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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307688
details
property
value
status
complete
benchmark
rta3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.517 seconds
cpu usage
979.515
user time
974.255
system time
5.26034
max virtual memory
1.9090172E7
max residence set size
7464956.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
979.20/291.47 WORST_CASE(Omega(n^1), ?) 979.20/291.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 979.20/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 979.20/291.47 979.20/291.47 979.20/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 979.20/291.47 979.20/291.47 (0) CpxTRS 979.20/291.47 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 979.20/291.47 (2) TRS for Loop Detection 979.20/291.47 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 979.20/291.47 (4) BEST 979.20/291.47 (5) proven lower bound 979.20/291.47 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 979.20/291.47 (7) BOUNDS(n^1, INF) 979.20/291.47 (8) TRS for Loop Detection 979.20/291.47 979.20/291.47 979.20/291.47 ---------------------------------------- 979.20/291.47 979.20/291.47 (0) 979.20/291.47 Obligation: 979.20/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 979.20/291.47 979.20/291.47 979.20/291.47 The TRS R consists of the following rules: 979.20/291.47 979.20/291.47 ack(0, y) -> s(y) 979.20/291.47 ack(s(x), 0) -> ack(x, s(0)) 979.20/291.47 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 979.20/291.47 f(s(x), y) -> f(x, s(x)) 979.20/291.47 f(x, s(y)) -> f(y, x) 979.20/291.47 f(x, y) -> ack(x, y) 979.20/291.47 ack(s(x), y) -> f(x, x) 979.20/291.47 979.20/291.47 S is empty. 979.20/291.47 Rewrite Strategy: FULL 979.20/291.47 ---------------------------------------- 979.20/291.47 979.20/291.47 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 979.20/291.47 Transformed a relative TRS into a decreasing-loop problem. 979.20/291.47 ---------------------------------------- 979.20/291.47 979.20/291.47 (2) 979.20/291.47 Obligation: 979.20/291.47 Analyzing the following TRS for decreasing loops: 979.20/291.47 979.20/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 979.20/291.47 979.20/291.47 979.20/291.47 The TRS R consists of the following rules: 979.20/291.47 979.20/291.47 ack(0, y) -> s(y) 979.20/291.47 ack(s(x), 0) -> ack(x, s(0)) 979.20/291.47 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 979.20/291.47 f(s(x), y) -> f(x, s(x)) 979.20/291.47 f(x, s(y)) -> f(y, x) 979.20/291.47 f(x, y) -> ack(x, y) 979.20/291.47 ack(s(x), y) -> f(x, x) 979.20/291.47 979.20/291.47 S is empty. 979.20/291.47 Rewrite Strategy: FULL 979.20/291.47 ---------------------------------------- 979.20/291.47 979.20/291.47 (3) DecreasingLoopProof (LOWER BOUND(ID)) 979.20/291.47 The following loop(s) give(s) rise to the lower bound Omega(n^1): 979.20/291.47 979.20/291.47 The rewrite sequence 979.20/291.47 979.20/291.47 ack(s(x), s(y)) ->^+ ack(x, ack(s(x), y)) 979.20/291.47 979.20/291.47 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 979.20/291.47 979.20/291.47 The pumping substitution is [y / s(y)]. 979.20/291.47 979.20/291.47 The result substitution is [ ]. 979.20/291.47 979.20/291.47 979.20/291.47 979.20/291.47 979.20/291.47 ---------------------------------------- 979.20/291.47 979.20/291.47 (4) 979.20/291.47 Complex Obligation (BEST) 979.20/291.47 979.20/291.47 ---------------------------------------- 979.20/291.47 979.20/291.47 (5) 979.20/291.47 Obligation: 979.20/291.47 Proved the lower bound n^1 for the following obligation: 979.20/291.47 979.20/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 979.20/291.47 979.20/291.47 979.20/291.47 The TRS R consists of the following rules: 979.20/291.47 979.20/291.47 ack(0, y) -> s(y) 979.20/291.47 ack(s(x), 0) -> ack(x, s(0)) 979.20/291.47 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 979.20/291.47 f(s(x), y) -> f(x, s(x))
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