Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313708

details

property	value
status	complete
benchmark	thiemann40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n126.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.17057 seconds
cpu usage	41.2635
user time	38.8134
system time	2.4502
max virtual memory	1.914436E7
max residence set size	3611600.0

stage attributes

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

output

20.50/6.11	WORST_CASE(Omega(n^1), O(n^1))
20.50/6.12	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.50/6.12	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.50/6.12	
20.50/6.12	
20.50/6.12	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.50/6.12	
20.50/6.12	(0) CpxTRS
20.50/6.12	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.50/6.12	(2) CpxWeightedTrs
20.50/6.12	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.50/6.12	    (4) CpxTypedWeightedTrs
20.50/6.12	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
20.50/6.12	    (6) CpxTypedWeightedCompleteTrs
20.50/6.12	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.50/6.12	    (8) CpxRNTS
20.50/6.12	    (9) CompleteCoflocoProof [FINISHED, 200 ms]
20.50/6.12	    (10) BOUNDS(1, n^1)
20.50/6.12	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.50/6.12	(12) TRS for Loop Detection
20.50/6.12	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.50/6.12	    (14) BEST
20.50/6.12	        (15) proven lower bound
20.50/6.12	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
20.50/6.12	            (17) BOUNDS(n^1, INF)
20.50/6.12	        (18) TRS for Loop Detection
20.50/6.12	
20.50/6.12	
20.50/6.12	----------------------------------------
20.50/6.12	
20.50/6.12	(0)
20.50/6.12	Obligation:
20.50/6.12	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.50/6.12	
20.50/6.12	
20.50/6.12	The TRS R consists of the following rules:
20.50/6.12	
20.50/6.12	   nonZero(0) -> false
20.50/6.12	   nonZero(s(x)) -> true
20.50/6.12	   p(0) -> 0
20.50/6.12	   p(s(x)) -> x
20.50/6.12	   id_inc(x) -> x
20.50/6.12	   id_inc(x) -> s(x)
20.50/6.12	   random(x) -> rand(x, 0)
20.50/6.12	   rand(x, y) -> if(nonZero(x), x, y)
20.50/6.12	   if(false, x, y) -> y
20.50/6.12	   if(true, x, y) -> rand(p(x), id_inc(y))
20.50/6.12	
20.50/6.12	S is empty.
20.50/6.12	Rewrite Strategy: INNERMOST
20.50/6.12	----------------------------------------
20.50/6.12	
20.50/6.12	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
20.50/6.12	Transformed relative TRS to weighted TRS
20.50/6.12	----------------------------------------
20.50/6.12	
20.50/6.12	(2)
20.50/6.12	Obligation:
20.50/6.12	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
20.50/6.12	
20.50/6.12	
20.50/6.12	The TRS R consists of the following rules:
20.50/6.12	
20.50/6.12	   nonZero(0) -> false [1]
20.50/6.12	   nonZero(s(x)) -> true [1]
20.50/6.12	   p(0) -> 0 [1]
20.50/6.12	   p(s(x)) -> x [1]
20.50/6.12	   id_inc(x) -> x [1]
20.50/6.12	   id_inc(x) -> s(x) [1]
20.50/6.12	   random(x) -> rand(x, 0) [1]
20.50/6.12	   rand(x, y) -> if(nonZero(x), x, y) [1]
20.50/6.12	   if(false, x, y) -> y [1]
20.50/6.12	   if(true, x, y) -> rand(p(x), id_inc(y)) [1]
20.50/6.12	
20.50/6.12	Rewrite Strategy: INNERMOST
20.50/6.12	----------------------------------------
20.50/6.12	
20.50/6.12	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
20.50/6.12	Infered types.
20.50/6.12	----------------------------------------
20.50/6.12	
20.50/6.12	(4)
20.50/6.12	Obligation:
20.50/6.12	Runtime Complexity Weighted TRS with Types.
20.50/6.12	The TRS R consists of the following rules:
20.50/6.12	
20.50/6.12	   nonZero(0) -> false [1]
20.50/6.12	   nonZero(s(x)) -> true [1]
20.50/6.12	   p(0) -> 0 [1]
20.50/6.12	   p(s(x)) -> x [1]
20.50/6.12	   id_inc(x) -> x [1]
20.50/6.12	   id_inc(x) -> s(x) [1]
20.50/6.12	   random(x) -> rand(x, 0) [1]
20.50/6.12	   rand(x, y) -> if(nonZero(x), x, y) [1]
20.50/6.12	   if(false, x, y) -> y [1]
20.50/6.12	   if(true, x, y) -> rand(p(x), id_inc(y)) [1]
20.50/6.12	
20.50/6.12	The TRS has the following type information:
20.50/6.12	nonZero :: 0:s -> false:true
20.50/6.12	0 :: 0:s

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40