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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308540
details
property
value
status
complete
benchmark
z10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.565 seconds
cpu usage
374.591
user time
366.262
system time
8.32899
max virtual memory
1.8282344E7
max residence set size
1.2861748E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
374.47/291.50 WORST_CASE(Omega(n^1), ?) 374.47/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 374.47/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 374.47/291.51 374.47/291.51 374.47/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 374.47/291.51 374.47/291.51 (0) CpxTRS 374.47/291.51 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 374.47/291.51 (2) TRS for Loop Detection 374.47/291.51 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 374.47/291.51 (4) BEST 374.47/291.51 (5) proven lower bound 374.47/291.51 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 374.47/291.51 (7) BOUNDS(n^1, INF) 374.47/291.51 (8) TRS for Loop Detection 374.47/291.51 374.47/291.51 374.47/291.51 ---------------------------------------- 374.47/291.51 374.47/291.51 (0) 374.47/291.51 Obligation: 374.47/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 374.47/291.51 374.47/291.51 374.47/291.51 The TRS R consists of the following rules: 374.47/291.51 374.47/291.51 a(lambda(x), y) -> lambda(a(x, p(1, a(y, t)))) 374.47/291.51 a(p(x, y), z) -> p(a(x, z), a(y, z)) 374.47/291.51 a(a(x, y), z) -> a(x, a(y, z)) 374.47/291.51 a(id, x) -> x 374.47/291.51 a(1, id) -> 1 374.47/291.51 a(t, id) -> t 374.47/291.51 a(1, p(x, y)) -> x 374.47/291.51 a(t, p(x, y)) -> y 374.47/291.51 374.47/291.51 S is empty. 374.47/291.51 Rewrite Strategy: FULL 374.47/291.51 ---------------------------------------- 374.47/291.51 374.47/291.51 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 374.47/291.51 Transformed a relative TRS into a decreasing-loop problem. 374.47/291.51 ---------------------------------------- 374.47/291.51 374.47/291.51 (2) 374.47/291.51 Obligation: 374.47/291.51 Analyzing the following TRS for decreasing loops: 374.47/291.51 374.47/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 374.47/291.51 374.47/291.51 374.47/291.51 The TRS R consists of the following rules: 374.47/291.51 374.47/291.51 a(lambda(x), y) -> lambda(a(x, p(1, a(y, t)))) 374.47/291.51 a(p(x, y), z) -> p(a(x, z), a(y, z)) 374.47/291.51 a(a(x, y), z) -> a(x, a(y, z)) 374.47/291.51 a(id, x) -> x 374.47/291.51 a(1, id) -> 1 374.47/291.51 a(t, id) -> t 374.47/291.51 a(1, p(x, y)) -> x 374.47/291.51 a(t, p(x, y)) -> y 374.47/291.51 374.47/291.51 S is empty. 374.47/291.51 Rewrite Strategy: FULL 374.47/291.51 ---------------------------------------- 374.47/291.51 374.47/291.51 (3) DecreasingLoopProof (LOWER BOUND(ID)) 374.47/291.51 The following loop(s) give(s) rise to the lower bound Omega(n^1): 374.47/291.51 374.47/291.51 The rewrite sequence 374.47/291.51 374.47/291.51 a(p(x, y), z) ->^+ p(a(x, z), a(y, z)) 374.47/291.51 374.47/291.51 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 374.47/291.51 374.47/291.51 The pumping substitution is [x / p(x, y)]. 374.47/291.51 374.47/291.51 The result substitution is [ ]. 374.47/291.51 374.47/291.51 374.47/291.51 374.47/291.51 374.47/291.51 ---------------------------------------- 374.47/291.51 374.47/291.51 (4) 374.47/291.51 Complex Obligation (BEST) 374.47/291.51 374.47/291.51 ---------------------------------------- 374.47/291.51 374.47/291.51 (5) 374.47/291.51 Obligation: 374.47/291.51 Proved the lower bound n^1 for the following obligation: 374.47/291.51 374.47/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 374.47/291.51 374.47/291.51 374.47/291.51 The TRS R consists of the following rules: 374.47/291.51 374.47/291.51 a(lambda(x), y) -> lambda(a(x, p(1, a(y, t)))) 374.47/291.51 a(p(x, y), z) -> p(a(x, z), a(y, z))
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