Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313642

details

property	value
status	complete
benchmark	Ex49_GM04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n043.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.21037 seconds
cpu usage	16.0596
user time	14.6504
system time	1.4092
max virtual memory	1.9275476E7
max residence set size	4009616.0

stage attributes

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

output

15.63/5.12	WORST_CASE(Omega(n^1), O(n^1))
15.63/5.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
15.63/5.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.63/5.13	
15.63/5.13	
15.63/5.13	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.63/5.13	
15.63/5.13	(0) CpxTRS
15.63/5.13	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
15.63/5.13	(2) CpxWeightedTrs
15.63/5.13	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
15.63/5.13	    (4) CpxTypedWeightedTrs
15.63/5.13	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
15.63/5.13	    (6) CpxTypedWeightedCompleteTrs
15.63/5.13	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
15.63/5.13	    (8) CpxRNTS
15.63/5.13	    (9) CompleteCoflocoProof [FINISHED, 333 ms]
15.63/5.13	    (10) BOUNDS(1, n^1)
15.63/5.13	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
15.63/5.13	(12) TRS for Loop Detection
15.63/5.13	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
15.63/5.13	    (14) BEST
15.63/5.13	        (15) proven lower bound
15.63/5.13	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
15.63/5.13	            (17) BOUNDS(n^1, INF)
15.63/5.13	        (18) TRS for Loop Detection
15.63/5.13	
15.63/5.13	
15.63/5.13	----------------------------------------
15.63/5.13	
15.63/5.13	(0)
15.63/5.13	Obligation:
15.63/5.13	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.63/5.13	
15.63/5.13	
15.63/5.13	The TRS R consists of the following rules:
15.63/5.13	
15.63/5.13	   minus(0, Y) -> 0
15.63/5.13	   minus(s(X), s(Y)) -> minus(X, Y)
15.63/5.13	   geq(X, 0) -> true
15.63/5.13	   geq(0, s(Y)) -> false
15.63/5.13	   geq(s(X), s(Y)) -> geq(X, Y)
15.63/5.13	   div(0, s(Y)) -> 0
15.63/5.13	   div(s(X), s(Y)) -> if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0)
15.63/5.13	   if(true, X, Y) -> X
15.63/5.13	   if(false, X, Y) -> Y
15.63/5.13	
15.63/5.13	S is empty.
15.63/5.13	Rewrite Strategy: INNERMOST
15.63/5.13	----------------------------------------
15.63/5.13	
15.63/5.13	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
15.63/5.13	Transformed relative TRS to weighted TRS
15.63/5.13	----------------------------------------
15.63/5.13	
15.63/5.13	(2)
15.63/5.13	Obligation:
15.63/5.13	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
15.63/5.13	
15.63/5.13	
15.63/5.13	The TRS R consists of the following rules:
15.63/5.13	
15.63/5.13	   minus(0, Y) -> 0 [1]
15.63/5.13	   minus(s(X), s(Y)) -> minus(X, Y) [1]
15.63/5.13	   geq(X, 0) -> true [1]
15.63/5.13	   geq(0, s(Y)) -> false [1]
15.63/5.13	   geq(s(X), s(Y)) -> geq(X, Y) [1]
15.63/5.13	   div(0, s(Y)) -> 0 [1]
15.63/5.13	   div(s(X), s(Y)) -> if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0) [1]
15.63/5.13	   if(true, X, Y) -> X [1]
15.63/5.13	   if(false, X, Y) -> Y [1]
15.63/5.13	
15.63/5.13	Rewrite Strategy: INNERMOST
15.63/5.13	----------------------------------------
15.63/5.13	
15.63/5.13	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
15.63/5.13	Infered types.
15.63/5.13	----------------------------------------
15.63/5.13	
15.63/5.13	(4)
15.63/5.13	Obligation:
15.63/5.13	Runtime Complexity Weighted TRS with Types.
15.63/5.13	The TRS R consists of the following rules:
15.63/5.13	
15.63/5.13	   minus(0, Y) -> 0 [1]
15.63/5.13	   minus(s(X), s(Y)) -> minus(X, Y) [1]
15.63/5.13	   geq(X, 0) -> true [1]
15.63/5.13	   geq(0, s(Y)) -> false [1]
15.63/5.13	   geq(s(X), s(Y)) -> geq(X, Y) [1]
15.63/5.13	   div(0, s(Y)) -> 0 [1]
15.63/5.13	   div(s(X), s(Y)) -> if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0) [1]
15.63/5.13	   if(true, X, Y) -> X [1]
15.63/5.13	   if(false, X, Y) -> Y [1]
15.63/5.13	
15.63/5.13	The TRS has the following type information:
15.63/5.13	minus :: 0:s -> 0:s -> 0:s
15.63/5.13	0 :: 0:s
15.63/5.13	s :: 0:s -> 0:s
15.63/5.13	geq :: 0:s -> 0:s -> true:false
15.63/5.13	true :: true:false

popout

output may be truncated. 'popout' for the full output.

job log

popout

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