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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313741
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
n103.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.253 seconds
cpu usage
1097.24
user time
1087.12
system time
10.1224
max virtual memory
3.7646756E7
max residence set size
1.4843488E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1094.32/291.53 WORST_CASE(Omega(n^1), ?) 1097.00/292.14 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1097.00/292.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1097.00/292.14 1097.00/292.14 1097.00/292.14 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1097.00/292.14 1097.00/292.14 (0) CpxTRS 1097.00/292.14 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1097.00/292.14 (2) CpxTRS 1097.00/292.14 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 1097.00/292.14 (4) CpxTRS 1097.00/292.14 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1097.00/292.14 (6) typed CpxTrs 1097.00/292.14 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1097.00/292.14 (8) typed CpxTrs 1097.00/292.14 (9) RewriteLemmaProof [LOWER BOUND(ID), 296 ms] 1097.00/292.14 (10) BEST 1097.00/292.14 (11) proven lower bound 1097.00/292.14 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1097.00/292.14 (13) BOUNDS(n^1, INF) 1097.00/292.14 (14) typed CpxTrs 1097.00/292.14 (15) RewriteLemmaProof [LOWER BOUND(ID), 386 ms] 1097.00/292.14 (16) BOUNDS(1, INF) 1097.00/292.14 1097.00/292.14 1097.00/292.14 ---------------------------------------- 1097.00/292.14 1097.00/292.14 (0) 1097.00/292.14 Obligation: 1097.00/292.14 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1097.00/292.14 1097.00/292.14 1097.00/292.14 The TRS R consists of the following rules: 1097.00/292.14 1097.00/292.14 numbers -> d(0) 1097.00/292.14 d(x) -> if(le(x, nr), x) 1097.00/292.14 if(true, x) -> cons(x, d(s(x))) 1097.00/292.14 if(false, x) -> nil 1097.00/292.14 le(0, y) -> true 1097.00/292.14 le(s(x), 0) -> false 1097.00/292.14 le(s(x), s(y)) -> le(x, y) 1097.00/292.14 nr -> ack(s(s(s(s(s(s(0)))))), 0) 1097.00/292.14 ack(0, x) -> s(x) 1097.00/292.14 ack(s(x), 0) -> ack(x, s(0)) 1097.00/292.14 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 1097.00/292.14 1097.00/292.14 S is empty. 1097.00/292.14 Rewrite Strategy: INNERMOST 1097.00/292.14 ---------------------------------------- 1097.00/292.14 1097.00/292.14 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1097.00/292.14 Renamed function symbols to avoid clashes with predefined symbol. 1097.00/292.14 ---------------------------------------- 1097.00/292.14 1097.00/292.14 (2) 1097.00/292.14 Obligation: 1097.00/292.14 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1097.00/292.14 1097.00/292.14 1097.00/292.14 The TRS R consists of the following rules: 1097.00/292.14 1097.00/292.14 numbers -> d(0') 1097.00/292.14 d(x) -> if(le(x, nr), x) 1097.00/292.14 if(true, x) -> cons(x, d(s(x))) 1097.00/292.14 if(false, x) -> nil 1097.00/292.14 le(0', y) -> true 1097.00/292.14 le(s(x), 0') -> false 1097.00/292.14 le(s(x), s(y)) -> le(x, y) 1097.00/292.14 nr -> ack(s(s(s(s(s(s(0')))))), 0') 1097.00/292.14 ack(0', x) -> s(x) 1097.00/292.14 ack(s(x), 0') -> ack(x, s(0')) 1097.00/292.14 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 1097.00/292.14 1097.00/292.14 S is empty. 1097.00/292.14 Rewrite Strategy: INNERMOST 1097.00/292.14 ---------------------------------------- 1097.00/292.14 1097.00/292.14 (3) SlicingProof (LOWER BOUND(ID)) 1097.00/292.14 Sliced the following arguments: 1097.00/292.14 cons/0 1097.00/292.14 1097.00/292.14 ---------------------------------------- 1097.00/292.14 1097.00/292.14 (4) 1097.00/292.14 Obligation: 1097.00/292.14 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1097.00/292.14 1097.00/292.14 1097.00/292.14 The TRS R consists of the following rules: 1097.00/292.14 1097.00/292.14 numbers -> d(0') 1097.00/292.14 d(x) -> if(le(x, nr), x) 1097.00/292.14 if(true, x) -> cons(d(s(x))) 1097.00/292.14 if(false, x) -> nil 1097.00/292.14 le(0', y) -> true 1097.00/292.14 le(s(x), 0') -> false 1097.00/292.14 le(s(x), s(y)) -> le(x, y) 1097.00/292.14 nr -> ack(s(s(s(s(s(s(0')))))), 0') 1097.00/292.14 ack(0', x) -> s(x)
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