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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307646
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.59 seconds
cpu usage
308.185
user time
306.206
system time
1.97862
max virtual memory
1.8281752E7
max residence set size
5350248.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
308.13/291.55 WORST_CASE(Omega(n^1), ?) 308.14/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 308.14/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 308.14/291.56 308.14/291.56 308.14/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.14/291.56 308.14/291.56 (0) CpxTRS 308.14/291.56 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 308.14/291.56 (2) TRS for Loop Detection 308.14/291.56 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 308.14/291.56 (4) BEST 308.14/291.56 (5) proven lower bound 308.14/291.56 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 308.14/291.56 (7) BOUNDS(n^1, INF) 308.14/291.56 (8) TRS for Loop Detection 308.14/291.56 308.14/291.56 308.14/291.56 ---------------------------------------- 308.14/291.56 308.14/291.56 (0) 308.14/291.56 Obligation: 308.14/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.14/291.56 308.14/291.56 308.14/291.56 The TRS R consists of the following rules: 308.14/291.56 308.14/291.56 cond1(true, x) -> cond2(even(x), x) 308.14/291.56 cond2(true, x) -> cond1(neq(x, 0), div2(x)) 308.14/291.56 cond2(false, x) -> cond1(neq(x, 0), p(x)) 308.14/291.56 neq(0, 0) -> false 308.14/291.56 neq(0, s(x)) -> true 308.14/291.56 neq(s(x), 0) -> true 308.14/291.56 neq(s(x), s(y)) -> neq(x, y) 308.14/291.56 even(0) -> true 308.14/291.56 even(s(0)) -> false 308.14/291.56 even(s(s(x))) -> even(x) 308.14/291.56 div2(0) -> 0 308.14/291.56 div2(s(0)) -> 0 308.14/291.56 div2(s(s(x))) -> s(div2(x)) 308.14/291.56 p(0) -> 0 308.14/291.56 p(s(x)) -> x 308.14/291.56 308.14/291.56 S is empty. 308.14/291.56 Rewrite Strategy: FULL 308.14/291.56 ---------------------------------------- 308.14/291.56 308.14/291.56 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 308.14/291.56 Transformed a relative TRS into a decreasing-loop problem. 308.14/291.56 ---------------------------------------- 308.14/291.56 308.14/291.56 (2) 308.14/291.56 Obligation: 308.14/291.56 Analyzing the following TRS for decreasing loops: 308.14/291.56 308.14/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.14/291.56 308.14/291.56 308.14/291.56 The TRS R consists of the following rules: 308.14/291.56 308.14/291.56 cond1(true, x) -> cond2(even(x), x) 308.14/291.56 cond2(true, x) -> cond1(neq(x, 0), div2(x)) 308.14/291.56 cond2(false, x) -> cond1(neq(x, 0), p(x)) 308.14/291.56 neq(0, 0) -> false 308.14/291.56 neq(0, s(x)) -> true 308.14/291.56 neq(s(x), 0) -> true 308.14/291.56 neq(s(x), s(y)) -> neq(x, y) 308.14/291.56 even(0) -> true 308.14/291.56 even(s(0)) -> false 308.14/291.56 even(s(s(x))) -> even(x) 308.14/291.56 div2(0) -> 0 308.14/291.56 div2(s(0)) -> 0 308.14/291.56 div2(s(s(x))) -> s(div2(x)) 308.14/291.56 p(0) -> 0 308.14/291.56 p(s(x)) -> x 308.14/291.56 308.14/291.56 S is empty. 308.14/291.56 Rewrite Strategy: FULL 308.14/291.56 ---------------------------------------- 308.14/291.56 308.14/291.56 (3) DecreasingLoopProof (LOWER BOUND(ID)) 308.14/291.56 The following loop(s) give(s) rise to the lower bound Omega(n^1): 308.14/291.56 308.14/291.56 The rewrite sequence 308.14/291.56 308.14/291.56 even(s(s(x))) ->^+ even(x) 308.14/291.56 308.14/291.56 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 308.14/291.56 308.14/291.56 The pumping substitution is [x / s(s(x))]. 308.14/291.56 308.14/291.56 The result substitution is [ ]. 308.14/291.56 308.14/291.56 308.14/291.56 308.14/291.56 308.14/291.56 ---------------------------------------- 308.14/291.56 308.14/291.56 (4) 308.14/291.56 Complex Obligation (BEST)
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