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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307885
details
property
value
status
complete
benchmark
aprove3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.551 seconds
cpu usage
306.497
user time
304.547
system time
1.95021
max virtual memory
1.8277336E7
max residence set size
5432040.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
306.36/291.50 WORST_CASE(Omega(n^1), ?) 306.36/291.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 306.36/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 306.36/291.50 306.36/291.50 306.36/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 306.36/291.50 306.36/291.50 (0) CpxTRS 306.36/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 306.36/291.50 (2) TRS for Loop Detection 306.36/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 306.36/291.50 (4) BEST 306.36/291.50 (5) proven lower bound 306.36/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 306.36/291.50 (7) BOUNDS(n^1, INF) 306.36/291.50 (8) TRS for Loop Detection 306.36/291.50 306.36/291.50 306.36/291.50 ---------------------------------------- 306.36/291.50 306.36/291.50 (0) 306.36/291.50 Obligation: 306.36/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 306.36/291.50 306.36/291.50 306.36/291.50 The TRS R consists of the following rules: 306.36/291.50 306.36/291.50 function(iszero, 0, dummy, dummy2) -> true 306.36/291.50 function(iszero, s(x), dummy, dummy2) -> false 306.36/291.50 function(p, 0, dummy, dummy2) -> 0 306.36/291.50 function(p, s(0), dummy, dummy2) -> 0 306.36/291.50 function(p, s(s(x)), dummy, dummy2) -> s(function(p, s(x), x, x)) 306.36/291.50 function(plus, dummy, x, y) -> function(if, function(iszero, x, x, x), x, y) 306.36/291.50 function(if, true, x, y) -> y 306.36/291.50 function(if, false, x, y) -> function(plus, function(third, x, y, y), function(p, x, x, y), s(y)) 306.36/291.50 function(third, x, y, z) -> z 306.36/291.50 306.36/291.50 S is empty. 306.36/291.50 Rewrite Strategy: FULL 306.36/291.50 ---------------------------------------- 306.36/291.50 306.36/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 306.36/291.50 Transformed a relative TRS into a decreasing-loop problem. 306.36/291.50 ---------------------------------------- 306.36/291.50 306.36/291.50 (2) 306.36/291.50 Obligation: 306.36/291.50 Analyzing the following TRS for decreasing loops: 306.36/291.50 306.36/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 306.36/291.50 306.36/291.50 306.36/291.50 The TRS R consists of the following rules: 306.36/291.50 306.36/291.50 function(iszero, 0, dummy, dummy2) -> true 306.36/291.50 function(iszero, s(x), dummy, dummy2) -> false 306.36/291.50 function(p, 0, dummy, dummy2) -> 0 306.36/291.50 function(p, s(0), dummy, dummy2) -> 0 306.36/291.50 function(p, s(s(x)), dummy, dummy2) -> s(function(p, s(x), x, x)) 306.36/291.50 function(plus, dummy, x, y) -> function(if, function(iszero, x, x, x), x, y) 306.36/291.50 function(if, true, x, y) -> y 306.36/291.50 function(if, false, x, y) -> function(plus, function(third, x, y, y), function(p, x, x, y), s(y)) 306.36/291.50 function(third, x, y, z) -> z 306.36/291.50 306.36/291.50 S is empty. 306.36/291.50 Rewrite Strategy: FULL 306.36/291.50 ---------------------------------------- 306.36/291.50 306.36/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 306.36/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 306.36/291.50 306.36/291.50 The rewrite sequence 306.36/291.50 306.36/291.50 function(p, s(s(x)), dummy, dummy2) ->^+ s(function(p, s(x), x, x)) 306.36/291.50 306.36/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 306.36/291.50 306.36/291.50 The pumping substitution is [x / s(x)]. 306.36/291.50 306.36/291.50 The result substitution is [dummy / x, dummy2 / x]. 306.36/291.50 306.36/291.50 306.36/291.50 306.36/291.50 306.36/291.50 ---------------------------------------- 306.36/291.50 306.36/291.50 (4) 306.36/291.50 Complex Obligation (BEST) 306.36/291.50 306.36/291.50 ---------------------------------------- 306.36/291.50 306.36/291.50 (5) 306.36/291.50 Obligation: 306.36/291.50 Proved the lower bound n^1 for the following obligation: 306.36/291.50 306.36/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 306.36/291.50 306.36/291.50 306.36/291.50 The TRS R consists of the following rules: 306.36/291.50
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