Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307884

details

property	value
status	complete
benchmark	cime2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n095.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.62217 seconds
cpu usage	23.7612
user time	22.2832
system time	1.47798
max virtual memory	1.9114556E7
max residence set size	3402632.0

stage attributes

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

output

23.42/7.57	WORST_CASE(Omega(n^1), O(n^1))
23.42/7.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
23.42/7.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
23.42/7.58	
23.42/7.58	
23.42/7.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.42/7.58	
23.42/7.58	(0) CpxTRS
23.42/7.58	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
23.42/7.58	(2) CpxTRS
23.42/7.58	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
23.42/7.58	    (4) CpxTRS
23.42/7.58	    (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
23.42/7.58	    (6) CdtProblem
23.42/7.58	    (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
23.42/7.58	    (8) CdtProblem
23.42/7.58	    (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
23.42/7.58	    (10) CdtProblem
23.42/7.58	    (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
23.42/7.58	    (12) CdtProblem
23.42/7.58	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 75 ms]
23.42/7.58	    (14) CdtProblem
23.42/7.58	    (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
23.42/7.58	    (16) BOUNDS(1, 1)
23.42/7.58	(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
23.42/7.58	(18) TRS for Loop Detection
23.42/7.58	    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
23.42/7.58	    (20) BEST
23.42/7.58	        (21) proven lower bound
23.42/7.58	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
23.42/7.58	            (23) BOUNDS(n^1, INF)
23.42/7.58	        (24) TRS for Loop Detection
23.42/7.58	
23.42/7.58	
23.42/7.58	----------------------------------------
23.42/7.58	
23.42/7.58	(0)
23.42/7.58	Obligation:
23.42/7.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.42/7.58	
23.42/7.58	
23.42/7.58	The TRS R consists of the following rules:
23.42/7.58	
23.42/7.58	   circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t))
23.42/7.58	   circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t))
23.42/7.58	   circ(cons(lift, s), cons(lift, t)) -> cons(lift, circ(s, t))
23.42/7.58	   circ(circ(s, t), u) -> circ(s, circ(t, u))
23.42/7.58	   circ(s, id) -> s
23.42/7.58	   circ(id, s) -> s
23.42/7.58	   circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u)
23.42/7.58	   subst(a, id) -> a
23.42/7.58	   msubst(a, id) -> a
23.42/7.58	   msubst(msubst(a, s), t) -> msubst(a, circ(s, t))
23.42/7.58	
23.42/7.58	S is empty.
23.42/7.58	Rewrite Strategy: FULL
23.42/7.58	----------------------------------------
23.42/7.58	
23.42/7.58	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
23.42/7.58	The TRS does not nest defined symbols.
23.42/7.58	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
23.42/7.58	circ(circ(s, t), u) -> circ(s, circ(t, u))
23.42/7.58	circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u)
23.42/7.58	msubst(msubst(a, s), t) -> msubst(a, circ(s, t))
23.42/7.58	
23.42/7.58	----------------------------------------
23.42/7.58	
23.42/7.58	(2)
23.42/7.58	Obligation:
23.42/7.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
23.42/7.58	
23.42/7.58	
23.42/7.58	The TRS R consists of the following rules:
23.42/7.58	
23.42/7.58	   circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t))
23.42/7.58	   circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t))
23.42/7.58	   circ(cons(lift, s), cons(lift, t)) -> cons(lift, circ(s, t))
23.42/7.58	   circ(s, id) -> s
23.42/7.58	   circ(id, s) -> s
23.42/7.58	   subst(a, id) -> a
23.42/7.58	   msubst(a, id) -> a
23.42/7.58	
23.42/7.58	S is empty.
23.42/7.58	Rewrite Strategy: FULL
23.42/7.58	----------------------------------------
23.42/7.58	
23.42/7.58	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
23.42/7.58	Converted rc-obligation to irc-obligation.
23.42/7.58	
23.42/7.58	As the TRS does not nest defined symbols, we have rc = irc.
23.42/7.58	----------------------------------------
23.42/7.58	
23.42/7.58	(4)
23.42/7.58	Obligation:
23.42/7.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
23.42/7.58	
23.42/7.58	
23.42/7.58	The TRS R consists of the following rules:
23.42/7.58	
23.42/7.58	   circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t))

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