Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313851

details

property	value
status	complete
benchmark	dup1_typed.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.53854 seconds
cpu usage	26.7835
user time	24.7506
system time	2.0329
max virtual memory	1.884566E7
max residence set size	3541476.0

stage attributes

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

output

13.19/4.49	WORST_CASE(Omega(n^1), O(n^1))
13.19/4.50	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
13.19/4.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.19/4.50	
13.19/4.50	
13.19/4.50	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1).
13.19/4.50	
13.19/4.50	(0) CpxRelTRS
13.19/4.50	(1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 154 ms]
13.19/4.50	(2) CpxRelTRS
13.19/4.50	(3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
13.19/4.50	(4) CdtProblem
13.19/4.50	    (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
13.19/4.50	    (6) CdtProblem
13.19/4.50	    (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
13.19/4.50	    (8) CdtProblem
13.19/4.50	    (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
13.19/4.50	    (10) CdtProblem
13.19/4.50	    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 45 ms]
13.19/4.50	    (12) CdtProblem
13.19/4.50	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 8 ms]
13.19/4.50	    (14) CdtProblem
13.19/4.50	    (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
13.19/4.50	    (16) BOUNDS(1, 1)
13.19/4.50	(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
13.19/4.50	(18) TRS for Loop Detection
13.19/4.50	    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
13.19/4.50	    (20) BEST
13.19/4.50	        (21) proven lower bound
13.19/4.50	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
13.19/4.50	            (23) BOUNDS(n^1, INF)
13.19/4.50	        (24) TRS for Loop Detection
13.19/4.50	
13.19/4.50	
13.19/4.50	----------------------------------------
13.19/4.50	
13.19/4.50	(0)
13.19/4.50	Obligation:
13.19/4.50	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1).
13.19/4.50	
13.19/4.50	
13.19/4.50	The TRS R consists of the following rules:
13.19/4.50	
13.19/4.50	   a(C(x1, x2), y) -> C(a(x1, y), a(x2, C(x1, x2)))
13.19/4.50	   a(Z, y) -> Z
13.19/4.50	   eqZList(C(x1, x2), C(y1, y2)) -> and(eqZList(x1, y1), eqZList(x2, y2))
13.19/4.50	   eqZList(C(x1, x2), Z) -> False
13.19/4.50	   eqZList(Z, C(y1, y2)) -> False
13.19/4.50	   eqZList(Z, Z) -> True
13.19/4.50	   second(C(x1, x2)) -> x2
13.19/4.50	   first(C(x1, x2)) -> x1
13.19/4.50	
13.19/4.50	The (relative) TRS S consists of the following rules:
13.19/4.50	
13.19/4.50	   and(False, False) -> False
13.19/4.50	   and(True, False) -> False
13.19/4.50	   and(False, True) -> False
13.19/4.50	   and(True, True) -> True
13.19/4.50	
13.19/4.50	Rewrite Strategy: INNERMOST
13.19/4.50	----------------------------------------
13.19/4.50	
13.19/4.50	(1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
13.19/4.50	proved termination of relative rules
13.19/4.50	----------------------------------------
13.19/4.50	
13.19/4.50	(2)
13.19/4.50	Obligation:
13.19/4.50	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1).
13.19/4.50	
13.19/4.50	
13.19/4.50	The TRS R consists of the following rules:
13.19/4.50	
13.19/4.50	   a(C(x1, x2), y) -> C(a(x1, y), a(x2, C(x1, x2)))
13.19/4.50	   a(Z, y) -> Z
13.19/4.50	   eqZList(C(x1, x2), C(y1, y2)) -> and(eqZList(x1, y1), eqZList(x2, y2))
13.19/4.50	   eqZList(C(x1, x2), Z) -> False
13.19/4.50	   eqZList(Z, C(y1, y2)) -> False
13.19/4.50	   eqZList(Z, Z) -> True
13.19/4.50	   second(C(x1, x2)) -> x2
13.19/4.50	   first(C(x1, x2)) -> x1
13.19/4.50	
13.19/4.50	The (relative) TRS S consists of the following rules:
13.19/4.50	
13.19/4.50	   and(False, False) -> False
13.19/4.50	   and(True, False) -> False
13.19/4.50	   and(False, True) -> False
13.19/4.50	   and(True, True) -> True
13.19/4.50	
13.19/4.50	Rewrite Strategy: INNERMOST
13.19/4.50	----------------------------------------
13.19/4.50	
13.19/4.50	(3) CpxTrsToCdtProof (UPPER BOUND(ID))
13.19/4.50	Converted Cpx (relative) TRS to CDT
13.19/4.50	----------------------------------------
13.19/4.50	
13.19/4.50	(4)
13.19/4.50	Obligation:
13.19/4.50	Complexity Dependency Tuples Problem
13.19/4.50

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40