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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307800
details
property
value
status
complete
benchmark
thiemann33.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.651 seconds
cpu usage
1087.65
user time
1077.32
system time
10.3299
max virtual memory
5.6409412E7
max residence set size
1.4967792E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1087.22/291.50 WORST_CASE(Omega(n^1), ?) 1087.42/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1087.42/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1087.42/291.55 1087.42/291.55 1087.42/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1087.42/291.55 1087.42/291.55 (0) CpxTRS 1087.42/291.55 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1087.42/291.55 (2) CpxTRS 1087.42/291.55 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 1087.42/291.55 (4) CpxTRS 1087.42/291.55 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1087.42/291.55 (6) typed CpxTrs 1087.42/291.55 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1087.42/291.55 (8) typed CpxTrs 1087.42/291.55 (9) RewriteLemmaProof [LOWER BOUND(ID), 270 ms] 1087.42/291.55 (10) BEST 1087.42/291.55 (11) proven lower bound 1087.42/291.55 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1087.42/291.55 (13) BOUNDS(n^1, INF) 1087.42/291.55 (14) typed CpxTrs 1087.42/291.55 (15) RewriteLemmaProof [LOWER BOUND(ID), 392 ms] 1087.42/291.55 (16) BOUNDS(1, INF) 1087.42/291.55 1087.42/291.55 1087.42/291.55 ---------------------------------------- 1087.42/291.55 1087.42/291.55 (0) 1087.42/291.55 Obligation: 1087.42/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1087.42/291.55 1087.42/291.55 1087.42/291.55 The TRS R consists of the following rules: 1087.42/291.55 1087.42/291.55 numbers -> d(0) 1087.42/291.55 d(x) -> if(le(x, nr), x) 1087.42/291.55 if(true, x) -> cons(x, d(s(x))) 1087.42/291.55 if(false, x) -> nil 1087.42/291.55 le(0, y) -> true 1087.42/291.55 le(s(x), 0) -> false 1087.42/291.55 le(s(x), s(y)) -> le(x, y) 1087.42/291.55 nr -> ack(s(s(s(s(s(s(0)))))), 0) 1087.42/291.55 ack(0, x) -> s(x) 1087.42/291.55 ack(s(x), 0) -> ack(x, s(0)) 1087.42/291.55 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 1087.42/291.55 1087.42/291.55 S is empty. 1087.42/291.55 Rewrite Strategy: FULL 1087.42/291.55 ---------------------------------------- 1087.42/291.55 1087.42/291.55 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1087.42/291.55 Renamed function symbols to avoid clashes with predefined symbol. 1087.42/291.55 ---------------------------------------- 1087.42/291.55 1087.42/291.55 (2) 1087.42/291.55 Obligation: 1087.42/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1087.42/291.55 1087.42/291.55 1087.42/291.55 The TRS R consists of the following rules: 1087.42/291.55 1087.42/291.55 numbers -> d(0') 1087.42/291.55 d(x) -> if(le(x, nr), x) 1087.42/291.55 if(true, x) -> cons(x, d(s(x))) 1087.42/291.55 if(false, x) -> nil 1087.42/291.55 le(0', y) -> true 1087.42/291.55 le(s(x), 0') -> false 1087.42/291.55 le(s(x), s(y)) -> le(x, y) 1087.42/291.55 nr -> ack(s(s(s(s(s(s(0')))))), 0') 1087.42/291.55 ack(0', x) -> s(x) 1087.42/291.55 ack(s(x), 0') -> ack(x, s(0')) 1087.42/291.55 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 1087.42/291.55 1087.42/291.55 S is empty. 1087.42/291.55 Rewrite Strategy: FULL 1087.42/291.55 ---------------------------------------- 1087.42/291.55 1087.42/291.55 (3) SlicingProof (LOWER BOUND(ID)) 1087.42/291.55 Sliced the following arguments: 1087.42/291.55 cons/0 1087.42/291.55 1087.42/291.55 ---------------------------------------- 1087.42/291.55 1087.42/291.55 (4) 1087.42/291.55 Obligation: 1087.42/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1087.42/291.55 1087.42/291.55 1087.42/291.55 The TRS R consists of the following rules: 1087.42/291.55 1087.42/291.55 numbers -> d(0') 1087.42/291.55 d(x) -> if(le(x, nr), x) 1087.42/291.55 if(true, x) -> cons(d(s(x))) 1087.42/291.55 if(false, x) -> nil 1087.42/291.55 le(0', y) -> true 1087.42/291.55 le(s(x), 0') -> false 1087.42/291.55 le(s(x), s(y)) -> le(x, y) 1087.42/291.55 nr -> ack(s(s(s(s(s(s(0')))))), 0') 1087.42/291.55 ack(0', x) -> s(x)
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