Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313898

details

property	value
status	complete
benchmark	8.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n089.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.5747 seconds
cpu usage	48.7471
user time	46.4232
system time	2.3239
max virtual memory	3.7715336E7
max residence set size	4408660.0

stage attributes

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

output

40.39/11.45	WORST_CASE(Omega(n^1), O(n^1))
48.39/13.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
48.39/13.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
48.39/13.49	
48.39/13.49	
48.39/13.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
48.39/13.49	
48.39/13.49	(0) CpxTRS
48.39/13.49	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
48.39/13.49	(2) CpxWeightedTrs
48.39/13.49	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
48.39/13.49	    (4) CpxTypedWeightedTrs
48.39/13.49	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
48.39/13.49	    (6) CpxTypedWeightedCompleteTrs
48.39/13.49	    (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
48.39/13.49	    (8) CpxTypedWeightedCompleteTrs
48.39/13.49	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
48.39/13.49	    (10) CpxRNTS
48.39/13.49	    (11) InliningProof [UPPER BOUND(ID), 297 ms]
48.39/13.49	    (12) CpxRNTS
48.39/13.49	    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
48.39/13.49	    (14) CpxRNTS
48.39/13.49	    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
48.39/13.49	    (16) CpxRNTS
48.39/13.49	    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
48.39/13.49	    (18) CpxRNTS
48.39/13.49	    (19) IntTrsBoundProof [UPPER BOUND(ID), 243 ms]
48.39/13.49	    (20) CpxRNTS
48.39/13.49	    (21) IntTrsBoundProof [UPPER BOUND(ID), 79 ms]
48.39/13.49	    (22) CpxRNTS
48.39/13.49	    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
48.39/13.49	    (24) CpxRNTS
48.39/13.49	    (25) IntTrsBoundProof [UPPER BOUND(ID), 647 ms]
48.39/13.49	    (26) CpxRNTS
48.39/13.49	    (27) IntTrsBoundProof [UPPER BOUND(ID), 110 ms]
48.39/13.49	    (28) CpxRNTS
48.39/13.49	    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
48.39/13.49	    (30) CpxRNTS
48.39/13.49	    (31) IntTrsBoundProof [UPPER BOUND(ID), 108 ms]
48.39/13.49	    (32) CpxRNTS
48.39/13.49	    (33) IntTrsBoundProof [UPPER BOUND(ID), 4 ms]
48.39/13.49	    (34) CpxRNTS
48.39/13.49	    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
48.39/13.49	    (36) CpxRNTS
48.39/13.49	    (37) IntTrsBoundProof [UPPER BOUND(ID), 386 ms]
48.39/13.49	    (38) CpxRNTS
48.39/13.49	    (39) IntTrsBoundProof [UPPER BOUND(ID), 166 ms]
48.39/13.49	    (40) CpxRNTS
48.39/13.49	    (41) FinalProof [FINISHED, 0 ms]
48.39/13.49	    (42) BOUNDS(1, n^1)
48.39/13.49	(43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
48.39/13.49	(44) TRS for Loop Detection
48.39/13.49	    (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
48.39/13.49	    (46) BEST
48.39/13.49	        (47) proven lower bound
48.39/13.49	            (48) LowerBoundPropagationProof [FINISHED, 0 ms]
48.39/13.49	            (49) BOUNDS(n^1, INF)
48.39/13.49	        (50) TRS for Loop Detection
48.39/13.49	
48.39/13.49	
48.39/13.49	----------------------------------------
48.39/13.49	
48.39/13.49	(0)
48.39/13.49	Obligation:
48.39/13.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
48.39/13.49	
48.39/13.49	
48.39/13.49	The TRS R consists of the following rules:
48.39/13.49	
48.39/13.49	   cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y))
48.39/13.49	   and(true, true) -> true
48.39/13.49	   and(x, false) -> false
48.39/13.49	   and(false, x) -> false
48.39/13.49	   gr(0, 0) -> false
48.39/13.49	   gr(0, x) -> false
48.39/13.49	   gr(s(x), 0) -> true
48.39/13.49	   gr(s(x), s(y)) -> gr(x, y)
48.39/13.49	   p(0) -> 0
48.39/13.49	   p(s(x)) -> x
48.39/13.49	
48.39/13.49	S is empty.
48.39/13.49	Rewrite Strategy: INNERMOST
48.39/13.49	----------------------------------------
48.39/13.49	
48.39/13.49	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
48.39/13.49	Transformed relative TRS to weighted TRS
48.39/13.49	----------------------------------------
48.39/13.49	
48.39/13.49	(2)
48.39/13.49	Obligation:
48.39/13.49	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
48.39/13.49	
48.39/13.49	
48.39/13.49	The TRS R consists of the following rules:
48.39/13.49	
48.39/13.49	   cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y)) [1]
48.39/13.49	   and(true, true) -> true [1]
48.39/13.49	   and(x, false) -> false [1]
48.39/13.49	   and(false, x) -> false [1]
48.39/13.49	   gr(0, 0) -> false [1]

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