Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313887

details

property	value
status	complete
benchmark	3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n125.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	24.2166 seconds
cpu usage	85.7459
user time	83.1575
system time	2.58841
max virtual memory	3.8073236E7
max residence set size	4891660.0

stage attributes

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

output

85.61/24.16	WORST_CASE(Omega(n^1), O(n^1))
85.61/24.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
85.61/24.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
85.61/24.17	
85.61/24.17	
85.61/24.17	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
85.61/24.17	
85.61/24.17	(0) CpxTRS
85.61/24.17	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
85.61/24.17	(2) CpxWeightedTrs
85.61/24.17	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
85.61/24.17	    (4) CpxTypedWeightedTrs
85.61/24.17	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
85.61/24.17	    (6) CpxTypedWeightedCompleteTrs
85.61/24.17	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms]
85.61/24.17	    (8) CpxRNTS
85.61/24.17	    (9) CompleteCoflocoProof [FINISHED, 262 ms]
85.61/24.17	    (10) BOUNDS(1, n^1)
85.61/24.17	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
85.61/24.17	(12) TRS for Loop Detection
85.61/24.17	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
85.61/24.17	    (14) BEST
85.61/24.17	        (15) proven lower bound
85.61/24.17	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
85.61/24.17	            (17) BOUNDS(n^1, INF)
85.61/24.17	        (18) TRS for Loop Detection
85.61/24.17	
85.61/24.17	
85.61/24.17	----------------------------------------
85.61/24.17	
85.61/24.17	(0)
85.61/24.17	Obligation:
85.61/24.17	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
85.61/24.17	
85.61/24.17	
85.61/24.17	The TRS R consists of the following rules:
85.61/24.17	
85.61/24.17	   cond(true, x, y) -> cond(gr(x, y), x, add(x, y))
85.61/24.17	   gr(0, x) -> false
85.61/24.17	   gr(s(x), 0) -> true
85.61/24.17	   gr(s(x), s(y)) -> gr(x, y)
85.61/24.17	   add(0, x) -> x
85.61/24.17	   add(s(x), y) -> s(add(x, y))
85.61/24.17	
85.61/24.17	S is empty.
85.61/24.17	Rewrite Strategy: INNERMOST
85.61/24.17	----------------------------------------
85.61/24.17	
85.61/24.17	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
85.61/24.17	Transformed relative TRS to weighted TRS
85.61/24.17	----------------------------------------
85.61/24.17	
85.61/24.17	(2)
85.61/24.17	Obligation:
85.61/24.17	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
85.61/24.17	
85.61/24.17	
85.61/24.17	The TRS R consists of the following rules:
85.61/24.17	
85.61/24.17	   cond(true, x, y) -> cond(gr(x, y), x, add(x, y)) [1]
85.61/24.17	   gr(0, x) -> false [1]
85.61/24.17	   gr(s(x), 0) -> true [1]
85.61/24.17	   gr(s(x), s(y)) -> gr(x, y) [1]
85.61/24.17	   add(0, x) -> x [1]
85.61/24.17	   add(s(x), y) -> s(add(x, y)) [1]
85.61/24.17	
85.61/24.17	Rewrite Strategy: INNERMOST
85.61/24.17	----------------------------------------
85.61/24.17	
85.61/24.17	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
85.61/24.17	Infered types.
85.61/24.17	----------------------------------------
85.61/24.17	
85.61/24.17	(4)
85.61/24.17	Obligation:
85.61/24.17	Runtime Complexity Weighted TRS with Types.
85.61/24.17	The TRS R consists of the following rules:
85.61/24.17	
85.61/24.17	   cond(true, x, y) -> cond(gr(x, y), x, add(x, y)) [1]
85.61/24.17	   gr(0, x) -> false [1]
85.61/24.17	   gr(s(x), 0) -> true [1]
85.61/24.17	   gr(s(x), s(y)) -> gr(x, y) [1]
85.61/24.17	   add(0, x) -> x [1]
85.61/24.17	   add(s(x), y) -> s(add(x, y)) [1]
85.61/24.17	
85.61/24.17	The TRS has the following type information:
85.61/24.17	cond :: true:false -> 0:s -> 0:s -> cond
85.61/24.17	true :: true:false
85.61/24.17	gr :: 0:s -> 0:s -> true:false
85.61/24.17	add :: 0:s -> 0:s -> 0:s
85.61/24.17	0 :: 0:s
85.61/24.17	false :: true:false
85.61/24.17	s :: 0:s -> 0:s
85.61/24.17	
85.61/24.17	Rewrite Strategy: INNERMOST
85.61/24.17	----------------------------------------
85.61/24.17	
85.61/24.17	(5) CompletionProof (UPPER BOUND(ID))
85.61/24.17	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
85.61/24.17

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