Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313841

details

property	value
status	complete
benchmark	cade06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n107.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.604 seconds
cpu usage	1016.92
user time	1003.87
system time	13.0482
max virtual memory	3.8189736E7
max residence set size	1.496734E7

stage attributes

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

output

1016.45/291.50	WORST_CASE(Omega(n^1), O(n^2))
1016.69/291.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1016.69/291.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1016.69/291.52	
1016.69/291.52	
1016.69/291.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
1016.69/291.52	
1016.69/291.52	(0) CpxTRS
1016.69/291.52	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
1016.69/291.52	(2) CpxWeightedTrs
1016.69/291.52	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1016.69/291.52	    (4) CpxTypedWeightedTrs
1016.69/291.52	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
1016.69/291.52	    (6) CpxTypedWeightedCompleteTrs
1016.69/291.52	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
1016.69/291.52	    (8) CpxRNTS
1016.69/291.52	    (9) CompleteCoflocoProof [FINISHED, 1251 ms]
1016.69/291.52	    (10) BOUNDS(1, n^2)
1016.69/291.52	(11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1016.69/291.52	(12) CpxTRS
1016.69/291.52	    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1016.69/291.52	    (14) typed CpxTrs
1016.69/291.52	    (15) OrderProof [LOWER BOUND(ID), 0 ms]
1016.69/291.52	    (16) typed CpxTrs
1016.69/291.52	    (17) RewriteLemmaProof [LOWER BOUND(ID), 275 ms]
1016.69/291.52	    (18) BEST
1016.69/291.52	        (19) proven lower bound
1016.69/291.52	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
1016.69/291.52	            (21) BOUNDS(n^1, INF)
1016.69/291.52	        (22) typed CpxTrs
1016.69/291.52	            (23) RewriteLemmaProof [LOWER BOUND(ID), 13 ms]
1016.69/291.52	            (24) typed CpxTrs
1016.69/291.52	
1016.69/291.52	
1016.69/291.52	----------------------------------------
1016.69/291.52	
1016.69/291.52	(0)
1016.69/291.52	Obligation:
1016.69/291.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
1016.69/291.52	
1016.69/291.52	
1016.69/291.52	The TRS R consists of the following rules:
1016.69/291.52	
1016.69/291.52	   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
1016.69/291.52	   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
1016.69/291.52	   plus(n, 0) -> n
1016.69/291.52	   plus(n, s(m)) -> s(plus(n, m))
1016.69/291.52	   gt(0, v) -> false
1016.69/291.52	   gt(s(u), 0) -> true
1016.69/291.52	   gt(s(u), s(v)) -> gt(u, v)
1016.69/291.52	
1016.69/291.52	S is empty.
1016.69/291.52	Rewrite Strategy: INNERMOST
1016.69/291.52	----------------------------------------
1016.69/291.52	
1016.69/291.52	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
1016.69/291.52	Transformed relative TRS to weighted TRS
1016.69/291.52	----------------------------------------
1016.69/291.52	
1016.69/291.52	(2)
1016.69/291.52	Obligation:
1016.69/291.52	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).
1016.69/291.52	
1016.69/291.52	
1016.69/291.52	The TRS R consists of the following rules:
1016.69/291.52	
1016.69/291.52	   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z) [1]
1016.69/291.52	   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)) [1]
1016.69/291.52	   plus(n, 0) -> n [1]
1016.69/291.52	   plus(n, s(m)) -> s(plus(n, m)) [1]
1016.69/291.52	   gt(0, v) -> false [1]
1016.69/291.52	   gt(s(u), 0) -> true [1]
1016.69/291.52	   gt(s(u), s(v)) -> gt(u, v) [1]
1016.69/291.52	
1016.69/291.52	Rewrite Strategy: INNERMOST
1016.69/291.52	----------------------------------------
1016.69/291.52	
1016.69/291.52	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
1016.69/291.52	Infered types.
1016.69/291.52	----------------------------------------
1016.69/291.52	
1016.69/291.52	(4)
1016.69/291.52	Obligation:
1016.69/291.52	Runtime Complexity Weighted TRS with Types.
1016.69/291.52	The TRS R consists of the following rules:
1016.69/291.52	
1016.69/291.52	   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z) [1]
1016.69/291.52	   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)) [1]
1016.69/291.52	   plus(n, 0) -> n [1]
1016.69/291.52	   plus(n, s(m)) -> s(plus(n, m)) [1]
1016.69/291.52	   gt(0, v) -> false [1]
1016.69/291.52	   gt(s(u), 0) -> true [1]
1016.69/291.52	   gt(s(u), s(v)) -> gt(u, v) [1]
1016.69/291.52	
1016.69/291.52	The TRS has the following type information:
1016.69/291.52	f :: true:false -> s:0 -> s:0 -> s:0 -> f
1016.69/291.52	true :: true:false
1016.69/291.52	gt :: s:0 -> s:0 -> true:false
1016.69/291.52	plus :: s:0 -> s:0 -> s:0
1016.69/291.52	s :: s:0 -> s:0

popout

output may be truncated. 'popout' for the full output.

job log

popout

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