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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313845
details
property
value
status
complete
benchmark
cade17.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
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.693 seconds
cpu usage
1123.74
user time
1109.73
system time
14.015
max virtual memory
3.8044664E7
max residence set size
1.4986144E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1123.11/292.54 WORST_CASE(Omega(n^2), ?) 1123.52/292.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1123.52/292.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1123.52/292.60 1123.52/292.60 1123.52/292.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1123.52/292.60 1123.52/292.60 (0) CpxTRS 1123.52/292.60 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1123.52/292.60 (2) CpxTRS 1123.52/292.60 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1123.52/292.60 (4) typed CpxTrs 1123.52/292.60 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1123.52/292.60 (6) typed CpxTrs 1123.52/292.60 (7) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] 1123.52/292.60 (8) BEST 1123.52/292.60 (9) proven lower bound 1123.52/292.60 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1123.52/292.60 (11) BOUNDS(n^1, INF) 1123.52/292.60 (12) typed CpxTrs 1123.52/292.60 (13) RewriteLemmaProof [LOWER BOUND(ID), 121 ms] 1123.52/292.60 (14) typed CpxTrs 1123.52/292.60 (15) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] 1123.52/292.60 (16) typed CpxTrs 1123.52/292.60 (17) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] 1123.52/292.60 (18) BEST 1123.52/292.60 (19) proven lower bound 1123.52/292.60 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1123.52/292.60 (21) BOUNDS(n^2, INF) 1123.52/292.60 (22) typed CpxTrs 1123.52/292.60 1123.52/292.60 1123.52/292.60 ---------------------------------------- 1123.52/292.60 1123.52/292.60 (0) 1123.52/292.60 Obligation: 1123.52/292.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1123.52/292.60 1123.52/292.60 1123.52/292.60 The TRS R consists of the following rules: 1123.52/292.60 1123.52/292.60 log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y) 1123.52/292.60 cond(true, x, y) -> s(0) 1123.52/292.60 cond(false, x, y) -> double(log(x, square(s(s(y))))) 1123.52/292.60 le(0, v) -> true 1123.52/292.60 le(s(u), 0) -> false 1123.52/292.60 le(s(u), s(v)) -> le(u, v) 1123.52/292.60 double(0) -> 0 1123.52/292.60 double(s(x)) -> s(s(double(x))) 1123.52/292.60 square(0) -> 0 1123.52/292.60 square(s(x)) -> s(plus(square(x), double(x))) 1123.52/292.60 plus(n, 0) -> n 1123.52/292.60 plus(n, s(m)) -> s(plus(n, m)) 1123.52/292.60 1123.52/292.60 S is empty. 1123.52/292.60 Rewrite Strategy: INNERMOST 1123.52/292.60 ---------------------------------------- 1123.52/292.60 1123.52/292.60 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1123.52/292.60 Renamed function symbols to avoid clashes with predefined symbol. 1123.52/292.60 ---------------------------------------- 1123.52/292.60 1123.52/292.60 (2) 1123.52/292.60 Obligation: 1123.52/292.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1123.52/292.60 1123.52/292.60 1123.52/292.60 The TRS R consists of the following rules: 1123.52/292.60 1123.52/292.60 log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y) 1123.52/292.60 cond(true, x, y) -> s(0') 1123.52/292.60 cond(false, x, y) -> double(log(x, square(s(s(y))))) 1123.52/292.60 le(0', v) -> true 1123.52/292.60 le(s(u), 0') -> false 1123.52/292.60 le(s(u), s(v)) -> le(u, v) 1123.52/292.60 double(0') -> 0' 1123.52/292.60 double(s(x)) -> s(s(double(x))) 1123.52/292.60 square(0') -> 0' 1123.52/292.60 square(s(x)) -> s(plus(square(x), double(x))) 1123.52/292.60 plus(n, 0') -> n 1123.52/292.60 plus(n, s(m)) -> s(plus(n, m)) 1123.52/292.60 1123.52/292.60 S is empty. 1123.52/292.60 Rewrite Strategy: INNERMOST 1123.52/292.60 ---------------------------------------- 1123.52/292.60 1123.52/292.60 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1123.52/292.60 Infered types. 1123.52/292.60 ---------------------------------------- 1123.52/292.60 1123.52/292.60 (4) 1123.52/292.60 Obligation: 1123.52/292.60 Innermost TRS: 1123.52/292.60 Rules: 1123.52/292.60 log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y) 1123.52/292.60 cond(true, x, y) -> s(0') 1123.52/292.60 cond(false, x, y) -> double(log(x, square(s(s(y))))) 1123.52/292.60 le(0', v) -> true 1123.52/292.60 le(s(u), 0') -> false 1123.52/292.60 le(s(u), s(v)) -> le(u, v)
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