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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307788
details
property
value
status
complete
benchmark
thiemann15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.529 seconds
cpu usage
318.271
user time
316.208
system time
2.06291
max virtual memory
1.8281828E7
max residence set size
5463392.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
318.14/291.49 WORST_CASE(Omega(n^1), ?) 318.14/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 318.14/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 318.14/291.50 318.14/291.50 318.14/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 318.14/291.50 318.14/291.50 (0) CpxTRS 318.14/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 318.14/291.50 (2) TRS for Loop Detection 318.14/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 318.14/291.50 (4) BEST 318.14/291.50 (5) proven lower bound 318.14/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 318.14/291.50 (7) BOUNDS(n^1, INF) 318.14/291.50 (8) TRS for Loop Detection 318.14/291.50 318.14/291.50 318.14/291.50 ---------------------------------------- 318.14/291.50 318.14/291.50 (0) 318.14/291.50 Obligation: 318.14/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 318.14/291.50 318.14/291.50 318.14/291.50 The TRS R consists of the following rules: 318.14/291.50 318.14/291.50 half(0) -> 0 318.14/291.50 half(s(0)) -> 0 318.14/291.50 half(s(s(x))) -> s(half(x)) 318.14/291.50 inc(0) -> 0 318.14/291.50 inc(s(x)) -> s(inc(x)) 318.14/291.50 zero(0) -> true 318.14/291.50 zero(s(x)) -> false 318.14/291.50 p(0) -> 0 318.14/291.50 p(s(x)) -> x 318.14/291.50 bits(x) -> bitIter(x, 0) 318.14/291.50 bitIter(x, y) -> if(zero(x), x, inc(y)) 318.14/291.50 if(true, x, y) -> p(y) 318.14/291.50 if(false, x, y) -> bitIter(half(x), y) 318.14/291.50 318.14/291.50 S is empty. 318.14/291.50 Rewrite Strategy: FULL 318.14/291.50 ---------------------------------------- 318.14/291.50 318.14/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 318.14/291.50 Transformed a relative TRS into a decreasing-loop problem. 318.14/291.50 ---------------------------------------- 318.14/291.50 318.14/291.50 (2) 318.14/291.50 Obligation: 318.14/291.50 Analyzing the following TRS for decreasing loops: 318.14/291.50 318.14/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 318.14/291.50 318.14/291.50 318.14/291.50 The TRS R consists of the following rules: 318.14/291.50 318.14/291.50 half(0) -> 0 318.14/291.50 half(s(0)) -> 0 318.14/291.50 half(s(s(x))) -> s(half(x)) 318.14/291.50 inc(0) -> 0 318.14/291.50 inc(s(x)) -> s(inc(x)) 318.14/291.50 zero(0) -> true 318.14/291.50 zero(s(x)) -> false 318.14/291.50 p(0) -> 0 318.14/291.50 p(s(x)) -> x 318.14/291.50 bits(x) -> bitIter(x, 0) 318.14/291.50 bitIter(x, y) -> if(zero(x), x, inc(y)) 318.14/291.50 if(true, x, y) -> p(y) 318.14/291.50 if(false, x, y) -> bitIter(half(x), y) 318.14/291.50 318.14/291.50 S is empty. 318.14/291.50 Rewrite Strategy: FULL 318.14/291.50 ---------------------------------------- 318.14/291.50 318.14/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 318.14/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 318.14/291.50 318.14/291.50 The rewrite sequence 318.14/291.50 318.14/291.50 half(s(s(x))) ->^+ s(half(x)) 318.14/291.50 318.14/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 318.14/291.50 318.14/291.50 The pumping substitution is [x / s(s(x))]. 318.14/291.50 318.14/291.50 The result substitution is [ ]. 318.14/291.50 318.14/291.50 318.14/291.50 318.14/291.50 318.14/291.50 ---------------------------------------- 318.14/291.50 318.14/291.50 (4) 318.14/291.50 Complex Obligation (BEST) 318.14/291.50 318.14/291.50 ---------------------------------------- 318.14/291.50 318.14/291.50 (5)
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