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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307641
details
property
value
status
complete
benchmark
list-sum-prod-assoc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n062.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.84 seconds
cpu usage
341.64
user time
336.181
system time
5.45926
max virtual memory
1.8281284E7
max residence set size
8969064.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
341.56/291.77 WORST_CASE(Omega(n^2), ?) 341.56/291.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 341.56/291.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 341.56/291.78 341.56/291.78 341.56/291.78 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 341.56/291.78 341.56/291.78 (0) CpxTRS 341.56/291.78 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 341.56/291.78 (2) CpxTRS 341.56/291.78 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 341.56/291.78 (4) typed CpxTrs 341.56/291.78 (5) OrderProof [LOWER BOUND(ID), 0 ms] 341.56/291.78 (6) typed CpxTrs 341.56/291.78 (7) RewriteLemmaProof [LOWER BOUND(ID), 359 ms] 341.56/291.78 (8) BEST 341.56/291.78 (9) proven lower bound 341.56/291.78 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 341.56/291.78 (11) BOUNDS(n^1, INF) 341.56/291.78 (12) typed CpxTrs 341.56/291.78 (13) RewriteLemmaProof [LOWER BOUND(ID), 4078 ms] 341.56/291.78 (14) BEST 341.56/291.78 (15) proven lower bound 341.56/291.78 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 341.56/291.78 (17) BOUNDS(n^2, INF) 341.56/291.78 (18) typed CpxTrs 341.56/291.78 (19) RewriteLemmaProof [LOWER BOUND(ID), 14 ms] 341.56/291.78 (20) typed CpxTrs 341.56/291.78 (21) RewriteLemmaProof [LOWER BOUND(ID), 455 ms] 341.56/291.78 (22) BOUNDS(1, INF) 341.56/291.78 341.56/291.78 341.56/291.78 ---------------------------------------- 341.56/291.78 341.56/291.78 (0) 341.56/291.78 Obligation: 341.56/291.78 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 341.56/291.78 341.56/291.78 341.56/291.78 The TRS R consists of the following rules: 341.56/291.78 341.56/291.78 +(x, 0) -> x 341.56/291.78 +(0, x) -> x 341.56/291.78 +(s(x), s(y)) -> s(s(+(x, y))) 341.56/291.78 +(+(x, y), z) -> +(x, +(y, z)) 341.56/291.78 *(x, 0) -> 0 341.56/291.78 *(0, x) -> 0 341.56/291.78 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) 341.56/291.78 *(*(x, y), z) -> *(x, *(y, z)) 341.56/291.78 sum(nil) -> 0 341.56/291.78 sum(cons(x, l)) -> +(x, sum(l)) 341.56/291.78 prod(nil) -> s(0) 341.56/291.78 prod(cons(x, l)) -> *(x, prod(l)) 341.56/291.78 341.56/291.78 S is empty. 341.56/291.78 Rewrite Strategy: FULL 341.56/291.78 ---------------------------------------- 341.56/291.78 341.56/291.78 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 341.56/291.78 Renamed function symbols to avoid clashes with predefined symbol. 341.56/291.78 ---------------------------------------- 341.56/291.78 341.56/291.78 (2) 341.56/291.78 Obligation: 341.56/291.78 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 341.56/291.78 341.56/291.78 341.56/291.78 The TRS R consists of the following rules: 341.56/291.78 341.56/291.78 +'(x, 0') -> x 341.56/291.78 +'(0', x) -> x 341.56/291.78 +'(s(x), s(y)) -> s(s(+'(x, y))) 341.56/291.78 +'(+'(x, y), z) -> +'(x, +'(y, z)) 341.56/291.78 *'(x, 0') -> 0' 341.56/291.78 *'(0', x) -> 0' 341.56/291.78 *'(s(x), s(y)) -> s(+'(*'(x, y), +'(x, y))) 341.56/291.78 *'(*'(x, y), z) -> *'(x, *'(y, z)) 341.56/291.78 sum(nil) -> 0' 341.56/291.78 sum(cons(x, l)) -> +'(x, sum(l)) 341.56/291.78 prod(nil) -> s(0') 341.56/291.78 prod(cons(x, l)) -> *'(x, prod(l)) 341.56/291.78 341.56/291.78 S is empty. 341.56/291.78 Rewrite Strategy: FULL 341.56/291.78 ---------------------------------------- 341.56/291.78 341.56/291.78 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 341.56/291.78 Infered types. 341.56/291.78 ---------------------------------------- 341.56/291.78 341.56/291.78 (4) 341.56/291.78 Obligation: 341.56/291.78 TRS: 341.56/291.78 Rules: 341.56/291.78 +'(x, 0') -> x 341.56/291.78 +'(0', x) -> x 341.56/291.78 +'(s(x), s(y)) -> s(s(+'(x, y))) 341.56/291.78 +'(+'(x, y), z) -> +'(x, +'(y, z)) 341.56/291.78 *'(x, 0') -> 0' 341.56/291.78 *'(0', x) -> 0'
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