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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308538
details
property
value
status
complete
benchmark
z16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.815 seconds
cpu usage
960.364
user time
938.934
system time
21.4302
max virtual memory
5.6031844E7
max residence set size
1.4937604E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
959.15/291.54 WORST_CASE(Omega(n^1), ?) 960.26/291.75 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 960.26/291.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 960.26/291.75 960.26/291.75 960.26/291.75 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 960.26/291.75 960.26/291.75 (0) CpxTRS 960.26/291.75 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 960.26/291.75 (2) TRS for Loop Detection 960.26/291.75 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 960.26/291.75 (4) BEST 960.26/291.75 (5) proven lower bound 960.26/291.75 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 960.26/291.75 (7) BOUNDS(n^1, INF) 960.26/291.75 (8) TRS for Loop Detection 960.26/291.75 960.26/291.75 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (0) 960.26/291.75 Obligation: 960.26/291.75 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 960.26/291.75 960.26/291.75 960.26/291.75 The TRS R consists of the following rules: 960.26/291.75 960.26/291.75 f(x, a(b(y))) -> f(a(b(b(x))), y) 960.26/291.75 f(a(x), y) -> f(x, a(y)) 960.26/291.75 f(b(x), y) -> f(x, b(y)) 960.26/291.75 960.26/291.75 S is empty. 960.26/291.75 Rewrite Strategy: FULL 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 960.26/291.75 Transformed a relative TRS into a decreasing-loop problem. 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (2) 960.26/291.75 Obligation: 960.26/291.75 Analyzing the following TRS for decreasing loops: 960.26/291.75 960.26/291.75 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 960.26/291.75 960.26/291.75 960.26/291.75 The TRS R consists of the following rules: 960.26/291.75 960.26/291.75 f(x, a(b(y))) -> f(a(b(b(x))), y) 960.26/291.75 f(a(x), y) -> f(x, a(y)) 960.26/291.75 f(b(x), y) -> f(x, b(y)) 960.26/291.75 960.26/291.75 S is empty. 960.26/291.75 Rewrite Strategy: FULL 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (3) DecreasingLoopProof (LOWER BOUND(ID)) 960.26/291.75 The following loop(s) give(s) rise to the lower bound Omega(n^1): 960.26/291.75 960.26/291.75 The rewrite sequence 960.26/291.75 960.26/291.75 f(x, a(b(y))) ->^+ f(a(b(b(x))), y) 960.26/291.75 960.26/291.75 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 960.26/291.75 960.26/291.75 The pumping substitution is [y / a(b(y))]. 960.26/291.75 960.26/291.75 The result substitution is [x / a(b(b(x)))]. 960.26/291.75 960.26/291.75 960.26/291.75 960.26/291.75 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (4) 960.26/291.75 Complex Obligation (BEST) 960.26/291.75 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (5) 960.26/291.75 Obligation: 960.26/291.75 Proved the lower bound n^1 for the following obligation: 960.26/291.75 960.26/291.75 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 960.26/291.75 960.26/291.75 960.26/291.75 The TRS R consists of the following rules: 960.26/291.75 960.26/291.75 f(x, a(b(y))) -> f(a(b(b(x))), y) 960.26/291.75 f(a(x), y) -> f(x, a(y)) 960.26/291.75 f(b(x), y) -> f(x, b(y)) 960.26/291.75 960.26/291.75 S is empty. 960.26/291.75 Rewrite Strategy: FULL 960.26/291.75 ---------------------------------------- 960.26/291.75 960.26/291.75 (6) LowerBoundPropagationProof (FINISHED) 960.26/291.75 Propagated lower bound. 960.26/291.75 ---------------------------------------- 960.26/291.75
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