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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308443
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
n157.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.541 seconds
cpu usage
957.959
user time
952.004
system time
5.95519
max virtual memory
3.7639888E7
max residence set size
8755748.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
957.81/291.49 WORST_CASE(Omega(n^1), ?) 957.81/291.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 957.81/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 957.81/291.50 957.81/291.50 957.81/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 957.81/291.50 957.81/291.50 (0) CpxTRS 957.81/291.50 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 957.81/291.50 (2) CpxTRS 957.81/291.50 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 957.81/291.50 (4) typed CpxTrs 957.81/291.50 (5) OrderProof [LOWER BOUND(ID), 0 ms] 957.81/291.50 (6) typed CpxTrs 957.81/291.50 (7) RewriteLemmaProof [LOWER BOUND(ID), 564 ms] 957.81/291.50 (8) proven lower bound 957.81/291.50 (9) LowerBoundPropagationProof [FINISHED, 0 ms] 957.81/291.50 (10) BOUNDS(n^1, INF) 957.81/291.50 957.81/291.50 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (0) 957.81/291.50 Obligation: 957.81/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 957.81/291.50 957.81/291.50 957.81/291.50 The TRS R consists of the following rules: 957.81/291.50 957.81/291.50 ack(0, y) -> s(y) 957.81/291.50 ack(s(x), 0) -> ack(x, s(0)) 957.81/291.50 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 957.81/291.50 957.81/291.50 S is empty. 957.81/291.50 Rewrite Strategy: FULL 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 957.81/291.50 Renamed function symbols to avoid clashes with predefined symbol. 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (2) 957.81/291.50 Obligation: 957.81/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 957.81/291.50 957.81/291.50 957.81/291.50 The TRS R consists of the following rules: 957.81/291.50 957.81/291.50 ack(0', y) -> s(y) 957.81/291.50 ack(s(x), 0') -> ack(x, s(0')) 957.81/291.50 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 957.81/291.50 957.81/291.50 S is empty. 957.81/291.50 Rewrite Strategy: FULL 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 957.81/291.50 Infered types. 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (4) 957.81/291.50 Obligation: 957.81/291.50 TRS: 957.81/291.50 Rules: 957.81/291.50 ack(0', y) -> s(y) 957.81/291.50 ack(s(x), 0') -> ack(x, s(0')) 957.81/291.50 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 957.81/291.50 957.81/291.50 Types: 957.81/291.50 ack :: 0':s -> 0':s -> 0':s 957.81/291.50 0' :: 0':s 957.81/291.50 s :: 0':s -> 0':s 957.81/291.50 hole_0':s1_0 :: 0':s 957.81/291.50 gen_0':s2_0 :: Nat -> 0':s 957.81/291.50 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (5) OrderProof (LOWER BOUND(ID)) 957.81/291.50 Heuristically decided to analyse the following defined symbols: 957.81/291.50 ack 957.81/291.50 ---------------------------------------- 957.81/291.50 957.81/291.50 (6) 957.81/291.50 Obligation: 957.81/291.50 TRS: 957.81/291.50 Rules: 957.81/291.50 ack(0', y) -> s(y) 957.81/291.50 ack(s(x), 0') -> ack(x, s(0')) 957.81/291.50 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 957.81/291.50 957.81/291.50 Types: 957.81/291.50 ack :: 0':s -> 0':s -> 0':s 957.81/291.50 0' :: 0':s 957.81/291.50 s :: 0':s -> 0':s 957.81/291.50 hole_0':s1_0 :: 0':s 957.81/291.50 gen_0':s2_0 :: Nat -> 0':s 957.81/291.50 957.81/291.50 957.81/291.50 Generator Equations: 957.81/291.50 gen_0':s2_0(0) <=> 0'
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