Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313881

details

property	value
status	complete
benchmark	boolprog.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n155.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.98323 seconds
cpu usage	34.8504
user time	33.0192
system time	1.83122
max virtual memory	3.8320688E7
max residence set size	4371356.0

stage attributes

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

output

34.56/9.93	WORST_CASE(Omega(n^1), O(n^1))
34.56/9.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
34.56/9.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
34.56/9.94	
34.56/9.94	
34.56/9.94	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
34.56/9.94	
34.56/9.94	(0) CpxTRS
34.56/9.94	(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
34.56/9.94	(2) CdtProblem
34.56/9.94	    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
34.56/9.94	    (4) CdtProblem
34.56/9.94	    (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
34.56/9.94	    (6) CdtProblem
34.56/9.94	    (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 101 ms]
34.56/9.94	    (8) CdtProblem
34.56/9.94	    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 25 ms]
34.56/9.94	    (10) CdtProblem
34.56/9.94	    (11) CdtKnowledgeProof [FINISHED, 0 ms]
34.56/9.94	    (12) BOUNDS(1, 1)
34.56/9.94	(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
34.56/9.94	(14) TRS for Loop Detection
34.56/9.94	    (15) DecreasingLoopProof [LOWER BOUND(ID), 34 ms]
34.56/9.94	    (16) BEST
34.56/9.94	        (17) proven lower bound
34.56/9.94	            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
34.56/9.94	            (19) BOUNDS(n^1, INF)
34.56/9.94	        (20) TRS for Loop Detection
34.56/9.94	
34.56/9.94	
34.56/9.94	----------------------------------------
34.56/9.94	
34.56/9.94	(0)
34.56/9.94	Obligation:
34.56/9.94	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
34.56/9.94	
34.56/9.94	
34.56/9.94	The TRS R consists of the following rules:
34.56/9.94	
34.56/9.94	   f4(S(x''), S(x'), x3, x4, S(x)) -> f2(S(x''), x', x3, x4, x)
34.56/9.94	   f4(S(x'), 0, x3, x4, S(x)) -> f3(x', 0, x3, x4, x)
34.56/9.94	   f2(x1, x2, S(x''), S(x'), S(x)) -> f5(x1, x2, S(x''), x', x)
34.56/9.94	   f2(x1, x2, S(x'), 0, S(x)) -> f3(x1, x2, x', 0, x)
34.56/9.94	   f4(S(x'), S(x), x3, x4, 0) -> 0
34.56/9.94	   f4(S(x), 0, x3, x4, 0) -> 0
34.56/9.94	   f2(x1, x2, S(x'), S(x), 0) -> 0
34.56/9.94	   f2(x1, x2, S(x), 0, 0) -> 0
34.56/9.94	   f0(x1, S(x'), x3, S(x), x5) -> f1(x', S(x'), x, S(x), S(x))
34.56/9.94	   f0(x1, S(x), x3, 0, x5) -> 0
34.56/9.94	   f6(x1, x2, x3, x4, S(x)) -> f0(x1, x2, x4, x3, x)
34.56/9.94	   f5(x1, x2, x3, x4, S(x)) -> f6(x2, x1, x3, x4, x)
34.56/9.94	   f3(x1, x2, x3, x4, S(x)) -> f4(x1, x2, x4, x3, x)
34.56/9.94	   f1(x1, x2, x3, x4, S(x)) -> f2(x2, x1, x3, x4, x)
34.56/9.94	   f6(x1, x2, x3, x4, 0) -> 0
34.56/9.94	   f5(x1, x2, x3, x4, 0) -> 0
34.56/9.94	   f4(0, x2, x3, x4, x5) -> 0
34.56/9.94	   f3(x1, x2, x3, x4, 0) -> 0
34.56/9.94	   f2(x1, x2, 0, x4, x5) -> 0
34.56/9.94	   f1(x1, x2, x3, x4, 0) -> 0
34.56/9.94	   f0(x1, 0, x3, x4, x5) -> 0
34.56/9.94	
34.56/9.94	S is empty.
34.56/9.94	Rewrite Strategy: INNERMOST
34.56/9.94	----------------------------------------
34.56/9.94	
34.56/9.94	(1) CpxTrsToCdtProof (UPPER BOUND(ID))
34.56/9.94	Converted Cpx (relative) TRS to CDT
34.56/9.94	----------------------------------------
34.56/9.94	
34.56/9.94	(2)
34.56/9.94	Obligation:
34.56/9.94	Complexity Dependency Tuples Problem
34.56/9.94	
34.56/9.94	Rules:
34.56/9.94	   f4(S(z0), S(z1), z2, z3, S(z4)) -> f2(S(z0), z1, z2, z3, z4)
34.56/9.94	   f4(S(z0), 0, z1, z2, S(z3)) -> f3(z0, 0, z1, z2, z3)
34.56/9.94	   f4(S(z0), S(z1), z2, z3, 0) -> 0
34.56/9.94	   f4(S(z0), 0, z1, z2, 0) -> 0
34.56/9.94	   f4(0, z0, z1, z2, z3) -> 0
34.56/9.94	   f2(z0, z1, S(z2), S(z3), S(z4)) -> f5(z0, z1, S(z2), z3, z4)
34.56/9.94	   f2(z0, z1, S(z2), 0, S(z3)) -> f3(z0, z1, z2, 0, z3)
34.56/9.94	   f2(z0, z1, S(z2), S(z3), 0) -> 0
34.56/9.94	   f2(z0, z1, S(z2), 0, 0) -> 0
34.56/9.94	   f2(z0, z1, 0, z2, z3) -> 0
34.56/9.94	   f0(z0, S(z1), z2, S(z3), z4) -> f1(z1, S(z1), z3, S(z3), S(z3))
34.56/9.94	   f0(z0, S(z1), z2, 0, z3) -> 0
34.56/9.94	   f0(z0, 0, z1, z2, z3) -> 0
34.56/9.94	   f6(z0, z1, z2, z3, S(z4)) -> f0(z0, z1, z3, z2, z4)
34.56/9.94	   f6(z0, z1, z2, z3, 0) -> 0
34.56/9.94	   f5(z0, z1, z2, z3, S(z4)) -> f6(z1, z0, z2, z3, z4)
34.56/9.94	   f5(z0, z1, z2, z3, 0) -> 0
34.56/9.94	   f3(z0, z1, z2, z3, S(z4)) -> f4(z0, z1, z3, z2, z4)
34.56/9.94	   f3(z0, z1, z2, z3, 0) -> 0
34.56/9.94	   f1(z0, z1, z2, z3, S(z4)) -> f2(z1, z0, z2, z3, z4)
34.56/9.94	   f1(z0, z1, z2, z3, 0) -> 0
34.56/9.94	Tuples:
34.56/9.94	   F4(S(z0), S(z1), z2, z3, S(z4)) -> c(F2(S(z0), z1, z2, z3, z4))
34.56/9.94	   F4(S(z0), 0, z1, z2, S(z3)) -> c1(F3(z0, 0, z1, z2, z3))
34.56/9.94	   F4(S(z0), S(z1), z2, z3, 0) -> c2
34.56/9.94	   F4(S(z0), 0, z1, z2, 0) -> c3

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