Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313572

details
property	value
status	complete
benchmark	4.57.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n158.star.cs.uiowa.edu
space	SK90
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.80621 seconds
cpu usage	10.6639
user time	9.91394
system time	0.749972
max virtual memory	1.8277336E7
max residence set size	2619184.0
stage attributes
key	value
starexec-result	WORST_CASE(?, O(1))
output
10.33/3.63	WORST_CASE(?, O(1))
10.33/3.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
10.33/3.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.33/3.67	
10.33/3.67	
10.33/3.67	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
10.33/3.67	
10.33/3.67	(0) CpxTRS
10.33/3.67	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 1918 ms]
10.33/3.67	(2) BOUNDS(1, 1)
10.33/3.67	
10.33/3.67	
10.33/3.67	----------------------------------------
10.33/3.67	
10.33/3.67	(0)
10.33/3.67	Obligation:
10.33/3.67	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
10.33/3.67	
10.33/3.67	
10.33/3.67	The TRS R consists of the following rules:
10.33/3.67	
10.33/3.67	   f(x, y, z) -> g(<=(x, y), x, y, z)
10.33/3.67	   g(true, x, y, z) -> z
10.33/3.67	   g(false, x, y, z) -> f(f(p(x), y, z), f(p(y), z, x), f(p(z), x, y))
10.33/3.67	   p(0) -> 0
10.33/3.67	   p(s(x)) -> x
10.33/3.67	
10.33/3.67	S is empty.
10.33/3.67	Rewrite Strategy: INNERMOST
10.33/3.67	----------------------------------------
10.33/3.67	
10.33/3.67	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
10.33/3.67	Constant runtime complexity proven by termination of constructor-based narrowing.
10.33/3.67	
10.33/3.67	The maximal most general narrowing sequences give rise to the following rewrite sequences:
10.33/3.67	
10.33/3.67	g(false, s(x0), s(x1), s(x2)) ->^* g(<=(g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0))), g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), s(x1)))
10.33/3.67	
10.33/3.67	g(false, 0, s(x0), s(x1)) ->^* g(<=(g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0)), g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0), g(<=(x1, 0), x1, 0, s(x0)))
10.33/3.67	
10.33/3.67	g(false, x0, s(x1), s(x2)) ->^* g(<=(g(<=(p(x0), s(x1)), p(x0), s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), x0)), g(<=(p(x0), s(x1)), p(x0), s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), x0), g(<=(x2, x0), x2, x0, s(x1)))
10.33/3.67	
10.33/3.67	g(false, s(x0), s(x1), s(x2)) ->^* g(<=(g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0))), g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), s(x1)))
10.33/3.67	
10.33/3.67	g(false, s(x0), s(x1), s(x2)) ->^* g(<=(g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0))), g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), s(x1)))
10.33/3.67	
10.33/3.67	g(false, 0, s(x0), s(x1)) ->^* g(<=(g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0)), g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0), g(<=(x1, 0), x1, 0, s(x0)))
10.33/3.67	
10.33/3.67	g(false, 0, s(x0), s(x1)) ->^* g(<=(g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0)), g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0), g(<=(x1, 0), x1, 0, s(x0)))
10.33/3.67	
10.33/3.67	g(false, x0, s(x1), s(x2)) ->^* g(<=(g(<=(p(x0), s(x1)), p(x0), s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), x0)), g(<=(p(x0), s(x1)), p(x0), s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), x0), g(<=(x2, x0), x2, x0, s(x1)))
10.33/3.67	
10.33/3.67	g(false, s(x0), 0, s(x1)) ->^* g(<=(g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0))), g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0)), g(<=(x1, s(x0)), x1, s(x0), 0))
10.33/3.67	
10.33/3.67	g(false, 0, 0, s(x0)) ->^* g(<=(g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0)), g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0), g(<=(x0, 0), x0, 0, 0))
10.33/3.67	
10.33/3.67	g(false, x0, 0, s(x1)) ->^* g(<=(g(<=(p(x0), 0), p(x0), 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), x0)), g(<=(p(x0), 0), p(x0), 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), x0), g(<=(x1, x0), x1, x0, 0))
10.33/3.67	
10.33/3.67	g(false, s(x0), 0, s(x1)) ->^* g(<=(g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0))), g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0)), g(<=(x1, s(x0)), x1, s(x0), 0))
10.33/3.67	
10.33/3.67	g(false, s(x0), 0, s(x1)) ->^* g(<=(g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0))), g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0)), g(<=(x1, s(x0)), x1, s(x0), 0))
10.33/3.67	
10.33/3.67	g(false, 0, 0, s(x0)) ->^* g(<=(g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0)), g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0), g(<=(x0, 0), x0, 0, 0))
10.33/3.67	
10.33/3.67	g(false, 0, 0, s(x0)) ->^* g(<=(g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0)), g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0), g(<=(x0, 0), x0, 0, 0))
10.33/3.67	
10.33/3.67	g(false, x0, 0, s(x1)) ->^* g(<=(g(<=(p(x0), 0), p(x0), 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), x0)), g(<=(p(x0), 0), p(x0), 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), x0), g(<=(x1, x0), x1, x0, 0))
10.33/3.67	
10.33/3.67	g(false, s(x0), x1, s(x2)) ->^* g(<=(g(<=(x0, x1), x0, x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), s(x0))), g(<=(x0, x1), x0, x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), x1))
10.33/3.67	
10.33/3.67	g(false, 0, x0, s(x1)) ->^* g(<=(g(<=(0, x0), 0, x0, s(x1)), g(<=(p(x0), s(x1)), p(x0), s(x1), 0)), g(<=(0, x0), 0, x0, s(x1)), g(<=(p(x0), s(x1)), p(x0), s(x1), 0), g(<=(x1, 0), x1, 0, x0))
10.33/3.67	
10.33/3.67	g(false, x0, x1, s(x2)) ->^* g(<=(g(<=(p(x0), x1), p(x0), x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), x0)), g(<=(p(x0), x1), p(x0), x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), x0), g(<=(x2, x0), x2, x0, x1))
10.33/3.67	
10.33/3.67	g(false, s(x0), s(x1), s(x2)) ->^* g(<=(g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0))), g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), s(x1)))
10.33/3.67	
10.33/3.67	g(false, s(x0), s(x1), s(x2)) ->^* g(<=(g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0))), g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), s(x1)))
10.33/3.67	
10.33/3.67	g(false, s(x0), 0, s(x1)) ->^* g(<=(g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0))), g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0)), g(<=(x1, s(x0)), x1, s(x0), 0))
10.33/3.67	
10.33/3.67	g(false, s(x0), 0, s(x1)) ->^* g(<=(g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0))), g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0)), g(<=(x1, s(x0)), x1, s(x0), 0))
10.33/3.67	
10.33/3.67	g(false, s(x0), x1, s(x2)) ->^* g(<=(g(<=(x0, x1), x0, x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), s(x0))), g(<=(x0, x1), x0, x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), x1))
10.33/3.67	
10.33/3.67	g(false, s(x0), s(x1), s(x2)) ->^* g(<=(g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0))), g(<=(x0, s(x1)), x0, s(x1), s(x2)), g(<=(x1, s(x2)), x1, s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), s(x1)))
10.33/3.67	
10.33/3.67	g(false, s(x0), 0, s(x1)) ->^* g(<=(g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0))), g(<=(x0, 0), x0, 0, s(x1)), g(<=(0, s(x1)), 0, s(x1), s(x0)), g(<=(x1, s(x0)), x1, s(x0), 0))
10.33/3.67	
10.33/3.67	g(false, s(x0), x1, s(x2)) ->^* g(<=(g(<=(x0, x1), x0, x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), s(x0))), g(<=(x0, x1), x0, x1, s(x2)), g(<=(p(x1), s(x2)), p(x1), s(x2), s(x0)), g(<=(x2, s(x0)), x2, s(x0), x1))
10.33/3.67	
10.33/3.67	g(false, 0, s(x0), s(x1)) ->^* g(<=(g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0)), g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0), g(<=(x1, 0), x1, 0, s(x0)))
10.33/3.67	
10.33/3.67	g(false, 0, s(x0), s(x1)) ->^* g(<=(g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0)), g(<=(0, s(x0)), 0, s(x0), s(x1)), g(<=(x0, s(x1)), x0, s(x1), 0), g(<=(x1, 0), x1, 0, s(x0)))
10.33/3.67	
10.33/3.67	g(false, 0, 0, s(x0)) ->^* g(<=(g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0)), g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0), g(<=(x0, 0), x0, 0, 0))
10.33/3.67	
10.33/3.67	g(false, 0, 0, s(x0)) ->^* g(<=(g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0)), g(<=(0, 0), 0, 0, s(x0)), g(<=(0, s(x0)), 0, s(x0), 0), g(<=(x0, 0), x0, 0, 0))
10.33/3.67	
10.33/3.67	g(false, 0, x0, s(x1)) ->^* g(<=(g(<=(0, x0), 0, x0, s(x1)), g(<=(p(x0), s(x1)), p(x0), s(x1), 0)), g(<=(0, x0), 0, x0, s(x1)), g(<=(p(x0), s(x1)), p(x0), s(x1), 0), g(<=(x1, 0), x1, 0, x0))
10.33/3.67
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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40