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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307852
details
property
value
status
complete
benchmark
test1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.579 seconds
cpu usage
364.834
user time
356.31
system time
8.52351
max virtual memory
3.7233784E7
max residence set size
1.1033964E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
364.70/291.51 WORST_CASE(Omega(n^1), ?) 364.70/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 364.70/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 364.70/291.51 364.70/291.51 364.70/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 364.70/291.51 364.70/291.51 (0) CpxTRS 364.70/291.51 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 364.70/291.51 (2) TRS for Loop Detection 364.70/291.51 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 364.70/291.51 (4) BEST 364.70/291.51 (5) proven lower bound 364.70/291.51 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 364.70/291.51 (7) BOUNDS(n^1, INF) 364.70/291.51 (8) TRS for Loop Detection 364.70/291.51 364.70/291.51 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (0) 364.70/291.51 Obligation: 364.70/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 364.70/291.51 364.70/291.51 364.70/291.51 The TRS R consists of the following rules: 364.70/291.51 364.70/291.51 f(s(x), y) -> f(x, s(s(x))) 364.70/291.51 f(x, s(s(y))) -> f(y, x) 364.70/291.51 364.70/291.51 S is empty. 364.70/291.51 Rewrite Strategy: FULL 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 364.70/291.51 Transformed a relative TRS into a decreasing-loop problem. 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (2) 364.70/291.51 Obligation: 364.70/291.51 Analyzing the following TRS for decreasing loops: 364.70/291.51 364.70/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 364.70/291.51 364.70/291.51 364.70/291.51 The TRS R consists of the following rules: 364.70/291.51 364.70/291.51 f(s(x), y) -> f(x, s(s(x))) 364.70/291.51 f(x, s(s(y))) -> f(y, x) 364.70/291.51 364.70/291.51 S is empty. 364.70/291.51 Rewrite Strategy: FULL 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (3) DecreasingLoopProof (LOWER BOUND(ID)) 364.70/291.51 The following loop(s) give(s) rise to the lower bound Omega(n^1): 364.70/291.51 364.70/291.51 The rewrite sequence 364.70/291.51 364.70/291.51 f(s(x), y) ->^+ f(x, s(s(x))) 364.70/291.51 364.70/291.51 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 364.70/291.51 364.70/291.51 The pumping substitution is [x / s(x)]. 364.70/291.51 364.70/291.51 The result substitution is [y / s(s(x))]. 364.70/291.51 364.70/291.51 364.70/291.51 364.70/291.51 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (4) 364.70/291.51 Complex Obligation (BEST) 364.70/291.51 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (5) 364.70/291.51 Obligation: 364.70/291.51 Proved the lower bound n^1 for the following obligation: 364.70/291.51 364.70/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 364.70/291.51 364.70/291.51 364.70/291.51 The TRS R consists of the following rules: 364.70/291.51 364.70/291.51 f(s(x), y) -> f(x, s(s(x))) 364.70/291.51 f(x, s(s(y))) -> f(y, x) 364.70/291.51 364.70/291.51 S is empty. 364.70/291.51 Rewrite Strategy: FULL 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (6) LowerBoundPropagationProof (FINISHED) 364.70/291.51 Propagated lower bound. 364.70/291.51 ---------------------------------------- 364.70/291.51 364.70/291.51 (7) 364.70/291.51 BOUNDS(n^1, INF) 364.70/291.51
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