Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308071

details

property	value
status	complete
benchmark	PEANO_nosorts_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n068.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.3153 seconds
cpu usage	25.0361
user time	23.2974
system time	1.7387
max virtual memory	1.9206832E7
max residence set size	3965644.0

stage attributes

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

output

23.23/7.16	WORST_CASE(Omega(n^1), O(n^1))
23.23/7.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
23.23/7.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
23.23/7.17	
23.23/7.17	
23.23/7.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.23/7.17	
23.23/7.17	(0) CpxTRS
23.23/7.17	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 8 ms]
23.23/7.17	(2) CpxTRS
23.23/7.17	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
23.23/7.17	    (4) CpxTRS
23.23/7.17	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 34 ms]
23.23/7.17	    (6) BOUNDS(1, n^1)
23.23/7.17	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
23.23/7.17	(8) TRS for Loop Detection
23.23/7.17	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
23.23/7.17	    (10) BEST
23.23/7.17	        (11) proven lower bound
23.23/7.17	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
23.23/7.17	            (13) BOUNDS(n^1, INF)
23.23/7.17	        (14) TRS for Loop Detection
23.23/7.17	
23.23/7.17	
23.23/7.17	----------------------------------------
23.23/7.17	
23.23/7.17	(0)
23.23/7.17	Obligation:
23.23/7.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.23/7.17	
23.23/7.17	
23.23/7.17	The TRS R consists of the following rules:
23.23/7.17	
23.23/7.17	   active(and(tt, X)) -> mark(X)
23.23/7.17	   active(plus(N, 0)) -> mark(N)
23.23/7.17	   active(plus(N, s(M))) -> mark(s(plus(N, M)))
23.23/7.17	   active(and(X1, X2)) -> and(active(X1), X2)
23.23/7.17	   active(plus(X1, X2)) -> plus(active(X1), X2)
23.23/7.17	   active(plus(X1, X2)) -> plus(X1, active(X2))
23.23/7.17	   active(s(X)) -> s(active(X))
23.23/7.17	   and(mark(X1), X2) -> mark(and(X1, X2))
23.23/7.17	   plus(mark(X1), X2) -> mark(plus(X1, X2))
23.23/7.17	   plus(X1, mark(X2)) -> mark(plus(X1, X2))
23.23/7.17	   s(mark(X)) -> mark(s(X))
23.23/7.17	   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
23.23/7.17	   proper(tt) -> ok(tt)
23.23/7.17	   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
23.23/7.17	   proper(0) -> ok(0)
23.23/7.17	   proper(s(X)) -> s(proper(X))
23.23/7.17	   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
23.23/7.17	   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
23.23/7.17	   s(ok(X)) -> ok(s(X))
23.23/7.17	   top(mark(X)) -> top(proper(X))
23.23/7.17	   top(ok(X)) -> top(active(X))
23.23/7.17	
23.23/7.17	S is empty.
23.23/7.17	Rewrite Strategy: FULL
23.23/7.17	----------------------------------------
23.23/7.17	
23.23/7.17	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
23.23/7.17	The following defined symbols can occur below the 0th argument of top: proper, active
23.23/7.17	The following defined symbols can occur below the 0th argument of proper: proper, active
23.23/7.17	The following defined symbols can occur below the 0th argument of active: proper, active
23.23/7.17	
23.23/7.17	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
23.23/7.17	active(and(tt, X)) -> mark(X)
23.23/7.17	active(plus(N, 0)) -> mark(N)
23.23/7.17	active(plus(N, s(M))) -> mark(s(plus(N, M)))
23.23/7.17	active(and(X1, X2)) -> and(active(X1), X2)
23.23/7.17	active(plus(X1, X2)) -> plus(active(X1), X2)
23.23/7.17	active(plus(X1, X2)) -> plus(X1, active(X2))
23.23/7.17	active(s(X)) -> s(active(X))
23.23/7.17	proper(and(X1, X2)) -> and(proper(X1), proper(X2))
23.23/7.17	proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
23.23/7.17	proper(s(X)) -> s(proper(X))
23.23/7.17	
23.23/7.17	----------------------------------------
23.23/7.17	
23.23/7.17	(2)
23.23/7.17	Obligation:
23.23/7.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
23.23/7.17	
23.23/7.17	
23.23/7.17	The TRS R consists of the following rules:
23.23/7.17	
23.23/7.17	   and(mark(X1), X2) -> mark(and(X1, X2))
23.23/7.17	   plus(mark(X1), X2) -> mark(plus(X1, X2))
23.23/7.17	   plus(X1, mark(X2)) -> mark(plus(X1, X2))
23.23/7.17	   s(mark(X)) -> mark(s(X))
23.23/7.17	   proper(tt) -> ok(tt)
23.23/7.17	   proper(0) -> ok(0)
23.23/7.17	   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
23.23/7.17	   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
23.23/7.17	   s(ok(X)) -> ok(s(X))
23.23/7.17	   top(mark(X)) -> top(proper(X))
23.23/7.17	   top(ok(X)) -> top(active(X))
23.23/7.17	
23.23/7.17	S is empty.
23.23/7.17	Rewrite Strategy: FULL
23.23/7.17	----------------------------------------

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