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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313724
details
property
value
status
complete
benchmark
thiemann32.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.785 seconds
cpu usage
1111.46
user time
1096.65
system time
14.8148
max virtual memory
5.700232E7
max residence set size
1.1794144E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1111.12/291.69 WORST_CASE(Omega(n^2), ?) 1111.12/291.72 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1111.12/291.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1111.12/291.72 1111.12/291.72 1111.12/291.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1111.12/291.72 1111.12/291.72 (0) CpxTRS 1111.12/291.72 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.12/291.72 (2) CpxTRS 1111.12/291.72 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 1111.12/291.72 (4) CpxTRS 1111.12/291.72 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.12/291.72 (6) typed CpxTrs 1111.12/291.72 (7) OrderProof [LOWER BOUND(ID), 0 ms] 1111.12/291.72 (8) typed CpxTrs 1111.12/291.72 (9) RewriteLemmaProof [LOWER BOUND(ID), 280 ms] 1111.12/291.72 (10) BEST 1111.12/291.72 (11) proven lower bound 1111.12/291.72 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1111.12/291.72 (13) BOUNDS(n^1, INF) 1111.12/291.72 (14) typed CpxTrs 1111.12/291.72 (15) RewriteLemmaProof [LOWER BOUND(ID), 81 ms] 1111.12/291.72 (16) typed CpxTrs 1111.12/291.72 (17) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] 1111.12/291.72 (18) BEST 1111.12/291.72 (19) proven lower bound 1111.12/291.72 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1111.12/291.72 (21) BOUNDS(n^2, INF) 1111.12/291.72 (22) typed CpxTrs 1111.12/291.72 1111.12/291.72 1111.12/291.72 ---------------------------------------- 1111.12/291.72 1111.12/291.72 (0) 1111.12/291.72 Obligation: 1111.12/291.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1111.12/291.72 1111.12/291.72 1111.12/291.72 The TRS R consists of the following rules: 1111.12/291.72 1111.12/291.72 table -> gen(s(0)) 1111.12/291.72 gen(x) -> if1(le(x, 10), x) 1111.12/291.72 if1(false, x) -> nil 1111.12/291.72 if1(true, x) -> if2(x, x) 1111.12/291.72 if2(x, y) -> if3(le(y, 10), x, y) 1111.12/291.72 if3(true, x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y))) 1111.12/291.72 if3(false, x, y) -> gen(s(x)) 1111.12/291.72 le(0, y) -> true 1111.12/291.72 le(s(x), 0) -> false 1111.12/291.72 le(s(x), s(y)) -> le(x, y) 1111.12/291.72 plus(0, y) -> y 1111.12/291.72 plus(s(x), y) -> s(plus(x, y)) 1111.12/291.72 times(0, y) -> 0 1111.12/291.72 times(s(x), y) -> plus(y, times(x, y)) 1111.12/291.72 10 -> s(s(s(s(s(s(s(s(s(s(0)))))))))) 1111.12/291.72 1111.12/291.72 S is empty. 1111.12/291.72 Rewrite Strategy: INNERMOST 1111.12/291.72 ---------------------------------------- 1111.12/291.72 1111.12/291.72 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1111.12/291.72 Renamed function symbols to avoid clashes with predefined symbol. 1111.12/291.72 ---------------------------------------- 1111.12/291.72 1111.12/291.72 (2) 1111.12/291.72 Obligation: 1111.12/291.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1111.12/291.72 1111.12/291.72 1111.12/291.72 The TRS R consists of the following rules: 1111.12/291.72 1111.12/291.72 table -> gen(s(0')) 1111.12/291.72 gen(x) -> if1(le(x, 10'), x) 1111.12/291.72 if1(false, x) -> nil 1111.12/291.72 if1(true, x) -> if2(x, x) 1111.12/291.72 if2(x, y) -> if3(le(y, 10'), x, y) 1111.12/291.72 if3(true, x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y))) 1111.12/291.72 if3(false, x, y) -> gen(s(x)) 1111.12/291.72 le(0', y) -> true 1111.12/291.72 le(s(x), 0') -> false 1111.12/291.72 le(s(x), s(y)) -> le(x, y) 1111.12/291.72 plus(0', y) -> y 1111.12/291.72 plus(s(x), y) -> s(plus(x, y)) 1111.12/291.72 times(0', y) -> 0' 1111.12/291.72 times(s(x), y) -> plus(y, times(x, y)) 1111.12/291.72 10' -> s(s(s(s(s(s(s(s(s(s(0')))))))))) 1111.12/291.72 1111.12/291.72 S is empty. 1111.12/291.72 Rewrite Strategy: INNERMOST 1111.12/291.72 ---------------------------------------- 1111.12/291.72 1111.12/291.72 (3) SlicingProof (LOWER BOUND(ID)) 1111.12/291.72 Sliced the following arguments: 1111.12/291.72 entry/0 1111.12/291.72 entry/1 1111.12/291.72 1111.12/291.72 ---------------------------------------- 1111.12/291.72 1111.12/291.72 (4)
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