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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313274
details
property
value
status
complete
benchmark
tpa4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n130.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.728 seconds
cpu usage
1110.55
user time
1096.65
system time
13.9055
max virtual memory
3.7375232E7
max residence set size
1.5029032E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1109.77/291.54 WORST_CASE(Omega(n^2), ?) 1110.26/291.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1110.26/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1110.26/291.60 1110.26/291.60 1110.26/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1110.26/291.60 1110.26/291.60 (0) CpxTRS 1110.26/291.60 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1110.26/291.60 (2) CpxTRS 1110.26/291.60 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1110.26/291.60 (4) typed CpxTrs 1110.26/291.60 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1110.26/291.60 (6) typed CpxTrs 1110.26/291.60 (7) RewriteLemmaProof [LOWER BOUND(ID), 240 ms] 1110.26/291.60 (8) BEST 1110.26/291.60 (9) proven lower bound 1110.26/291.60 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1110.26/291.60 (11) BOUNDS(n^1, INF) 1110.26/291.60 (12) typed CpxTrs 1110.26/291.60 (13) RewriteLemmaProof [LOWER BOUND(ID), 51 ms] 1110.26/291.60 (14) typed CpxTrs 1110.26/291.60 (15) RewriteLemmaProof [LOWER BOUND(ID), 84 ms] 1110.26/291.60 (16) BEST 1110.26/291.60 (17) proven lower bound 1110.26/291.60 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1110.26/291.60 (19) BOUNDS(n^2, INF) 1110.26/291.60 (20) typed CpxTrs 1110.26/291.60 1110.26/291.60 1110.26/291.60 ---------------------------------------- 1110.26/291.60 1110.26/291.60 (0) 1110.26/291.60 Obligation: 1110.26/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1110.26/291.60 1110.26/291.60 1110.26/291.60 The TRS R consists of the following rules: 1110.26/291.60 1110.26/291.60 -(x, 0) -> x 1110.26/291.60 -(s(x), s(y)) -> -(x, y) 1110.26/291.60 +(0, y) -> y 1110.26/291.60 +(s(x), y) -> s(+(x, y)) 1110.26/291.60 *(x, 0) -> 0 1110.26/291.60 *(x, s(y)) -> +(x, *(x, y)) 1110.26/291.60 p(s(x)) -> x 1110.26/291.60 f(s(x)) -> f(-(p(*(s(x), s(x))), *(s(x), s(x)))) 1110.26/291.60 1110.26/291.60 S is empty. 1110.26/291.60 Rewrite Strategy: INNERMOST 1110.26/291.60 ---------------------------------------- 1110.26/291.60 1110.26/291.60 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1110.26/291.60 Renamed function symbols to avoid clashes with predefined symbol. 1110.26/291.60 ---------------------------------------- 1110.26/291.60 1110.26/291.60 (2) 1110.26/291.60 Obligation: 1110.26/291.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1110.26/291.60 1110.26/291.60 1110.26/291.60 The TRS R consists of the following rules: 1110.26/291.60 1110.26/291.60 -(x, 0') -> x 1110.26/291.60 -(s(x), s(y)) -> -(x, y) 1110.26/291.60 +'(0', y) -> y 1110.26/291.60 +'(s(x), y) -> s(+'(x, y)) 1110.26/291.60 *'(x, 0') -> 0' 1110.26/291.60 *'(x, s(y)) -> +'(x, *'(x, y)) 1110.26/291.60 p(s(x)) -> x 1110.26/291.60 f(s(x)) -> f(-(p(*'(s(x), s(x))), *'(s(x), s(x)))) 1110.26/291.60 1110.26/291.60 S is empty. 1110.26/291.60 Rewrite Strategy: INNERMOST 1110.26/291.60 ---------------------------------------- 1110.26/291.60 1110.26/291.60 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1110.26/291.60 Infered types. 1110.26/291.60 ---------------------------------------- 1110.26/291.60 1110.26/291.60 (4) 1110.26/291.60 Obligation: 1110.26/291.60 Innermost TRS: 1110.26/291.60 Rules: 1110.26/291.60 -(x, 0') -> x 1110.26/291.60 -(s(x), s(y)) -> -(x, y) 1110.26/291.60 +'(0', y) -> y 1110.26/291.60 +'(s(x), y) -> s(+'(x, y)) 1110.26/291.60 *'(x, 0') -> 0' 1110.26/291.60 *'(x, s(y)) -> +'(x, *'(x, y)) 1110.26/291.60 p(s(x)) -> x 1110.26/291.60 f(s(x)) -> f(-(p(*'(s(x), s(x))), *'(s(x), s(x)))) 1110.26/291.60 1110.26/291.60 Types: 1110.26/291.60 - :: 0':s -> 0':s -> 0':s 1110.26/291.60 0' :: 0':s 1110.26/291.60 s :: 0':s -> 0':s 1110.26/291.60 +' :: 0':s -> 0':s -> 0':s 1110.26/291.60 *' :: 0':s -> 0':s -> 0':s 1110.26/291.60 p :: 0':s -> 0':s
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