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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307724
details
property
value
status
complete
benchmark
#3.26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.571 seconds
cpu usage
704.899
user time
698.672
system time
6.22729
max virtual memory
1.9018676E7
max residence set size
8934548.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
704.74/291.52 WORST_CASE(Omega(n^1), ?) 704.82/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 704.82/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 704.82/291.53 704.82/291.53 704.82/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 704.82/291.53 704.82/291.53 (0) CpxTRS 704.82/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 704.82/291.53 (2) TRS for Loop Detection 704.82/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 704.82/291.53 (4) BEST 704.82/291.53 (5) proven lower bound 704.82/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 704.82/291.53 (7) BOUNDS(n^1, INF) 704.82/291.53 (8) TRS for Loop Detection 704.82/291.53 704.82/291.53 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (0) 704.82/291.53 Obligation: 704.82/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 704.82/291.53 704.82/291.53 704.82/291.53 The TRS R consists of the following rules: 704.82/291.53 704.82/291.53 f(x) -> s(x) 704.82/291.53 f(s(s(x))) -> s(f(f(x))) 704.82/291.53 704.82/291.53 S is empty. 704.82/291.53 Rewrite Strategy: FULL 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 704.82/291.53 Transformed a relative TRS into a decreasing-loop problem. 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (2) 704.82/291.53 Obligation: 704.82/291.53 Analyzing the following TRS for decreasing loops: 704.82/291.53 704.82/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 704.82/291.53 704.82/291.53 704.82/291.53 The TRS R consists of the following rules: 704.82/291.53 704.82/291.53 f(x) -> s(x) 704.82/291.53 f(s(s(x))) -> s(f(f(x))) 704.82/291.53 704.82/291.53 S is empty. 704.82/291.53 Rewrite Strategy: FULL 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 704.82/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 704.82/291.53 704.82/291.53 The rewrite sequence 704.82/291.53 704.82/291.53 f(s(s(x))) ->^+ s(f(f(x))) 704.82/291.53 704.82/291.53 gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0]. 704.82/291.53 704.82/291.53 The pumping substitution is [x / s(s(x))]. 704.82/291.53 704.82/291.53 The result substitution is [ ]. 704.82/291.53 704.82/291.53 704.82/291.53 704.82/291.53 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (4) 704.82/291.53 Complex Obligation (BEST) 704.82/291.53 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (5) 704.82/291.53 Obligation: 704.82/291.53 Proved the lower bound n^1 for the following obligation: 704.82/291.53 704.82/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 704.82/291.53 704.82/291.53 704.82/291.53 The TRS R consists of the following rules: 704.82/291.53 704.82/291.53 f(x) -> s(x) 704.82/291.53 f(s(s(x))) -> s(f(f(x))) 704.82/291.53 704.82/291.53 S is empty. 704.82/291.53 Rewrite Strategy: FULL 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (6) LowerBoundPropagationProof (FINISHED) 704.82/291.53 Propagated lower bound. 704.82/291.53 ---------------------------------------- 704.82/291.53 704.82/291.53 (7) 704.82/291.53 BOUNDS(n^1, INF) 704.82/291.53
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