Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308262

details

property	value
status	complete
benchmark	ExProp7_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.40106 seconds
cpu usage	22.0262
user time	20.4784
system time	1.54781
max virtual memory	1.9013208E7
max residence set size	3901856.0

stage attributes

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

output

21.78/7.33	WORST_CASE(Omega(n^1), O(n^1))
21.78/7.34	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
21.78/7.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
21.78/7.34	
21.78/7.34	
21.78/7.34	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
21.78/7.34	
21.78/7.34	(0) CpxTRS
21.78/7.34	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
21.78/7.34	(2) CpxTRS
21.78/7.34	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
21.78/7.34	    (4) CpxTRS
21.78/7.34	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 26 ms]
21.78/7.34	    (6) BOUNDS(1, n^1)
21.78/7.34	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
21.78/7.34	(8) TRS for Loop Detection
21.78/7.34	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
21.78/7.34	    (10) BEST
21.78/7.34	        (11) proven lower bound
21.78/7.34	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
21.78/7.34	            (13) BOUNDS(n^1, INF)
21.78/7.34	        (14) TRS for Loop Detection
21.78/7.34	
21.78/7.34	
21.78/7.34	----------------------------------------
21.78/7.34	
21.78/7.34	(0)
21.78/7.34	Obligation:
21.78/7.34	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
21.78/7.34	
21.78/7.34	
21.78/7.34	The TRS R consists of the following rules:
21.78/7.34	
21.78/7.34	   active(f(0)) -> mark(cons(0, f(s(0))))
21.78/7.34	   active(f(s(0))) -> mark(f(p(s(0))))
21.78/7.34	   active(p(s(X))) -> mark(X)
21.78/7.34	   active(f(X)) -> f(active(X))
21.78/7.34	   active(cons(X1, X2)) -> cons(active(X1), X2)
21.78/7.34	   active(s(X)) -> s(active(X))
21.78/7.34	   active(p(X)) -> p(active(X))
21.78/7.34	   f(mark(X)) -> mark(f(X))
21.78/7.34	   cons(mark(X1), X2) -> mark(cons(X1, X2))
21.78/7.34	   s(mark(X)) -> mark(s(X))
21.78/7.34	   p(mark(X)) -> mark(p(X))
21.78/7.34	   proper(f(X)) -> f(proper(X))
21.78/7.34	   proper(0) -> ok(0)
21.78/7.34	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
21.78/7.34	   proper(s(X)) -> s(proper(X))
21.78/7.34	   proper(p(X)) -> p(proper(X))
21.78/7.34	   f(ok(X)) -> ok(f(X))
21.78/7.34	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
21.78/7.34	   s(ok(X)) -> ok(s(X))
21.78/7.34	   p(ok(X)) -> ok(p(X))
21.78/7.34	   top(mark(X)) -> top(proper(X))
21.78/7.34	   top(ok(X)) -> top(active(X))
21.78/7.34	
21.78/7.34	S is empty.
21.78/7.34	Rewrite Strategy: FULL
21.78/7.34	----------------------------------------
21.78/7.34	
21.78/7.34	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
21.78/7.34	The following defined symbols can occur below the 0th argument of top: proper, active
21.78/7.34	The following defined symbols can occur below the 0th argument of proper: proper, active
21.78/7.34	The following defined symbols can occur below the 0th argument of active: proper, active
21.78/7.34	
21.78/7.34	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
21.78/7.34	active(f(0)) -> mark(cons(0, f(s(0))))
21.78/7.34	active(f(s(0))) -> mark(f(p(s(0))))
21.78/7.34	active(p(s(X))) -> mark(X)
21.78/7.34	active(f(X)) -> f(active(X))
21.78/7.34	active(cons(X1, X2)) -> cons(active(X1), X2)
21.78/7.34	active(s(X)) -> s(active(X))
21.78/7.34	active(p(X)) -> p(active(X))
21.78/7.34	proper(f(X)) -> f(proper(X))
21.78/7.34	proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
21.78/7.34	proper(s(X)) -> s(proper(X))
21.78/7.34	proper(p(X)) -> p(proper(X))
21.78/7.34	
21.78/7.34	----------------------------------------
21.78/7.34	
21.78/7.34	(2)
21.78/7.34	Obligation:
21.78/7.34	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
21.78/7.34	
21.78/7.34	
21.78/7.34	The TRS R consists of the following rules:
21.78/7.34	
21.78/7.34	   f(mark(X)) -> mark(f(X))
21.78/7.34	   cons(mark(X1), X2) -> mark(cons(X1, X2))
21.78/7.34	   s(mark(X)) -> mark(s(X))
21.78/7.34	   p(mark(X)) -> mark(p(X))
21.78/7.34	   proper(0) -> ok(0)
21.78/7.34	   f(ok(X)) -> ok(f(X))
21.78/7.34	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
21.78/7.34	   s(ok(X)) -> ok(s(X))
21.78/7.34	   p(ok(X)) -> ok(p(X))
21.78/7.34	   top(mark(X)) -> top(proper(X))
21.78/7.34	   top(ok(X)) -> top(active(X))
21.78/7.35	
21.78/7.35	S is empty.

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