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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307887
details
property
value
status
complete
benchmark
tpa3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.621 seconds
cpu usage
315.302
user time
313.133
system time
2.16955
max virtual memory
1.8281316E7
max residence set size
5676152.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
314.84/291.47 WORST_CASE(Omega(n^2), ?) 314.84/291.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 314.84/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 314.84/291.48 314.84/291.48 314.84/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 314.84/291.48 314.84/291.48 (0) CpxTRS 314.84/291.48 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 314.84/291.48 (2) CpxTRS 314.84/291.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 314.84/291.48 (4) typed CpxTrs 314.84/291.48 (5) OrderProof [LOWER BOUND(ID), 0 ms] 314.84/291.48 (6) typed CpxTrs 314.84/291.48 (7) RewriteLemmaProof [LOWER BOUND(ID), 278 ms] 314.84/291.48 (8) BEST 314.84/291.48 (9) proven lower bound 314.84/291.48 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 314.84/291.48 (11) BOUNDS(n^1, INF) 314.84/291.48 (12) typed CpxTrs 314.84/291.48 (13) RewriteLemmaProof [LOWER BOUND(ID), 62 ms] 314.84/291.48 (14) typed CpxTrs 314.84/291.48 (15) RewriteLemmaProof [LOWER BOUND(ID), 87 ms] 314.84/291.48 (16) BEST 314.84/291.48 (17) proven lower bound 314.84/291.48 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 314.84/291.48 (19) BOUNDS(n^2, INF) 314.84/291.48 (20) typed CpxTrs 314.84/291.48 314.84/291.48 314.84/291.48 ---------------------------------------- 314.84/291.48 314.84/291.48 (0) 314.84/291.48 Obligation: 314.84/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 314.84/291.48 314.84/291.48 314.84/291.48 The TRS R consists of the following rules: 314.84/291.48 314.84/291.48 -(x, 0) -> x 314.84/291.48 -(s(x), s(y)) -> -(x, y) 314.84/291.48 +(0, y) -> y 314.84/291.48 +(s(x), y) -> s(+(x, y)) 314.84/291.48 *(x, 0) -> 0 314.84/291.48 *(x, s(y)) -> +(x, *(x, y)) 314.84/291.48 f(s(x)) -> f(-(*(s(s(0)), s(x)), s(s(x)))) 314.84/291.48 314.84/291.48 S is empty. 314.84/291.48 Rewrite Strategy: FULL 314.84/291.48 ---------------------------------------- 314.84/291.48 314.84/291.48 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 314.84/291.48 Renamed function symbols to avoid clashes with predefined symbol. 314.84/291.48 ---------------------------------------- 314.84/291.48 314.84/291.48 (2) 314.84/291.48 Obligation: 314.84/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 314.84/291.48 314.84/291.48 314.84/291.48 The TRS R consists of the following rules: 314.84/291.48 314.84/291.48 -(x, 0') -> x 314.84/291.48 -(s(x), s(y)) -> -(x, y) 314.84/291.48 +'(0', y) -> y 314.84/291.48 +'(s(x), y) -> s(+'(x, y)) 314.84/291.48 *'(x, 0') -> 0' 314.84/291.48 *'(x, s(y)) -> +'(x, *'(x, y)) 314.84/291.48 f(s(x)) -> f(-(*'(s(s(0')), s(x)), s(s(x)))) 314.84/291.48 314.84/291.48 S is empty. 314.84/291.48 Rewrite Strategy: FULL 314.84/291.48 ---------------------------------------- 314.84/291.48 314.84/291.48 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 314.84/291.48 Infered types. 314.84/291.48 ---------------------------------------- 314.84/291.48 314.84/291.48 (4) 314.84/291.48 Obligation: 314.84/291.48 TRS: 314.84/291.48 Rules: 314.84/291.48 -(x, 0') -> x 314.84/291.48 -(s(x), s(y)) -> -(x, y) 314.84/291.48 +'(0', y) -> y 314.84/291.48 +'(s(x), y) -> s(+'(x, y)) 314.84/291.48 *'(x, 0') -> 0' 314.84/291.48 *'(x, s(y)) -> +'(x, *'(x, y)) 314.84/291.48 f(s(x)) -> f(-(*'(s(s(0')), s(x)), s(s(x)))) 314.84/291.48 314.84/291.48 Types: 314.84/291.48 - :: 0':s -> 0':s -> 0':s 314.84/291.48 0' :: 0':s 314.84/291.48 s :: 0':s -> 0':s 314.84/291.48 +' :: 0':s -> 0':s -> 0':s 314.84/291.48 *' :: 0':s -> 0':s -> 0':s 314.84/291.48 f :: 0':s -> f 314.84/291.48 hole_0':s1_0 :: 0':s 314.84/291.48 hole_f2_0 :: f 314.84/291.48 gen_0':s3_0 :: Nat -> 0':s
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