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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313562
details
property
value
status
complete
benchmark
#4.29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.651 seconds
cpu usage
1114.44
user time
1100.54
system time
13.9021
max virtual memory
3.7381316E7
max residence set size
1.5077912E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1114.11/291.55 WORST_CASE(Omega(n^1), ?) 1114.32/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1114.32/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1114.32/291.58 1114.32/291.58 1114.32/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.32/291.58 1114.32/291.58 (0) CpxTRS 1114.32/291.58 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1114.32/291.58 (2) TRS for Loop Detection 1114.32/291.58 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1114.32/291.58 (4) BEST 1114.32/291.58 (5) proven lower bound 1114.32/291.58 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1114.32/291.58 (7) BOUNDS(n^1, INF) 1114.32/291.58 (8) TRS for Loop Detection 1114.32/291.58 1114.32/291.58 1114.32/291.58 ---------------------------------------- 1114.32/291.58 1114.32/291.58 (0) 1114.32/291.58 Obligation: 1114.32/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.32/291.58 1114.32/291.58 1114.32/291.58 The TRS R consists of the following rules: 1114.32/291.58 1114.32/291.58 even(0) -> true 1114.32/291.58 even(s(0)) -> false 1114.32/291.58 even(s(s(x))) -> even(x) 1114.32/291.58 half(0) -> 0 1114.32/291.58 half(s(s(x))) -> s(half(x)) 1114.32/291.58 plus(0, y) -> y 1114.32/291.58 plus(s(x), y) -> s(plus(x, y)) 1114.32/291.58 times(0, y) -> 0 1114.32/291.58 times(s(x), y) -> if_times(even(s(x)), s(x), y) 1114.32/291.58 if_times(true, s(x), y) -> plus(times(half(s(x)), y), times(half(s(x)), y)) 1114.32/291.58 if_times(false, s(x), y) -> plus(y, times(x, y)) 1114.32/291.58 1114.32/291.58 S is empty. 1114.32/291.58 Rewrite Strategy: INNERMOST 1114.32/291.58 ---------------------------------------- 1114.32/291.58 1114.32/291.58 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1114.32/291.58 Transformed a relative TRS into a decreasing-loop problem. 1114.32/291.58 ---------------------------------------- 1114.32/291.58 1114.32/291.58 (2) 1114.32/291.58 Obligation: 1114.32/291.58 Analyzing the following TRS for decreasing loops: 1114.32/291.58 1114.32/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.32/291.58 1114.32/291.58 1114.32/291.58 The TRS R consists of the following rules: 1114.32/291.58 1114.32/291.58 even(0) -> true 1114.32/291.58 even(s(0)) -> false 1114.32/291.58 even(s(s(x))) -> even(x) 1114.32/291.58 half(0) -> 0 1114.32/291.58 half(s(s(x))) -> s(half(x)) 1114.32/291.58 plus(0, y) -> y 1114.32/291.58 plus(s(x), y) -> s(plus(x, y)) 1114.32/291.58 times(0, y) -> 0 1114.32/291.58 times(s(x), y) -> if_times(even(s(x)), s(x), y) 1114.32/291.58 if_times(true, s(x), y) -> plus(times(half(s(x)), y), times(half(s(x)), y)) 1114.32/291.58 if_times(false, s(x), y) -> plus(y, times(x, y)) 1114.32/291.58 1114.32/291.58 S is empty. 1114.32/291.58 Rewrite Strategy: INNERMOST 1114.32/291.58 ---------------------------------------- 1114.32/291.58 1114.32/291.58 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1114.32/291.58 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1114.32/291.58 1114.32/291.58 The rewrite sequence 1114.32/291.58 1114.32/291.58 even(s(s(x))) ->^+ even(x) 1114.32/291.58 1114.32/291.58 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1114.32/291.58 1114.32/291.58 The pumping substitution is [x / s(s(x))]. 1114.32/291.58 1114.32/291.58 The result substitution is [ ]. 1114.32/291.58 1114.32/291.58 1114.32/291.58 1114.32/291.58 1114.32/291.58 ---------------------------------------- 1114.32/291.58 1114.32/291.58 (4) 1114.32/291.58 Complex Obligation (BEST) 1114.32/291.58 1114.32/291.58 ---------------------------------------- 1114.32/291.58 1114.32/291.58 (5) 1114.32/291.58 Obligation: 1114.32/291.58 Proved the lower bound n^1 for the following obligation: 1114.32/291.58 1114.32/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
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