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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313343
details
property
value
status
complete
benchmark
t003.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.609 seconds
cpu usage
777.922
user time
764.465
system time
13.4566
max virtual memory
1.907908E7
max residence set size
1.4884344E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
777.80/291.53 WORST_CASE(Omega(n^1), ?) 777.80/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 777.80/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 777.80/291.54 777.80/291.54 777.80/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 777.80/291.54 777.80/291.54 (0) CpxTRS 777.80/291.54 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 777.80/291.54 (2) CpxTRS 777.80/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 777.80/291.54 (4) typed CpxTrs 777.80/291.54 (5) OrderProof [LOWER BOUND(ID), 0 ms] 777.80/291.54 (6) typed CpxTrs 777.80/291.54 (7) RewriteLemmaProof [LOWER BOUND(ID), 277 ms] 777.80/291.54 (8) BEST 777.80/291.54 (9) proven lower bound 777.80/291.54 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 777.80/291.54 (11) BOUNDS(n^1, INF) 777.80/291.54 (12) typed CpxTrs 777.80/291.54 (13) RewriteLemmaProof [LOWER BOUND(ID), 22 ms] 777.80/291.54 (14) typed CpxTrs 777.80/291.54 777.80/291.54 777.80/291.54 ---------------------------------------- 777.80/291.54 777.80/291.54 (0) 777.80/291.54 Obligation: 777.80/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 777.80/291.54 777.80/291.54 777.80/291.54 The TRS R consists of the following rules: 777.80/291.54 777.80/291.54 -(x, 0) -> x 777.80/291.54 -(s(x), s(y)) -> -(x, y) 777.80/291.54 <=(0, y) -> true 777.80/291.54 <=(s(x), 0) -> false 777.80/291.54 <=(s(x), s(y)) -> <=(x, y) 777.80/291.54 if(true, x, y) -> x 777.80/291.54 if(false, x, y) -> y 777.80/291.54 perfectp(0) -> false 777.80/291.54 perfectp(s(x)) -> f(x, s(0), s(x), s(x)) 777.80/291.54 f(0, y, 0, u) -> true 777.80/291.54 f(0, y, s(z), u) -> false 777.80/291.54 f(s(x), 0, z, u) -> f(x, u, -(z, s(x)), u) 777.80/291.54 f(s(x), s(y), z, u) -> if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u)) 777.80/291.54 777.80/291.54 S is empty. 777.80/291.54 Rewrite Strategy: INNERMOST 777.80/291.54 ---------------------------------------- 777.80/291.54 777.80/291.54 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 777.80/291.54 Renamed function symbols to avoid clashes with predefined symbol. 777.80/291.54 ---------------------------------------- 777.80/291.54 777.80/291.54 (2) 777.80/291.54 Obligation: 777.80/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 777.80/291.54 777.80/291.54 777.80/291.54 The TRS R consists of the following rules: 777.80/291.54 777.80/291.54 -(x, 0') -> x 777.80/291.54 -(s(x), s(y)) -> -(x, y) 777.80/291.54 <=(0', y) -> true 777.80/291.54 <=(s(x), 0') -> false 777.80/291.54 <=(s(x), s(y)) -> <=(x, y) 777.80/291.54 if(true, x, y) -> x 777.80/291.54 if(false, x, y) -> y 777.80/291.54 perfectp(0') -> false 777.80/291.54 perfectp(s(x)) -> f(x, s(0'), s(x), s(x)) 777.80/291.54 f(0', y, 0', u) -> true 777.80/291.54 f(0', y, s(z), u) -> false 777.80/291.54 f(s(x), 0', z, u) -> f(x, u, -(z, s(x)), u) 777.80/291.54 f(s(x), s(y), z, u) -> if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u)) 777.80/291.54 777.80/291.54 S is empty. 777.80/291.54 Rewrite Strategy: INNERMOST 777.80/291.54 ---------------------------------------- 777.80/291.54 777.80/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 777.80/291.54 Infered types. 777.80/291.54 ---------------------------------------- 777.80/291.54 777.80/291.54 (4) 777.80/291.54 Obligation: 777.80/291.54 Innermost TRS: 777.80/291.54 Rules: 777.80/291.54 -(x, 0') -> x 777.80/291.54 -(s(x), s(y)) -> -(x, y) 777.80/291.54 <=(0', y) -> true 777.80/291.54 <=(s(x), 0') -> false 777.80/291.54 <=(s(x), s(y)) -> <=(x, y) 777.80/291.54 if(true, x, y) -> x 777.80/291.54 if(false, x, y) -> y 777.80/291.54 perfectp(0') -> false 777.80/291.54 perfectp(s(x)) -> f(x, s(0'), s(x), s(x)) 777.80/291.54 f(0', y, 0', u) -> true 777.80/291.54 f(0', y, s(z), u) -> false 777.80/291.54 f(s(x), 0', z, u) -> f(x, u, -(z, s(x)), u)
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