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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313606
details
property
value
status
complete
benchmark
2.51.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.583 seconds
cpu usage
945.522
user time
940.498
system time
5.02486
max virtual memory
1.8930576E7
max residence set size
7647388.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
945.25/291.54 WORST_CASE(Omega(n^1), ?) 945.25/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 945.25/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 945.25/291.54 945.25/291.54 945.25/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 945.25/291.54 945.25/291.54 (0) CpxTRS 945.25/291.54 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 945.25/291.54 (2) CpxTRS 945.25/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 945.25/291.54 (4) typed CpxTrs 945.25/291.54 (5) OrderProof [LOWER BOUND(ID), 0 ms] 945.25/291.54 (6) typed CpxTrs 945.25/291.54 (7) RewriteLemmaProof [LOWER BOUND(ID), 577 ms] 945.25/291.54 (8) proven lower bound 945.25/291.54 (9) LowerBoundPropagationProof [FINISHED, 0 ms] 945.25/291.54 (10) BOUNDS(n^1, INF) 945.25/291.54 945.25/291.54 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (0) 945.25/291.54 Obligation: 945.25/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 945.25/291.54 945.25/291.54 945.25/291.54 The TRS R consists of the following rules: 945.25/291.54 945.25/291.54 ack(0, y) -> s(y) 945.25/291.54 ack(s(x), 0) -> ack(x, s(0)) 945.25/291.54 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 945.25/291.54 945.25/291.54 S is empty. 945.25/291.54 Rewrite Strategy: INNERMOST 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 945.25/291.54 Renamed function symbols to avoid clashes with predefined symbol. 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (2) 945.25/291.54 Obligation: 945.25/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 945.25/291.54 945.25/291.54 945.25/291.54 The TRS R consists of the following rules: 945.25/291.54 945.25/291.54 ack(0', y) -> s(y) 945.25/291.54 ack(s(x), 0') -> ack(x, s(0')) 945.25/291.54 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 945.25/291.54 945.25/291.54 S is empty. 945.25/291.54 Rewrite Strategy: INNERMOST 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 945.25/291.54 Infered types. 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (4) 945.25/291.54 Obligation: 945.25/291.54 Innermost TRS: 945.25/291.54 Rules: 945.25/291.54 ack(0', y) -> s(y) 945.25/291.54 ack(s(x), 0') -> ack(x, s(0')) 945.25/291.54 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 945.25/291.54 945.25/291.54 Types: 945.25/291.54 ack :: 0':s -> 0':s -> 0':s 945.25/291.54 0' :: 0':s 945.25/291.54 s :: 0':s -> 0':s 945.25/291.54 hole_0':s1_0 :: 0':s 945.25/291.54 gen_0':s2_0 :: Nat -> 0':s 945.25/291.54 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (5) OrderProof (LOWER BOUND(ID)) 945.25/291.54 Heuristically decided to analyse the following defined symbols: 945.25/291.54 ack 945.25/291.54 ---------------------------------------- 945.25/291.54 945.25/291.54 (6) 945.25/291.54 Obligation: 945.25/291.54 Innermost TRS: 945.25/291.54 Rules: 945.25/291.54 ack(0', y) -> s(y) 945.25/291.54 ack(s(x), 0') -> ack(x, s(0')) 945.25/291.54 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 945.25/291.54 945.25/291.54 Types: 945.25/291.54 ack :: 0':s -> 0':s -> 0':s 945.25/291.54 0' :: 0':s 945.25/291.54 s :: 0':s -> 0':s 945.25/291.54 hole_0':s1_0 :: 0':s 945.25/291.54 gen_0':s2_0 :: Nat -> 0':s 945.25/291.54 945.25/291.54 945.25/291.54 Generator Equations: 945.25/291.54 gen_0':s2_0(0) <=> 0'
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