Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313815

details

property	value
status	complete
benchmark	gcd2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n125.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	297.804 seconds
cpu usage	1118.29
user time	1106.21
system time	12.0757
max virtual memory	5.7520336E7
max residence set size	1.4957492E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

1117.68/297.58	WORST_CASE(Omega(n^1), O(n^3))
1117.89/297.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1117.89/297.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1117.89/297.64	
1117.89/297.64	
1117.89/297.64	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3).
1117.89/297.64	
1117.89/297.64	(0) CpxRelTRS
1117.89/297.64	(1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 223 ms]
1117.89/297.64	(2) CpxRelTRS
1117.89/297.64	(3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
1117.89/297.64	(4) CpxWeightedTrs
1117.89/297.64	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1117.89/297.64	    (6) CpxTypedWeightedTrs
1117.89/297.64	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
1117.89/297.64	    (8) CpxTypedWeightedCompleteTrs
1117.89/297.64	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
1117.89/297.64	    (10) CpxRNTS
1117.89/297.64	    (11) CompleteCoflocoProof [FINISHED, 109.2 s]
1117.89/297.64	    (12) BOUNDS(1, n^3)
1117.89/297.64	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1117.89/297.64	(14) CpxRelTRS
1117.89/297.64	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1117.89/297.64	    (16) typed CpxTrs
1117.89/297.64	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
1117.89/297.64	    (18) typed CpxTrs
1117.89/297.64	    (19) RewriteLemmaProof [LOWER BOUND(ID), 282 ms]
1117.89/297.64	    (20) BEST
1117.89/297.64	        (21) proven lower bound
1117.89/297.64	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
1117.89/297.64	            (23) BOUNDS(n^1, INF)
1117.89/297.64	        (24) typed CpxTrs
1117.89/297.64	            (25) RewriteLemmaProof [LOWER BOUND(ID), 60 ms]
1117.89/297.64	            (26) typed CpxTrs
1117.89/297.64	            (27) RewriteLemmaProof [LOWER BOUND(ID), 70 ms]
1117.89/297.64	            (28) typed CpxTrs
1117.89/297.64	            (29) RewriteLemmaProof [LOWER BOUND(ID), 49 ms]
1117.89/297.64	            (30) typed CpxTrs
1117.89/297.64	
1117.89/297.64	
1117.89/297.64	----------------------------------------
1117.89/297.64	
1117.89/297.64	(0)
1117.89/297.64	Obligation:
1117.89/297.64	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3).
1117.89/297.64	
1117.89/297.64	
1117.89/297.64	The TRS R consists of the following rules:
1117.89/297.64	
1117.89/297.64	   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys))
1117.89/297.64	   @(Nil, ys) -> ys
1117.89/297.64	   gt0(Cons(x, xs), Nil) -> True
1117.89/297.64	   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs)
1117.89/297.64	   gcd(Nil, Nil) -> Nil
1117.89/297.64	   gcd(Nil, Cons(x, xs)) -> Nil
1117.89/297.64	   gcd(Cons(x, xs), Nil) -> Nil
1117.89/297.64	   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs))
1117.89/297.64	   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs))
1117.89/297.64	   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys))
1117.89/297.64	   eqList(Cons(x, xs), Nil) -> False
1117.89/297.64	   eqList(Nil, Cons(y, ys)) -> False
1117.89/297.64	   eqList(Nil, Nil) -> True
1117.89/297.64	   lgth(Nil) -> Nil
1117.89/297.64	   gt0(Nil, y) -> False
1117.89/297.64	   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y)
1117.89/297.64	   goal(x, y) -> gcd(x, y)
1117.89/297.64	
1117.89/297.64	The (relative) TRS S consists of the following rules:
1117.89/297.64	
1117.89/297.64	   and(False, False) -> False
1117.89/297.64	   and(True, False) -> False
1117.89/297.64	   and(False, True) -> False
1117.89/297.64	   and(True, True) -> True
1117.89/297.64	   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs)
1117.89/297.64	   monus[Ite](True, Cons(x, xs), y) -> xs
1117.89/297.64	   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y)
1117.89/297.64	   gcd[Ite](True, x, y) -> x
1117.89/297.64	   gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x)
1117.89/297.64	   gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y))
1117.89/297.64	
1117.89/297.64	Rewrite Strategy: INNERMOST
1117.89/297.64	----------------------------------------
1117.89/297.64	
1117.89/297.64	(1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
1117.89/297.64	proved termination of relative rules
1117.89/297.64	----------------------------------------
1117.89/297.64	
1117.89/297.64	(2)
1117.89/297.64	Obligation:
1117.89/297.64	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3).
1117.89/297.64	
1117.89/297.64	
1117.89/297.64	The TRS R consists of the following rules:
1117.89/297.64	
1117.89/297.64	   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys))
1117.89/297.64	   @(Nil, ys) -> ys
1117.89/297.64	   gt0(Cons(x, xs), Nil) -> True
1117.89/297.64	   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs)
1117.89/297.64	   gcd(Nil, Nil) -> Nil
1117.89/297.64	   gcd(Nil, Cons(x, xs)) -> Nil

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