Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313576

details

property	value
status	complete
benchmark	4.13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.13852 seconds
cpu usage	22.8405
user time	21.2018
system time	1.63871
max virtual memory	1.8944312E7
max residence set size	4022656.0

stage attributes

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

output

22.33/7.27	WORST_CASE(Omega(n^1), O(n^1))
22.45/7.88	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.45/7.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.45/7.88	
22.45/7.88	
22.45/7.88	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.45/7.88	
22.45/7.88	(0) CpxTRS
22.45/7.88	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
22.45/7.88	(2) CpxWeightedTrs
22.45/7.88	    (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.45/7.88	    (4) CpxWeightedTrs
22.45/7.88	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.45/7.88	    (6) CpxTypedWeightedTrs
22.45/7.88	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
22.45/7.88	    (8) CpxTypedWeightedCompleteTrs
22.45/7.88	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.45/7.88	    (10) CpxTypedWeightedCompleteTrs
22.45/7.88	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
22.45/7.88	    (12) CpxRNTS
22.45/7.88	    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
22.45/7.88	    (14) CpxRNTS
22.45/7.88	    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
22.45/7.88	    (16) CpxRNTS
22.45/7.88	    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.45/7.88	    (18) CpxRNTS
22.45/7.88	    (19) IntTrsBoundProof [UPPER BOUND(ID), 991 ms]
22.45/7.88	    (20) CpxRNTS
22.45/7.88	    (21) IntTrsBoundProof [UPPER BOUND(ID), 219 ms]
22.45/7.88	    (22) CpxRNTS
22.45/7.88	    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.45/7.88	    (24) CpxRNTS
22.45/7.88	    (25) IntTrsBoundProof [UPPER BOUND(ID), 211 ms]
22.45/7.88	    (26) CpxRNTS
22.45/7.88	    (27) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
22.45/7.88	    (28) CpxRNTS
22.45/7.88	    (29) FinalProof [FINISHED, 0 ms]
22.45/7.88	    (30) BOUNDS(1, n^1)
22.45/7.88	(31) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
22.45/7.88	(32) TRS for Loop Detection
22.45/7.88	    (33) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
22.45/7.88	    (34) BEST
22.45/7.88	        (35) proven lower bound
22.45/7.88	            (36) LowerBoundPropagationProof [FINISHED, 0 ms]
22.45/7.88	            (37) BOUNDS(n^1, INF)
22.45/7.88	        (38) TRS for Loop Detection
22.45/7.88	
22.45/7.88	
22.45/7.88	----------------------------------------
22.45/7.88	
22.45/7.88	(0)
22.45/7.88	Obligation:
22.45/7.88	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.45/7.88	
22.45/7.88	
22.45/7.88	The TRS R consists of the following rules:
22.45/7.88	
22.45/7.88	   -(0, y) -> 0
22.45/7.88	   -(x, 0) -> x
22.45/7.88	   -(x, s(y)) -> if(greater(x, s(y)), s(-(x, p(s(y)))), 0)
22.45/7.88	   p(0) -> 0
22.45/7.88	   p(s(x)) -> x
22.45/7.88	
22.45/7.88	S is empty.
22.45/7.88	Rewrite Strategy: INNERMOST
22.45/7.88	----------------------------------------
22.45/7.88	
22.45/7.88	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
22.45/7.88	Transformed relative TRS to weighted TRS
22.45/7.88	----------------------------------------
22.45/7.88	
22.45/7.88	(2)
22.45/7.88	Obligation:
22.45/7.88	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
22.45/7.88	
22.45/7.88	
22.45/7.88	The TRS R consists of the following rules:
22.45/7.88	
22.45/7.88	   -(0, y) -> 0 [1]
22.45/7.88	   -(x, 0) -> x [1]
22.45/7.88	   -(x, s(y)) -> if(greater(x, s(y)), s(-(x, p(s(y)))), 0) [1]
22.45/7.88	   p(0) -> 0 [1]
22.45/7.88	   p(s(x)) -> x [1]
22.45/7.88	
22.45/7.88	Rewrite Strategy: INNERMOST
22.45/7.88	----------------------------------------
22.45/7.88	
22.45/7.88	(3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
22.45/7.88	Renamed defined symbols to avoid conflicts with arithmetic symbols:
22.45/7.88	
22.45/7.88	- => minus
22.45/7.88	
22.45/7.88	----------------------------------------
22.45/7.88	
22.45/7.88	(4)
22.45/7.88	Obligation:
22.45/7.88	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
22.45/7.88	
22.45/7.88	
22.45/7.88	The TRS R consists of the following rules:

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