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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307810
details
property
value
status
complete
benchmark
identity.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n065.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.595 seconds
cpu usage
884.874
user time
874.0
system time
10.8732
max virtual memory
5.6609132E7
max residence set size
1.0198836E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
884.71/291.54 WORST_CASE(Omega(n^1), ?) 884.71/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 884.71/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 884.71/291.54 884.71/291.54 884.71/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 884.71/291.54 884.71/291.54 (0) CpxTRS 884.71/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 884.71/291.54 (2) TRS for Loop Detection 884.71/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 884.71/291.54 (4) BEST 884.71/291.54 (5) proven lower bound 884.71/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 884.71/291.54 (7) BOUNDS(n^1, INF) 884.71/291.54 (8) TRS for Loop Detection 884.71/291.54 884.71/291.54 884.71/291.54 ---------------------------------------- 884.71/291.54 884.71/291.54 (0) 884.71/291.54 Obligation: 884.71/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 884.71/291.54 884.71/291.54 884.71/291.54 The TRS R consists of the following rules: 884.71/291.54 884.71/291.54 g(x, 0) -> 0 884.71/291.54 g(d, s(x)) -> s(s(g(d, x))) 884.71/291.54 g(h, s(0)) -> 0 884.71/291.54 g(h, s(s(x))) -> s(g(h, x)) 884.71/291.54 double(x) -> g(d, x) 884.71/291.54 half(x) -> g(h, x) 884.71/291.54 f(s(x), y) -> f(half(s(x)), double(y)) 884.71/291.54 f(s(0), y) -> y 884.71/291.54 id(x) -> f(x, s(0)) 884.71/291.54 884.71/291.54 S is empty. 884.71/291.54 Rewrite Strategy: FULL 884.71/291.54 ---------------------------------------- 884.71/291.54 884.71/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 884.71/291.54 Transformed a relative TRS into a decreasing-loop problem. 884.71/291.54 ---------------------------------------- 884.71/291.54 884.71/291.54 (2) 884.71/291.54 Obligation: 884.71/291.54 Analyzing the following TRS for decreasing loops: 884.71/291.54 884.71/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 884.71/291.54 884.71/291.54 884.71/291.54 The TRS R consists of the following rules: 884.71/291.54 884.71/291.54 g(x, 0) -> 0 884.71/291.54 g(d, s(x)) -> s(s(g(d, x))) 884.71/291.54 g(h, s(0)) -> 0 884.71/291.54 g(h, s(s(x))) -> s(g(h, x)) 884.71/291.54 double(x) -> g(d, x) 884.71/291.54 half(x) -> g(h, x) 884.71/291.54 f(s(x), y) -> f(half(s(x)), double(y)) 884.71/291.54 f(s(0), y) -> y 884.71/291.54 id(x) -> f(x, s(0)) 884.71/291.54 884.71/291.54 S is empty. 884.71/291.54 Rewrite Strategy: FULL 884.71/291.54 ---------------------------------------- 884.71/291.54 884.71/291.54 (3) DecreasingLoopProof (LOWER BOUND(ID)) 884.71/291.54 The following loop(s) give(s) rise to the lower bound Omega(n^1): 884.71/291.54 884.71/291.54 The rewrite sequence 884.71/291.54 884.71/291.54 g(h, s(s(x))) ->^+ s(g(h, x)) 884.71/291.54 884.71/291.54 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 884.71/291.54 884.71/291.54 The pumping substitution is [x / s(s(x))]. 884.71/291.54 884.71/291.54 The result substitution is [ ]. 884.71/291.54 884.71/291.54 884.71/291.54 884.71/291.54 884.71/291.54 ---------------------------------------- 884.71/291.54 884.71/291.54 (4) 884.71/291.54 Complex Obligation (BEST) 884.71/291.54 884.71/291.54 ---------------------------------------- 884.71/291.54 884.71/291.54 (5) 884.71/291.54 Obligation: 884.71/291.54 Proved the lower bound n^1 for the following obligation: 884.71/291.54 884.71/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 884.71/291.54 884.71/291.54 884.71/291.54 The TRS R consists of the following rules: 884.71/291.54
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