Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308131

details

property	value
status	complete
benchmark	Ex4_4_Luc96b_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n041.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.62417 seconds
cpu usage	19.7443
user time	18.1914
system time	1.55287
max virtual memory	1.9011748E7
max residence set size	3816408.0

stage attributes

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

output

19.60/6.58	WORST_CASE(Omega(n^1), O(n^1))
19.60/6.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
19.60/6.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.60/6.59	
19.60/6.59	
19.60/6.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
19.60/6.59	
19.60/6.59	(0) CpxTRS
19.60/6.59	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
19.60/6.59	(2) CpxTRS
19.60/6.59	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
19.60/6.59	    (4) CpxTRS
19.60/6.59	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 8 ms]
19.60/6.59	    (6) BOUNDS(1, n^1)
19.60/6.59	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
19.60/6.59	(8) TRS for Loop Detection
19.60/6.59	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
19.60/6.59	    (10) BEST
19.60/6.59	        (11) proven lower bound
19.60/6.59	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
19.60/6.59	            (13) BOUNDS(n^1, INF)
19.60/6.59	        (14) TRS for Loop Detection
19.60/6.59	
19.60/6.59	
19.60/6.59	----------------------------------------
19.60/6.59	
19.60/6.59	(0)
19.60/6.59	Obligation:
19.60/6.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
19.60/6.59	
19.60/6.59	
19.60/6.59	The TRS R consists of the following rules:
19.60/6.59	
19.60/6.59	   active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
19.60/6.59	   active(f(X1, X2)) -> f(active(X1), X2)
19.60/6.59	   active(g(X)) -> g(active(X))
19.60/6.59	   f(mark(X1), X2) -> mark(f(X1, X2))
19.60/6.59	   g(mark(X)) -> mark(g(X))
19.60/6.59	   proper(f(X1, X2)) -> f(proper(X1), proper(X2))
19.60/6.59	   proper(g(X)) -> g(proper(X))
19.60/6.59	   f(ok(X1), ok(X2)) -> ok(f(X1, X2))
19.60/6.59	   g(ok(X)) -> ok(g(X))
19.60/6.59	   top(mark(X)) -> top(proper(X))
19.60/6.59	   top(ok(X)) -> top(active(X))
19.60/6.59	
19.60/6.59	S is empty.
19.60/6.59	Rewrite Strategy: FULL
19.60/6.59	----------------------------------------
19.60/6.59	
19.60/6.59	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
19.60/6.59	The following defined symbols can occur below the 0th argument of top: proper, active
19.60/6.59	The following defined symbols can occur below the 0th argument of proper: proper, active
19.60/6.59	The following defined symbols can occur below the 0th argument of active: proper, active
19.60/6.59	
19.60/6.59	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
19.60/6.59	active(f(g(X), Y)) -> mark(f(X, f(g(X), Y)))
19.60/6.59	active(f(X1, X2)) -> f(active(X1), X2)
19.60/6.59	active(g(X)) -> g(active(X))
19.60/6.59	proper(f(X1, X2)) -> f(proper(X1), proper(X2))
19.60/6.59	proper(g(X)) -> g(proper(X))
19.60/6.59	
19.60/6.59	----------------------------------------
19.60/6.59	
19.60/6.59	(2)
19.60/6.59	Obligation:
19.60/6.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
19.60/6.59	
19.60/6.59	
19.60/6.59	The TRS R consists of the following rules:
19.60/6.59	
19.60/6.59	   f(mark(X1), X2) -> mark(f(X1, X2))
19.60/6.59	   g(mark(X)) -> mark(g(X))
19.60/6.59	   f(ok(X1), ok(X2)) -> ok(f(X1, X2))
19.60/6.59	   g(ok(X)) -> ok(g(X))
19.60/6.59	   top(mark(X)) -> top(proper(X))
19.60/6.59	   top(ok(X)) -> top(active(X))
19.60/6.59	
19.60/6.59	S is empty.
19.60/6.59	Rewrite Strategy: FULL
19.60/6.59	----------------------------------------
19.60/6.59	
19.60/6.59	(3) RelTrsToTrsProof (UPPER BOUND(ID))
19.60/6.59	transformed relative TRS to TRS
19.60/6.59	----------------------------------------
19.60/6.59	
19.60/6.59	(4)
19.60/6.59	Obligation:
19.60/6.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
19.60/6.59	
19.60/6.59	
19.60/6.59	The TRS R consists of the following rules:
19.60/6.59	
19.60/6.59	   f(mark(X1), X2) -> mark(f(X1, X2))
19.60/6.59	   g(mark(X)) -> mark(g(X))
19.60/6.59	   f(ok(X1), ok(X2)) -> ok(f(X1, X2))
19.60/6.59	   g(ok(X)) -> ok(g(X))
19.60/6.59	   top(mark(X)) -> top(proper(X))
19.60/6.59	   top(ok(X)) -> top(active(X))
19.60/6.59	
19.60/6.59	S is empty.

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11