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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307797
details
property
value
status
complete
benchmark
thiemann12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n165.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.602 seconds
cpu usage
306.049
user time
303.759
system time
2.2905
max virtual memory
1.8279384E7
max residence set size
5455880.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
305.94/291.56 WORST_CASE(Omega(n^1), ?) 305.94/291.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 305.94/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 305.94/291.57 305.94/291.57 305.94/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.94/291.57 305.94/291.57 (0) CpxTRS 305.94/291.57 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 305.94/291.57 (2) TRS for Loop Detection 305.94/291.57 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 305.94/291.57 (4) BEST 305.94/291.57 (5) proven lower bound 305.94/291.57 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 305.94/291.57 (7) BOUNDS(n^1, INF) 305.94/291.57 (8) TRS for Loop Detection 305.94/291.57 305.94/291.57 305.94/291.57 ---------------------------------------- 305.94/291.57 305.94/291.57 (0) 305.94/291.57 Obligation: 305.94/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.94/291.57 305.94/291.57 305.94/291.57 The TRS R consists of the following rules: 305.94/291.57 305.94/291.57 half(0) -> 0 305.94/291.57 half(s(0)) -> 0 305.94/291.57 half(s(s(x))) -> s(half(x)) 305.94/291.57 le(0, y) -> true 305.94/291.57 le(s(x), 0) -> false 305.94/291.57 le(s(x), s(y)) -> le(x, y) 305.94/291.57 inc(0) -> 0 305.94/291.57 inc(s(x)) -> s(inc(x)) 305.94/291.57 log(x) -> log2(x, 0) 305.94/291.57 log2(x, y) -> if(le(x, s(0)), x, inc(y)) 305.94/291.57 if(true, x, s(y)) -> y 305.94/291.57 if(false, x, y) -> log2(half(x), y) 305.94/291.57 305.94/291.57 S is empty. 305.94/291.57 Rewrite Strategy: FULL 305.94/291.57 ---------------------------------------- 305.94/291.57 305.94/291.57 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 305.94/291.57 Transformed a relative TRS into a decreasing-loop problem. 305.94/291.57 ---------------------------------------- 305.94/291.57 305.94/291.57 (2) 305.94/291.57 Obligation: 305.94/291.57 Analyzing the following TRS for decreasing loops: 305.94/291.57 305.94/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.94/291.57 305.94/291.57 305.94/291.57 The TRS R consists of the following rules: 305.94/291.57 305.94/291.57 half(0) -> 0 305.94/291.57 half(s(0)) -> 0 305.94/291.57 half(s(s(x))) -> s(half(x)) 305.94/291.57 le(0, y) -> true 305.94/291.57 le(s(x), 0) -> false 305.94/291.57 le(s(x), s(y)) -> le(x, y) 305.94/291.57 inc(0) -> 0 305.94/291.57 inc(s(x)) -> s(inc(x)) 305.94/291.57 log(x) -> log2(x, 0) 305.94/291.57 log2(x, y) -> if(le(x, s(0)), x, inc(y)) 305.94/291.57 if(true, x, s(y)) -> y 305.94/291.57 if(false, x, y) -> log2(half(x), y) 305.94/291.57 305.94/291.57 S is empty. 305.94/291.57 Rewrite Strategy: FULL 305.94/291.57 ---------------------------------------- 305.94/291.57 305.94/291.57 (3) DecreasingLoopProof (LOWER BOUND(ID)) 305.94/291.57 The following loop(s) give(s) rise to the lower bound Omega(n^1): 305.94/291.57 305.94/291.57 The rewrite sequence 305.94/291.57 305.94/291.57 half(s(s(x))) ->^+ s(half(x)) 305.94/291.57 305.94/291.57 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 305.94/291.57 305.94/291.57 The pumping substitution is [x / s(s(x))]. 305.94/291.57 305.94/291.57 The result substitution is [ ]. 305.94/291.57 305.94/291.57 305.94/291.57 305.94/291.57 305.94/291.57 ---------------------------------------- 305.94/291.57 305.94/291.57 (4) 305.94/291.57 Complex Obligation (BEST) 305.94/291.57 305.94/291.57 ---------------------------------------- 305.94/291.57 305.94/291.57 (5) 305.94/291.57 Obligation: 305.94/291.57 Proved the lower bound n^1 for the following obligation:
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