Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313716

details

property	value
status	complete
benchmark	otto02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n040.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.751 seconds
cpu usage	1111.45
user time	1095.44
system time	16.0135
max virtual memory	3.8541948E7
max residence set size	1.498236E7

stage attributes

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

output

1111.19/291.65	WORST_CASE(Omega(n^1), O(n^2))
1111.29/291.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1111.29/291.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1111.29/291.68	
1111.29/291.68	
1111.29/291.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
1111.29/291.68	
1111.29/291.68	(0) CpxTRS
1111.29/291.68	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
1111.29/291.68	(2) CpxWeightedTrs
1111.29/291.68	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1111.29/291.68	    (4) CpxTypedWeightedTrs
1111.29/291.68	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
1111.29/291.68	    (6) CpxTypedWeightedCompleteTrs
1111.29/291.68	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
1111.29/291.68	    (8) CpxRNTS
1111.29/291.68	    (9) CompleteCoflocoProof [FINISHED, 1208 ms]
1111.29/291.68	    (10) BOUNDS(1, n^2)
1111.29/291.68	(11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1111.29/291.68	(12) CpxTRS
1111.29/291.68	    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1111.29/291.68	    (14) typed CpxTrs
1111.29/291.68	    (15) OrderProof [LOWER BOUND(ID), 0 ms]
1111.29/291.68	    (16) typed CpxTrs
1111.29/291.68	    (17) RewriteLemmaProof [LOWER BOUND(ID), 274 ms]
1111.29/291.68	    (18) BEST
1111.29/291.68	        (19) proven lower bound
1111.29/291.68	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
1111.29/291.68	            (21) BOUNDS(n^1, INF)
1111.29/291.68	        (22) typed CpxTrs
1111.29/291.68	            (23) RewriteLemmaProof [LOWER BOUND(ID), 10 ms]
1111.29/291.68	            (24) typed CpxTrs
1111.29/291.68	            (25) RewriteLemmaProof [LOWER BOUND(ID), 0 ms]
1111.29/291.68	            (26) typed CpxTrs
1111.29/291.68	            (27) RewriteLemmaProof [LOWER BOUND(ID), 0 ms]
1111.29/291.68	            (28) typed CpxTrs
1111.29/291.68	
1111.29/291.68	
1111.29/291.68	----------------------------------------
1111.29/291.68	
1111.29/291.68	(0)
1111.29/291.68	Obligation:
1111.29/291.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
1111.29/291.68	
1111.29/291.68	
1111.29/291.68	The TRS R consists of the following rules:
1111.29/291.68	
1111.29/291.68	   app(x, y) -> helpa(0, plus(length(x), length(y)), x, y)
1111.29/291.68	   plus(x, 0) -> x
1111.29/291.68	   plus(x, s(y)) -> s(plus(x, y))
1111.29/291.68	   length(nil) -> 0
1111.29/291.68	   length(cons(x, y)) -> s(length(y))
1111.29/291.68	   helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
1111.29/291.68	   ge(x, 0) -> true
1111.29/291.68	   ge(0, s(x)) -> false
1111.29/291.68	   ge(s(x), s(y)) -> ge(x, y)
1111.29/291.68	   if(true, c, l, ys, zs) -> nil
1111.29/291.68	   if(false, c, l, ys, zs) -> helpb(c, l, ys, zs)
1111.29/291.68	   take(0, cons(x, xs), ys) -> x
1111.29/291.68	   take(0, nil, cons(y, ys)) -> y
1111.29/291.68	   take(s(c), cons(x, xs), ys) -> take(c, xs, ys)
1111.29/291.68	   take(s(c), nil, cons(y, ys)) -> take(c, nil, ys)
1111.29/291.68	   helpb(c, l, ys, zs) -> cons(take(c, ys, zs), helpa(s(c), l, ys, zs))
1111.29/291.68	
1111.29/291.68	S is empty.
1111.29/291.68	Rewrite Strategy: INNERMOST
1111.29/291.68	----------------------------------------
1111.29/291.68	
1111.29/291.68	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
1111.29/291.68	Transformed relative TRS to weighted TRS
1111.29/291.68	----------------------------------------
1111.29/291.68	
1111.29/291.68	(2)
1111.29/291.68	Obligation:
1111.29/291.68	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).
1111.29/291.68	
1111.29/291.68	
1111.29/291.68	The TRS R consists of the following rules:
1111.29/291.68	
1111.29/291.68	   app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1]
1111.29/291.68	   plus(x, 0) -> x [1]
1111.29/291.68	   plus(x, s(y)) -> s(plus(x, y)) [1]
1111.29/291.68	   length(nil) -> 0 [1]
1111.29/291.68	   length(cons(x, y)) -> s(length(y)) [1]
1111.29/291.68	   helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1]
1111.29/291.68	   ge(x, 0) -> true [1]
1111.29/291.68	   ge(0, s(x)) -> false [1]
1111.29/291.68	   ge(s(x), s(y)) -> ge(x, y) [1]
1111.29/291.68	   if(true, c, l, ys, zs) -> nil [1]
1111.29/291.68	   if(false, c, l, ys, zs) -> helpb(c, l, ys, zs) [1]
1111.29/291.68	   take(0, cons(x, xs), ys) -> x [1]
1111.29/291.68	   take(0, nil, cons(y, ys)) -> y [1]
1111.29/291.68	   take(s(c), cons(x, xs), ys) -> take(c, xs, ys) [1]
1111.29/291.68	   take(s(c), nil, cons(y, ys)) -> take(c, nil, ys) [1]
1111.29/291.68	   helpb(c, l, ys, zs) -> cons(take(c, ys, zs), helpa(s(c), l, ys, zs)) [1]
1111.29/291.68	
1111.29/291.68	Rewrite Strategy: INNERMOST
1111.29/291.68	----------------------------------------
1111.29/291.68	
1111.29/291.68	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))

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