Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313277

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	n156.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.57 seconds
cpu usage	1004.68
user time	992.354
system time	12.3255
max virtual memory	5.6605336E7
max residence set size	1.507132E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

1004.54/291.49	WORST_CASE(Omega(n^1), ?)
1004.54/291.49	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
1004.54/291.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1004.54/291.49	
1004.54/291.49	(0) CpxTRS
1004.54/291.49	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1004.54/291.49	(2) TRS for Loop Detection
1004.54/291.49	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1004.54/291.49	(4) BEST
1004.54/291.49	    (5) proven lower bound
1004.54/291.49	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1004.54/291.49	        (7) BOUNDS(n^1, INF)
1004.54/291.49	    (8) TRS for Loop Detection
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	----------------------------------------
1004.54/291.49	
1004.54/291.49	(0)
1004.54/291.49	Obligation:
1004.54/291.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	The TRS R consists of the following rules:
1004.54/291.49	
1004.54/291.49	   function(iszero, 0, dummy, dummy2) -> true
1004.54/291.49	   function(iszero, s(x), dummy, dummy2) -> false
1004.54/291.49	   function(p, 0, dummy, dummy2) -> 0
1004.54/291.49	   function(p, s(0), dummy, dummy2) -> 0
1004.54/291.49	   function(p, s(s(x)), dummy, dummy2) -> s(function(p, s(x), x, x))
1004.54/291.49	   function(plus, dummy, x, y) -> function(if, function(iszero, x, x, x), x, y)
1004.54/291.49	   function(if, true, x, y) -> y
1004.54/291.49	   function(if, false, x, y) -> function(plus, function(third, x, y, y), function(p, x, x, y), s(y))
1004.54/291.49	   function(third, x, y, z) -> z
1004.54/291.49	
1004.54/291.49	S is empty.
1004.54/291.49	Rewrite Strategy: INNERMOST
1004.54/291.49	----------------------------------------
1004.54/291.49	
1004.54/291.49	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1004.54/291.49	Transformed a relative TRS into a decreasing-loop problem.
1004.54/291.49	----------------------------------------
1004.54/291.49	
1004.54/291.49	(2)
1004.54/291.49	Obligation:
1004.54/291.49	Analyzing the following TRS for decreasing loops:
1004.54/291.49	
1004.54/291.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	The TRS R consists of the following rules:
1004.54/291.49	
1004.54/291.49	   function(iszero, 0, dummy, dummy2) -> true
1004.54/291.49	   function(iszero, s(x), dummy, dummy2) -> false
1004.54/291.49	   function(p, 0, dummy, dummy2) -> 0
1004.54/291.49	   function(p, s(0), dummy, dummy2) -> 0
1004.54/291.49	   function(p, s(s(x)), dummy, dummy2) -> s(function(p, s(x), x, x))
1004.54/291.49	   function(plus, dummy, x, y) -> function(if, function(iszero, x, x, x), x, y)
1004.54/291.49	   function(if, true, x, y) -> y
1004.54/291.49	   function(if, false, x, y) -> function(plus, function(third, x, y, y), function(p, x, x, y), s(y))
1004.54/291.49	   function(third, x, y, z) -> z
1004.54/291.49	
1004.54/291.49	S is empty.
1004.54/291.49	Rewrite Strategy: INNERMOST
1004.54/291.49	----------------------------------------
1004.54/291.49	
1004.54/291.49	(3) DecreasingLoopProof (LOWER BOUND(ID))
1004.54/291.49	The following loop(s) give(s) rise to the lower bound Omega(n^1):
1004.54/291.49	
1004.54/291.49	The rewrite sequence
1004.54/291.49	
1004.54/291.49	function(p, s(s(x)), dummy, dummy2) ->^+ s(function(p, s(x), x, x))
1004.54/291.49	
1004.54/291.49	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
1004.54/291.49	
1004.54/291.49	The pumping substitution is [x / s(x)].
1004.54/291.49	
1004.54/291.49	The result substitution is [dummy / x, dummy2 / x].
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	----------------------------------------
1004.54/291.49	
1004.54/291.49	(4)
1004.54/291.49	Complex Obligation (BEST)
1004.54/291.49	
1004.54/291.49	----------------------------------------
1004.54/291.49	
1004.54/291.49	(5)
1004.54/291.49	Obligation:
1004.54/291.49	Proved the lower bound n^1 for the following obligation:
1004.54/291.49	
1004.54/291.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1004.54/291.49	
1004.54/291.49	
1004.54/291.49	The TRS R consists of the following rules:
1004.54/291.49

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