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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307700
details
property
value
status
complete
benchmark
#3.4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.572 seconds
cpu usage
815.752
user time
804.459
system time
11.2926
max virtual memory
3.7785228E7
max residence set size
1.2687756E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
815.54/291.48 WORST_CASE(Omega(n^1), ?) 815.54/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 815.54/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 815.54/291.49 815.54/291.49 815.54/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 815.54/291.49 815.54/291.49 (0) CpxTRS 815.54/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 815.54/291.49 (2) CpxTRS 815.54/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 815.54/291.49 (4) typed CpxTrs 815.54/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 815.54/291.49 (6) typed CpxTrs 815.54/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] 815.54/291.49 (8) BEST 815.54/291.49 (9) proven lower bound 815.54/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 815.54/291.49 (11) BOUNDS(n^1, INF) 815.54/291.49 (12) typed CpxTrs 815.54/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 334 ms] 815.54/291.49 (14) typed CpxTrs 815.54/291.49 815.54/291.49 815.54/291.49 ---------------------------------------- 815.54/291.49 815.54/291.49 (0) 815.54/291.49 Obligation: 815.54/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 815.54/291.49 815.54/291.49 815.54/291.49 The TRS R consists of the following rules: 815.54/291.49 815.54/291.49 minus(x, 0) -> x 815.54/291.49 minus(s(x), s(y)) -> minus(x, y) 815.54/291.49 quot(0, s(y)) -> 0 815.54/291.49 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 815.54/291.49 plus(0, y) -> y 815.54/291.49 plus(s(x), y) -> s(plus(x, y)) 815.54/291.49 minus(minus(x, y), z) -> minus(x, plus(y, z)) 815.54/291.49 815.54/291.49 S is empty. 815.54/291.49 Rewrite Strategy: FULL 815.54/291.49 ---------------------------------------- 815.54/291.49 815.54/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 815.54/291.49 Renamed function symbols to avoid clashes with predefined symbol. 815.54/291.49 ---------------------------------------- 815.54/291.49 815.54/291.49 (2) 815.54/291.49 Obligation: 815.54/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 815.54/291.49 815.54/291.49 815.54/291.49 The TRS R consists of the following rules: 815.54/291.49 815.54/291.49 minus(x, 0') -> x 815.54/291.49 minus(s(x), s(y)) -> minus(x, y) 815.54/291.49 quot(0', s(y)) -> 0' 815.54/291.49 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 815.54/291.49 plus(0', y) -> y 815.54/291.49 plus(s(x), y) -> s(plus(x, y)) 815.54/291.49 minus(minus(x, y), z) -> minus(x, plus(y, z)) 815.54/291.49 815.54/291.49 S is empty. 815.54/291.49 Rewrite Strategy: FULL 815.54/291.49 ---------------------------------------- 815.54/291.49 815.54/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 815.54/291.49 Infered types. 815.54/291.49 ---------------------------------------- 815.54/291.49 815.54/291.49 (4) 815.54/291.49 Obligation: 815.54/291.49 TRS: 815.54/291.49 Rules: 815.54/291.49 minus(x, 0') -> x 815.54/291.49 minus(s(x), s(y)) -> minus(x, y) 815.54/291.49 quot(0', s(y)) -> 0' 815.54/291.49 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 815.54/291.49 plus(0', y) -> y 815.54/291.49 plus(s(x), y) -> s(plus(x, y)) 815.54/291.49 minus(minus(x, y), z) -> minus(x, plus(y, z)) 815.54/291.49 815.54/291.49 Types: 815.54/291.49 minus :: 0':s -> 0':s -> 0':s 815.54/291.49 0' :: 0':s 815.54/291.49 s :: 0':s -> 0':s 815.54/291.49 quot :: 0':s -> 0':s -> 0':s 815.54/291.49 plus :: 0':s -> 0':s -> 0':s 815.54/291.49 hole_0':s1_0 :: 0':s 815.54/291.49 gen_0':s2_0 :: Nat -> 0':s 815.54/291.49 815.54/291.49 ---------------------------------------- 815.54/291.49 815.54/291.49 (5) OrderProof (LOWER BOUND(ID)) 815.54/291.49 Heuristically decided to analyse the following defined symbols: 815.54/291.49 minus, quot, plus 815.54/291.49 815.54/291.49 They will be analysed ascendingly in the following order:
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