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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313926
details
property
value
status
complete
benchmark
21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n122.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.521 seconds
cpu usage
644.472
user time
640.988
system time
3.48386
max virtual memory
1.9076616E7
max residence set size
5723072.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
644.36/291.47 WORST_CASE(Omega(n^2), ?) 644.36/291.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 644.36/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 644.36/291.47 644.36/291.47 644.36/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 644.36/291.47 644.36/291.47 (0) CpxTRS 644.36/291.47 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 644.36/291.47 (2) CpxTRS 644.36/291.47 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 644.36/291.47 (4) typed CpxTrs 644.36/291.47 (5) OrderProof [LOWER BOUND(ID), 0 ms] 644.36/291.47 (6) typed CpxTrs 644.36/291.47 (7) RewriteLemmaProof [LOWER BOUND(ID), 265 ms] 644.36/291.47 (8) BEST 644.36/291.47 (9) proven lower bound 644.36/291.47 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 644.36/291.47 (11) BOUNDS(n^1, INF) 644.36/291.47 (12) typed CpxTrs 644.36/291.47 (13) RewriteLemmaProof [LOWER BOUND(ID), 52 ms] 644.36/291.47 (14) BEST 644.36/291.47 (15) proven lower bound 644.36/291.47 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 644.36/291.47 (17) BOUNDS(n^2, INF) 644.36/291.47 (18) typed CpxTrs 644.36/291.47 (19) RewriteLemmaProof [LOWER BOUND(ID), 698 ms] 644.36/291.47 (20) BOUNDS(1, INF) 644.36/291.47 644.36/291.47 644.36/291.47 ---------------------------------------- 644.36/291.47 644.36/291.47 (0) 644.36/291.47 Obligation: 644.36/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 644.36/291.47 644.36/291.47 644.36/291.47 The TRS R consists of the following rules: 644.36/291.47 644.36/291.47 p(s(x)) -> x 644.36/291.47 fact(0) -> s(0) 644.36/291.47 fact(s(x)) -> *(s(x), fact(p(s(x)))) 644.36/291.47 *(0, y) -> 0 644.36/291.47 *(s(x), y) -> +(*(x, y), y) 644.36/291.47 +(x, 0) -> x 644.36/291.47 +(x, s(y)) -> s(+(x, y)) 644.36/291.47 644.36/291.47 S is empty. 644.36/291.47 Rewrite Strategy: INNERMOST 644.36/291.47 ---------------------------------------- 644.36/291.47 644.36/291.47 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 644.36/291.47 Renamed function symbols to avoid clashes with predefined symbol. 644.36/291.47 ---------------------------------------- 644.36/291.47 644.36/291.47 (2) 644.36/291.47 Obligation: 644.36/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 644.36/291.47 644.36/291.47 644.36/291.47 The TRS R consists of the following rules: 644.36/291.47 644.36/291.47 p(s(x)) -> x 644.36/291.47 fact(0') -> s(0') 644.36/291.47 fact(s(x)) -> *'(s(x), fact(p(s(x)))) 644.36/291.47 *'(0', y) -> 0' 644.36/291.47 *'(s(x), y) -> +'(*'(x, y), y) 644.36/291.47 +'(x, 0') -> x 644.36/291.47 +'(x, s(y)) -> s(+'(x, y)) 644.36/291.47 644.36/291.47 S is empty. 644.36/291.47 Rewrite Strategy: INNERMOST 644.36/291.47 ---------------------------------------- 644.36/291.47 644.36/291.47 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 644.36/291.47 Infered types. 644.36/291.47 ---------------------------------------- 644.36/291.47 644.36/291.47 (4) 644.36/291.47 Obligation: 644.36/291.47 Innermost TRS: 644.36/291.47 Rules: 644.36/291.47 p(s(x)) -> x 644.36/291.47 fact(0') -> s(0') 644.36/291.47 fact(s(x)) -> *'(s(x), fact(p(s(x)))) 644.36/291.47 *'(0', y) -> 0' 644.36/291.47 *'(s(x), y) -> +'(*'(x, y), y) 644.36/291.47 +'(x, 0') -> x 644.36/291.47 +'(x, s(y)) -> s(+'(x, y)) 644.36/291.47 644.36/291.47 Types: 644.36/291.47 p :: s:0' -> s:0' 644.36/291.47 s :: s:0' -> s:0' 644.36/291.47 fact :: s:0' -> s:0' 644.36/291.47 0' :: s:0' 644.36/291.47 *' :: s:0' -> s:0' -> s:0' 644.36/291.47 +' :: s:0' -> s:0' -> s:0' 644.36/291.47 hole_s:0'1_0 :: s:0' 644.36/291.47 gen_s:0'2_0 :: Nat -> s:0' 644.36/291.47
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