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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307930
details
property
value
status
complete
benchmark
cade10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.553 seconds
cpu usage
305.543
user time
302.98
system time
2.56251
max virtual memory
1.8279384E7
max residence set size
5564220.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
305.36/291.51 WORST_CASE(Omega(n^1), ?) 305.36/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 305.36/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 305.36/291.52 305.36/291.52 305.36/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.36/291.52 305.36/291.52 (0) CpxTRS 305.36/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 305.36/291.52 (2) CpxTRS 305.36/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 305.36/291.52 (4) typed CpxTrs 305.36/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 305.36/291.52 (6) typed CpxTrs 305.36/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] 305.36/291.52 (8) BEST 305.36/291.52 (9) proven lower bound 305.36/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 305.36/291.52 (11) BOUNDS(n^1, INF) 305.36/291.52 (12) typed CpxTrs 305.36/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 150 ms] 305.36/291.52 (14) typed CpxTrs 305.36/291.52 305.36/291.52 305.36/291.52 ---------------------------------------- 305.36/291.52 305.36/291.52 (0) 305.36/291.52 Obligation: 305.36/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.36/291.52 305.36/291.52 305.36/291.52 The TRS R consists of the following rules: 305.36/291.52 305.36/291.52 f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) 305.36/291.52 trunc(0) -> 0 305.36/291.52 trunc(s(0)) -> 0 305.36/291.52 trunc(s(s(x))) -> s(s(trunc(x))) 305.36/291.52 gt(0, v) -> false 305.36/291.52 gt(s(u), 0) -> true 305.36/291.52 gt(s(u), s(v)) -> gt(u, v) 305.36/291.52 305.36/291.52 S is empty. 305.36/291.52 Rewrite Strategy: FULL 305.36/291.52 ---------------------------------------- 305.36/291.52 305.36/291.52 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 305.36/291.52 Renamed function symbols to avoid clashes with predefined symbol. 305.36/291.52 ---------------------------------------- 305.36/291.52 305.36/291.52 (2) 305.36/291.52 Obligation: 305.36/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 305.36/291.52 305.36/291.52 305.36/291.52 The TRS R consists of the following rules: 305.36/291.52 305.36/291.52 f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) 305.36/291.52 trunc(0') -> 0' 305.36/291.52 trunc(s(0')) -> 0' 305.36/291.52 trunc(s(s(x))) -> s(s(trunc(x))) 305.36/291.52 gt(0', v) -> false 305.36/291.52 gt(s(u), 0') -> true 305.36/291.52 gt(s(u), s(v)) -> gt(u, v) 305.36/291.52 305.36/291.52 S is empty. 305.36/291.52 Rewrite Strategy: FULL 305.36/291.52 ---------------------------------------- 305.36/291.52 305.36/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 305.36/291.52 Infered types. 305.36/291.52 ---------------------------------------- 305.36/291.52 305.36/291.52 (4) 305.36/291.52 Obligation: 305.36/291.52 TRS: 305.36/291.52 Rules: 305.36/291.52 f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) 305.36/291.52 trunc(0') -> 0' 305.36/291.52 trunc(s(0')) -> 0' 305.36/291.52 trunc(s(s(x))) -> s(s(trunc(x))) 305.36/291.52 gt(0', v) -> false 305.36/291.52 gt(s(u), 0') -> true 305.36/291.52 gt(s(u), s(v)) -> gt(u, v) 305.36/291.52 305.36/291.52 Types: 305.36/291.52 f :: true:false -> s:0' -> s:0' -> f 305.36/291.52 true :: true:false 305.36/291.52 gt :: s:0' -> s:0' -> true:false 305.36/291.52 trunc :: s:0' -> s:0' 305.36/291.52 s :: s:0' -> s:0' 305.36/291.52 0' :: s:0' 305.36/291.52 false :: true:false 305.36/291.52 hole_f1_0 :: f 305.36/291.52 hole_true:false2_0 :: true:false 305.36/291.52 hole_s:0'3_0 :: s:0' 305.36/291.52 gen_s:0'4_0 :: Nat -> s:0' 305.36/291.52 305.36/291.52 ---------------------------------------- 305.36/291.52 305.36/291.52 (5) OrderProof (LOWER BOUND(ID))
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