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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308541
details
property
value
status
complete
benchmark
z13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.605 seconds
cpu usage
1083.8
user time
1065.78
system time
18.0288
max virtual memory
5.5904308E7
max residence set size
1.4703464E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1083.45/291.51 WORST_CASE(Omega(n^1), ?) 1083.45/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1083.45/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1083.45/291.53 1083.45/291.53 1083.45/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1083.45/291.53 1083.45/291.53 (0) CpxTRS 1083.45/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1083.45/291.53 (2) TRS for Loop Detection 1083.45/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1083.45/291.53 (4) BEST 1083.45/291.53 (5) proven lower bound 1083.45/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1083.45/291.53 (7) BOUNDS(n^1, INF) 1083.45/291.53 (8) TRS for Loop Detection 1083.45/291.53 1083.45/291.53 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (0) 1083.45/291.53 Obligation: 1083.45/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1083.45/291.53 1083.45/291.53 1083.45/291.53 The TRS R consists of the following rules: 1083.45/291.53 1083.45/291.53 f(x, a(b(y))) -> f(a(a(x)), y) 1083.45/291.53 f(x, b(a(y))) -> f(b(b(x)), y) 1083.45/291.53 f(a(x), y) -> f(x, a(y)) 1083.45/291.53 f(b(x), y) -> f(x, b(y)) 1083.45/291.53 1083.45/291.53 S is empty. 1083.45/291.53 Rewrite Strategy: FULL 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1083.45/291.53 Transformed a relative TRS into a decreasing-loop problem. 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (2) 1083.45/291.53 Obligation: 1083.45/291.53 Analyzing the following TRS for decreasing loops: 1083.45/291.53 1083.45/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1083.45/291.53 1083.45/291.53 1083.45/291.53 The TRS R consists of the following rules: 1083.45/291.53 1083.45/291.53 f(x, a(b(y))) -> f(a(a(x)), y) 1083.45/291.53 f(x, b(a(y))) -> f(b(b(x)), y) 1083.45/291.53 f(a(x), y) -> f(x, a(y)) 1083.45/291.53 f(b(x), y) -> f(x, b(y)) 1083.45/291.53 1083.45/291.53 S is empty. 1083.45/291.53 Rewrite Strategy: FULL 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1083.45/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1083.45/291.53 1083.45/291.53 The rewrite sequence 1083.45/291.53 1083.45/291.53 f(x, a(b(y))) ->^+ f(a(a(x)), y) 1083.45/291.53 1083.45/291.53 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1083.45/291.53 1083.45/291.53 The pumping substitution is [y / a(b(y))]. 1083.45/291.53 1083.45/291.53 The result substitution is [x / a(a(x))]. 1083.45/291.53 1083.45/291.53 1083.45/291.53 1083.45/291.53 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (4) 1083.45/291.53 Complex Obligation (BEST) 1083.45/291.53 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (5) 1083.45/291.53 Obligation: 1083.45/291.53 Proved the lower bound n^1 for the following obligation: 1083.45/291.53 1083.45/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1083.45/291.53 1083.45/291.53 1083.45/291.53 The TRS R consists of the following rules: 1083.45/291.53 1083.45/291.53 f(x, a(b(y))) -> f(a(a(x)), y) 1083.45/291.53 f(x, b(a(y))) -> f(b(b(x)), y) 1083.45/291.53 f(a(x), y) -> f(x, a(y)) 1083.45/291.53 f(b(x), y) -> f(x, b(y)) 1083.45/291.53 1083.45/291.53 S is empty. 1083.45/291.53 Rewrite Strategy: FULL 1083.45/291.53 ---------------------------------------- 1083.45/291.53 1083.45/291.53 (6) LowerBoundPropagationProof (FINISHED)
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