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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307690
details
property
value
status
complete
benchmark
#3.19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.53 seconds
cpu usage
325.931
user time
322.42
system time
3.51068
max virtual memory
1.8281476E7
max residence set size
7035304.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
325.79/291.48 WORST_CASE(Omega(n^1), ?) 325.87/291.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 325.87/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 325.87/291.49 325.87/291.49 325.87/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 325.87/291.49 325.87/291.49 (0) CpxTRS 325.87/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 325.87/291.49 (2) CpxTRS 325.87/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 325.87/291.49 (4) typed CpxTrs 325.87/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 325.87/291.49 (6) typed CpxTrs 325.87/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 284 ms] 325.87/291.49 (8) BEST 325.87/291.49 (9) proven lower bound 325.87/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 325.87/291.49 (11) BOUNDS(n^1, INF) 325.87/291.49 (12) typed CpxTrs 325.87/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 95 ms] 325.87/291.49 (14) typed CpxTrs 325.87/291.49 (15) RewriteLemmaProof [LOWER BOUND(ID), 64 ms] 325.87/291.49 (16) BOUNDS(1, INF) 325.87/291.49 325.87/291.49 325.87/291.49 ---------------------------------------- 325.87/291.49 325.87/291.49 (0) 325.87/291.49 Obligation: 325.87/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 325.87/291.49 325.87/291.49 325.87/291.49 The TRS R consists of the following rules: 325.87/291.49 325.87/291.49 minus(x, 0) -> x 325.87/291.49 minus(s(x), s(y)) -> minus(x, y) 325.87/291.49 double(0) -> 0 325.87/291.49 double(s(x)) -> s(s(double(x))) 325.87/291.49 plus(0, y) -> y 325.87/291.49 plus(s(x), y) -> s(plus(x, y)) 325.87/291.49 plus(s(x), y) -> plus(x, s(y)) 325.87/291.49 plus(s(x), y) -> s(plus(minus(x, y), double(y))) 325.87/291.49 plus(s(plus(x, y)), z) -> s(plus(plus(x, y), z)) 325.87/291.49 325.87/291.49 S is empty. 325.87/291.49 Rewrite Strategy: FULL 325.87/291.49 ---------------------------------------- 325.87/291.49 325.87/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 325.87/291.49 Renamed function symbols to avoid clashes with predefined symbol. 325.87/291.49 ---------------------------------------- 325.87/291.49 325.87/291.49 (2) 325.87/291.49 Obligation: 325.87/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 325.87/291.49 325.87/291.49 325.87/291.49 The TRS R consists of the following rules: 325.87/291.49 325.87/291.49 minus(x, 0') -> x 325.87/291.49 minus(s(x), s(y)) -> minus(x, y) 325.87/291.49 double(0') -> 0' 325.87/291.49 double(s(x)) -> s(s(double(x))) 325.87/291.49 plus(0', y) -> y 325.87/291.49 plus(s(x), y) -> s(plus(x, y)) 325.87/291.49 plus(s(x), y) -> plus(x, s(y)) 325.87/291.49 plus(s(x), y) -> s(plus(minus(x, y), double(y))) 325.87/291.49 plus(s(plus(x, y)), z) -> s(plus(plus(x, y), z)) 325.87/291.49 325.87/291.49 S is empty. 325.87/291.49 Rewrite Strategy: FULL 325.87/291.49 ---------------------------------------- 325.87/291.49 325.87/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 325.87/291.49 Infered types. 325.87/291.49 ---------------------------------------- 325.87/291.49 325.87/291.49 (4) 325.87/291.49 Obligation: 325.87/291.49 TRS: 325.87/291.49 Rules: 325.87/291.49 minus(x, 0') -> x 325.87/291.49 minus(s(x), s(y)) -> minus(x, y) 325.87/291.49 double(0') -> 0' 325.87/291.49 double(s(x)) -> s(s(double(x))) 325.87/291.49 plus(0', y) -> y 325.87/291.49 plus(s(x), y) -> s(plus(x, y)) 325.87/291.49 plus(s(x), y) -> plus(x, s(y)) 325.87/291.49 plus(s(x), y) -> s(plus(minus(x, y), double(y))) 325.87/291.49 plus(s(plus(x, y)), z) -> s(plus(plus(x, y), z)) 325.87/291.49 325.87/291.49 Types: 325.87/291.49 minus :: 0':s -> 0':s -> 0':s 325.87/291.49 0' :: 0':s 325.87/291.49 s :: 0':s -> 0':s 325.87/291.49 double :: 0':s -> 0':s 325.87/291.49 plus :: 0':s -> 0':s -> 0':s 325.87/291.49 hole_0':s1_0 :: 0':s 325.87/291.49 gen_0':s2_0 :: Nat -> 0':s
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