291.51 ---------------------------------------- 309.73/291.51 309.73/291.51 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 309.73/291.51 Transformed a relative TRS into a decreasing-loop problem. 309.73/291.51 ---------------------------------------- 309.73/291.51 309.73/291.51 (2) 309.73/291.51 Obligation: 309.73/291.51 Analyzing the following TRS for decreasing loops: 309.73/291.51 309.73/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.73/291.51 309.73/291.51 309.73/291.51 The TRS R consists of the following rules: 309.73/291.51 309.73/291.51 p(0) -> s(s(0)) 309.73/291.51 p(s(x)) -> x 309.73/291.51 p(p(s(x))) -> p(x) 309.73/291.51 le(p(s(x)), x) -> le(x, x) 309.73/291.51 le(0, y) -> true 309.73/291.51 le(s(x), 0) -> false 309.73/291.51 le(s(x), s(y)) -> le(x, y) 309.73/291.51 minus(x, y) -> if(le(x, y), x, y) 309.73/291.51 if(true, x, y) -> 0 309.73/291.51 if(false, x, y) -> s(minus(p(x), y)) 309.73/291.51 309.73/291.51 S is empty. 309.73/291.51 Rewrite Strategy: FULL 309.73/291.51 ---------------------------------------- 309.73/291.51 309.73/291.51 (3) DecreasingLoopProof (LOWER BOUND(ID)) 309.73/291.51 The following loop(s) give(s) rise to the lower bound Omega(n^1): 309.73/291.51 309.73/291.51 The rewrite sequence 309.73/291.51 309.73/291.51 le(s(x), s(y)) ->^+ le(x, y) 309.73/291.51 309.73/291.51 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 309.73/291.51 309.73/291.51 The pumping substitution is [x / s(x), y / s(y)]. 309.73/291.51 309.73/291.51 The result substitution is [ ]. 309.73/291.51 309.73/291.51 309.73/291.51 309.73/291.51 309.73/291.51 ---------------------------------------- 309.73/291.51 309.73/291.51 (4) 309.73/291.51 Complex Obligation (BEST) 309.73/291.51 309.73/291.51 ---------------------------------------- 309.73/291.51 309.73/291.51 (5) 309.73/291.51 Obligation: 309.73/291.51 Proved the lower bound n^1 for the following obligation: 309.73/291.51 309.73/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.73/291.51 309.73/291.51
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