Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308397

details

property	value
status	complete
benchmark	4.28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.99473 seconds
cpu usage	32.486
user time	30.6588
system time	1.82715
max virtual memory	1.8943368E7
max residence set size	3963020.0

stage attributes

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

output

32.34/9.92	WORST_CASE(Omega(n^1), O(n^1))
32.34/9.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
32.34/9.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
32.34/9.94	
32.34/9.94	
32.34/9.94	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
32.34/9.94	
32.34/9.94	(0) CpxTRS
32.34/9.94	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	(2) CpxTRS
32.34/9.94	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
32.34/9.94	    (4) CpxTRS
32.34/9.94	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
32.34/9.94	    (6) CpxWeightedTrs
32.34/9.94	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
32.34/9.94	    (8) CpxTypedWeightedTrs
32.34/9.94	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	    (10) CpxTypedWeightedCompleteTrs
32.34/9.94	    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
32.34/9.94	    (12) CpxTypedWeightedCompleteTrs
32.34/9.94	    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	    (14) CpxRNTS
32.34/9.94	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
32.34/9.94	    (16) CpxRNTS
32.34/9.94	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
32.34/9.94	    (18) CpxRNTS
32.34/9.94	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	    (20) CpxRNTS
32.34/9.94	    (21) IntTrsBoundProof [UPPER BOUND(ID), 273 ms]
32.34/9.94	    (22) CpxRNTS
32.34/9.94	    (23) IntTrsBoundProof [UPPER BOUND(ID), 86 ms]
32.34/9.94	    (24) CpxRNTS
32.34/9.94	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	    (26) CpxRNTS
32.34/9.94	    (27) IntTrsBoundProof [UPPER BOUND(ID), 264 ms]
32.34/9.94	    (28) CpxRNTS
32.34/9.94	    (29) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
32.34/9.94	    (30) CpxRNTS
32.34/9.94	    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	    (32) CpxRNTS
32.34/9.94	    (33) IntTrsBoundProof [UPPER BOUND(ID), 465 ms]
32.34/9.94	    (34) CpxRNTS
32.34/9.94	    (35) IntTrsBoundProof [UPPER BOUND(ID), 83 ms]
32.34/9.94	    (36) CpxRNTS
32.34/9.94	    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
32.34/9.94	    (38) CpxRNTS
32.34/9.94	    (39) IntTrsBoundProof [UPPER BOUND(ID), 140 ms]
32.34/9.94	    (40) CpxRNTS
32.34/9.94	    (41) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
32.34/9.94	    (42) CpxRNTS
32.34/9.94	    (43) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
32.34/9.94	    (44) CpxRNTS
32.34/9.94	    (45) IntTrsBoundProof [UPPER BOUND(ID), 361 ms]
32.34/9.94	    (46) CpxRNTS
32.34/9.94	    (47) IntTrsBoundProof [UPPER BOUND(ID), 105 ms]
32.34/9.94	    (48) CpxRNTS
32.34/9.94	    (49) FinalProof [FINISHED, 0 ms]
32.34/9.94	    (50) BOUNDS(1, n^1)
32.34/9.94	(51) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
32.34/9.94	(52) TRS for Loop Detection
32.34/9.94	    (53) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
32.34/9.94	    (54) BEST
32.34/9.94	        (55) proven lower bound
32.34/9.94	            (56) LowerBoundPropagationProof [FINISHED, 0 ms]
32.34/9.94	            (57) BOUNDS(n^1, INF)
32.34/9.94	        (58) TRS for Loop Detection
32.34/9.94	
32.34/9.94	
32.34/9.94	----------------------------------------
32.34/9.94	
32.34/9.94	(0)
32.34/9.94	Obligation:
32.34/9.94	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
32.34/9.94	
32.34/9.94	
32.34/9.94	The TRS R consists of the following rules:
32.34/9.94	
32.34/9.94	   f(x, nil) -> g(nil, x)
32.34/9.94	   f(x, g(y, z)) -> g(f(x, y), z)
32.34/9.94	   ++(x, nil) -> x
32.34/9.94	   ++(x, g(y, z)) -> g(++(x, y), z)
32.34/9.94	   null(nil) -> true
32.34/9.94	   null(g(x, y)) -> false
32.34/9.94	   mem(nil, y) -> false
32.34/9.94	   mem(g(x, y), z) -> or(=(y, z), mem(x, z))
32.34/9.94	   mem(x, max(x)) -> not(null(x))
32.34/9.94	   max(g(g(nil, x), y)) -> max'(x, y)
32.34/9.94	   max(g(g(g(x, y), z), u)) -> max'(max(g(g(x, y), z)), u)
32.34/9.94	
32.34/9.94	S is empty.
32.34/9.94	Rewrite Strategy: FULL
32.34/9.94	----------------------------------------
32.34/9.94	
32.34/9.94	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
32.34/9.94	The TRS does not nest defined symbols.
32.34/9.94	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
32.34/9.94	mem(x, max(x)) -> not(null(x))
32.34/9.94	
32.34/9.94	----------------------------------------
32.34/9.94

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