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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313684
details
property
value
status
complete
benchmark
rta2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.578 seconds
cpu usage
354.692
user time
347.296
system time
7.39594
max virtual memory
3.819182E7
max residence set size
1.0707136E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
354.59/291.52 WORST_CASE(Omega(n^1), ?) 354.59/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 354.59/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 354.59/291.53 354.59/291.53 354.59/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 354.59/291.53 354.59/291.53 (0) CpxTRS 354.59/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 354.59/291.53 (2) TRS for Loop Detection 354.59/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 354.59/291.53 (4) BEST 354.59/291.53 (5) proven lower bound 354.59/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 354.59/291.53 (7) BOUNDS(n^1, INF) 354.59/291.53 (8) TRS for Loop Detection 354.59/291.53 354.59/291.53 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (0) 354.59/291.53 Obligation: 354.59/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 354.59/291.53 354.59/291.53 354.59/291.53 The TRS R consists of the following rules: 354.59/291.53 354.59/291.53 f(s(x), y) -> f(x, s(x)) 354.59/291.53 f(x, s(y)) -> f(y, x) 354.59/291.53 354.59/291.53 S is empty. 354.59/291.53 Rewrite Strategy: INNERMOST 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 354.59/291.53 Transformed a relative TRS into a decreasing-loop problem. 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (2) 354.59/291.53 Obligation: 354.59/291.53 Analyzing the following TRS for decreasing loops: 354.59/291.53 354.59/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 354.59/291.53 354.59/291.53 354.59/291.53 The TRS R consists of the following rules: 354.59/291.53 354.59/291.53 f(s(x), y) -> f(x, s(x)) 354.59/291.53 f(x, s(y)) -> f(y, x) 354.59/291.53 354.59/291.53 S is empty. 354.59/291.53 Rewrite Strategy: INNERMOST 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 354.59/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 354.59/291.53 354.59/291.53 The rewrite sequence 354.59/291.53 354.59/291.53 f(s(x), y) ->^+ f(x, s(x)) 354.59/291.53 354.59/291.53 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 354.59/291.53 354.59/291.53 The pumping substitution is [x / s(x)]. 354.59/291.53 354.59/291.53 The result substitution is [y / s(x)]. 354.59/291.53 354.59/291.53 354.59/291.53 354.59/291.53 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (4) 354.59/291.53 Complex Obligation (BEST) 354.59/291.53 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (5) 354.59/291.53 Obligation: 354.59/291.53 Proved the lower bound n^1 for the following obligation: 354.59/291.53 354.59/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 354.59/291.53 354.59/291.53 354.59/291.53 The TRS R consists of the following rules: 354.59/291.53 354.59/291.53 f(s(x), y) -> f(x, s(x)) 354.59/291.53 f(x, s(y)) -> f(y, x) 354.59/291.53 354.59/291.53 S is empty. 354.59/291.53 Rewrite Strategy: INNERMOST 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (6) LowerBoundPropagationProof (FINISHED) 354.59/291.53 Propagated lower bound. 354.59/291.53 ---------------------------------------- 354.59/291.53 354.59/291.53 (7) 354.59/291.53 BOUNDS(n^1, INF) 354.59/291.53
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