Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307817

details

property	value
status	complete
benchmark	sizeChange.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.557 seconds
cpu usage	325.303
user time	322.861
system time	2.44175
max virtual memory	3.6711848E7
max residence set size	5388612.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

325.20/291.51	WORST_CASE(Omega(n^1), O(n^2))
325.20/291.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
325.20/291.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
325.20/291.52	
325.20/291.52	
325.20/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
325.20/291.52	
325.20/291.52	(0) CpxTRS
325.20/291.52	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
325.20/291.52	(2) CpxTRS
325.20/291.52	    (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
325.20/291.52	    (4) CdtProblem
325.20/291.52	    (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
325.20/291.52	    (6) CdtProblem
325.20/291.52	    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
325.20/291.52	    (8) CdtProblem
325.20/291.52	    (9) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
325.20/291.52	    (10) CdtProblem
325.20/291.52	    (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
325.20/291.52	    (12) CdtProblem
325.20/291.52	    (13) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
325.20/291.52	    (14) CdtProblem
325.20/291.52	    (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 10 ms]
325.20/291.52	    (16) CdtProblem
325.20/291.52	    (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 44 ms]
325.20/291.52	    (18) CdtProblem
325.20/291.52	    (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 42 ms]
325.20/291.52	    (20) CdtProblem
325.20/291.52	    (21) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
325.20/291.52	    (22) BOUNDS(1, 1)
325.20/291.52	(23) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
325.20/291.52	(24) TRS for Loop Detection
325.20/291.52	    (25) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
325.20/291.52	    (26) BEST
325.20/291.52	        (27) proven lower bound
325.20/291.52	            (28) LowerBoundPropagationProof [FINISHED, 0 ms]
325.20/291.52	            (29) BOUNDS(n^1, INF)
325.20/291.52	        (30) TRS for Loop Detection
325.20/291.52	
325.20/291.52	
325.20/291.52	----------------------------------------
325.20/291.52	
325.20/291.52	(0)
325.20/291.52	Obligation:
325.20/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
325.20/291.52	
325.20/291.52	
325.20/291.52	The TRS R consists of the following rules:
325.20/291.52	
325.20/291.52	   r(xs, ys, zs, nil) -> xs
325.20/291.52	   r(xs, nil, zs, cons(w, ws)) -> r(xs, xs, cons(succ(zero), zs), ws)
325.20/291.52	   r(xs, cons(y, ys), nil, cons(w, ws)) -> r(xs, xs, cons(succ(zero), nil), ws)
325.20/291.52	   r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) -> r(ys, cons(y, ys), zs, cons(succ(zero), cons(w, ws)))
325.20/291.52	
325.20/291.52	S is empty.
325.20/291.52	Rewrite Strategy: FULL
325.20/291.52	----------------------------------------
325.20/291.52	
325.20/291.52	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
325.20/291.52	Converted rc-obligation to irc-obligation.
325.20/291.52	
325.20/291.52	As the TRS does not nest defined symbols, we have rc = irc.
325.20/291.52	----------------------------------------
325.20/291.52	
325.20/291.52	(2)
325.20/291.52	Obligation:
325.20/291.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2).
325.20/291.52	
325.20/291.52	
325.20/291.52	The TRS R consists of the following rules:
325.20/291.52	
325.20/291.52	   r(xs, ys, zs, nil) -> xs
325.20/291.52	   r(xs, nil, zs, cons(w, ws)) -> r(xs, xs, cons(succ(zero), zs), ws)
325.20/291.52	   r(xs, cons(y, ys), nil, cons(w, ws)) -> r(xs, xs, cons(succ(zero), nil), ws)
325.20/291.52	   r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) -> r(ys, cons(y, ys), zs, cons(succ(zero), cons(w, ws)))
325.20/291.52	
325.20/291.52	S is empty.
325.20/291.52	Rewrite Strategy: INNERMOST
325.20/291.52	----------------------------------------
325.20/291.52	
325.20/291.52	(3) CpxTrsToCdtProof (UPPER BOUND(ID))
325.20/291.52	Converted Cpx (relative) TRS to CDT
325.20/291.52	----------------------------------------
325.20/291.52	
325.20/291.52	(4)
325.20/291.52	Obligation:
325.20/291.52	Complexity Dependency Tuples Problem
325.20/291.52	
325.20/291.52	Rules:
325.20/291.52	   r(z0, z1, z2, nil) -> z0
325.20/291.52	   r(z0, nil, z1, cons(z2, z3)) -> r(z0, z0, cons(succ(zero), z1), z3)
325.20/291.52	   r(z0, cons(z1, z2), nil, cons(z3, z4)) -> r(z0, z0, cons(succ(zero), nil), z4)
325.20/291.52	   r(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> r(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))
325.20/291.52	Tuples:
325.20/291.52	   R(z0, z1, z2, nil) -> c
325.20/291.52	   R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3))
325.20/291.52	   R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4))
325.20/291.52	   R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6))))
325.20/291.52	S tuples:
325.20/291.52	   R(z0, z1, z2, nil) -> c

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