Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308062

details

property	value
status	complete
benchmark	Ex14_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n172.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.41699 seconds
cpu usage	26.0
user time	24.1438
system time	1.85622
max virtual memory	1.9076052E7
max residence set size	3945156.0

stage attributes

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

output

25.58/8.94	WORST_CASE(Omega(n^1), O(n^1))
25.58/8.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
25.58/8.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
25.58/8.95	
25.58/8.95	
25.58/8.95	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
25.58/8.95	
25.58/8.95	(0) CpxTRS
25.58/8.95	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 1 ms]
25.58/8.95	(2) CpxTRS
25.58/8.95	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
25.58/8.95	    (4) CpxTRS
25.58/8.95	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 185 ms]
25.58/8.95	    (6) BOUNDS(1, n^1)
25.58/8.95	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
25.58/8.95	(8) TRS for Loop Detection
25.58/8.95	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
25.58/8.95	    (10) BEST
25.58/8.95	        (11) proven lower bound
25.58/8.95	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
25.58/8.95	            (13) BOUNDS(n^1, INF)
25.58/8.95	        (14) TRS for Loop Detection
25.58/8.95	
25.58/8.95	
25.58/8.95	----------------------------------------
25.58/8.95	
25.58/8.95	(0)
25.58/8.95	Obligation:
25.58/8.95	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
25.58/8.95	
25.58/8.95	
25.58/8.95	The TRS R consists of the following rules:
25.58/8.95	
25.58/8.95	   active(h(X)) -> mark(g(X, X))
25.58/8.95	   active(g(a, X)) -> mark(f(b, X))
25.58/8.95	   active(f(X, X)) -> mark(h(a))
25.58/8.95	   active(a) -> mark(b)
25.58/8.95	   active(h(X)) -> h(active(X))
25.58/8.95	   active(g(X1, X2)) -> g(active(X1), X2)
25.58/8.95	   active(f(X1, X2)) -> f(active(X1), X2)
25.58/8.95	   h(mark(X)) -> mark(h(X))
25.58/8.95	   g(mark(X1), X2) -> mark(g(X1, X2))
25.58/8.95	   f(mark(X1), X2) -> mark(f(X1, X2))
25.58/8.95	   proper(h(X)) -> h(proper(X))
25.58/8.95	   proper(g(X1, X2)) -> g(proper(X1), proper(X2))
25.58/8.95	   proper(a) -> ok(a)
25.58/8.95	   proper(f(X1, X2)) -> f(proper(X1), proper(X2))
25.58/8.95	   proper(b) -> ok(b)
25.58/8.95	   h(ok(X)) -> ok(h(X))
25.58/8.95	   g(ok(X1), ok(X2)) -> ok(g(X1, X2))
25.58/8.95	   f(ok(X1), ok(X2)) -> ok(f(X1, X2))
25.58/8.95	   top(mark(X)) -> top(proper(X))
25.58/8.95	   top(ok(X)) -> top(active(X))
25.58/8.95	
25.58/8.95	S is empty.
25.58/8.95	Rewrite Strategy: FULL
25.58/8.95	----------------------------------------
25.58/8.95	
25.58/8.95	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
25.58/8.95	The following defined symbols can occur below the 0th argument of top: proper, active
25.58/8.95	The following defined symbols can occur below the 0th argument of proper: proper, active
25.58/8.95	The following defined symbols can occur below the 0th argument of active: proper, active
25.58/8.95	
25.58/8.95	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
25.58/8.95	active(h(X)) -> mark(g(X, X))
25.58/8.95	active(g(a, X)) -> mark(f(b, X))
25.58/8.95	active(f(X, X)) -> mark(h(a))
25.58/8.95	active(h(X)) -> h(active(X))
25.58/8.95	active(g(X1, X2)) -> g(active(X1), X2)
25.58/8.95	active(f(X1, X2)) -> f(active(X1), X2)
25.58/8.95	proper(h(X)) -> h(proper(X))
25.58/8.95	proper(g(X1, X2)) -> g(proper(X1), proper(X2))
25.58/8.95	proper(f(X1, X2)) -> f(proper(X1), proper(X2))
25.58/8.95	
25.58/8.95	----------------------------------------
25.58/8.95	
25.58/8.95	(2)
25.58/8.95	Obligation:
25.58/8.95	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
25.58/8.95	
25.58/8.95	
25.58/8.95	The TRS R consists of the following rules:
25.58/8.95	
25.58/8.95	   active(a) -> mark(b)
25.58/8.95	   h(mark(X)) -> mark(h(X))
25.58/8.95	   g(mark(X1), X2) -> mark(g(X1, X2))
25.58/8.95	   f(mark(X1), X2) -> mark(f(X1, X2))
25.58/8.95	   proper(a) -> ok(a)
25.58/8.95	   proper(b) -> ok(b)
25.58/8.95	   h(ok(X)) -> ok(h(X))
25.58/8.95	   g(ok(X1), ok(X2)) -> ok(g(X1, X2))
25.58/8.95	   f(ok(X1), ok(X2)) -> ok(f(X1, X2))
25.58/8.95	   top(mark(X)) -> top(proper(X))
25.58/8.95	   top(ok(X)) -> top(active(X))
25.58/8.95	
25.58/8.95	S is empty.
25.58/8.95	Rewrite Strategy: FULL
25.58/8.95	----------------------------------------
25.58/8.95	
25.58/8.95	(3) RelTrsToTrsProof (UPPER BOUND(ID))

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