Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308373

details

property	value
status	complete
benchmark	Ex5_7_Luc97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n063.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.3433 seconds
cpu usage	44.5634
user time	42.1372
system time	2.42619
max virtual memory	3.7772328E7
max residence set size	4297096.0

stage attributes

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

output

44.21/13.27	WORST_CASE(Omega(n^1), O(n^1))
44.21/13.29	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
44.21/13.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
44.21/13.29	
44.21/13.29	
44.21/13.29	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
44.21/13.29	
44.21/13.29	(0) CpxTRS
44.21/13.29	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
44.21/13.29	(2) CpxTRS
44.21/13.29	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
44.21/13.29	    (4) CpxTRS
44.21/13.29	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 167 ms]
44.21/13.29	    (6) BOUNDS(1, n^1)
44.21/13.29	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
44.21/13.29	(8) CpxTRS
44.21/13.29	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
44.21/13.29	    (10) typed CpxTrs
44.21/13.29	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
44.21/13.29	    (12) typed CpxTrs
44.21/13.29	    (13) RewriteLemmaProof [LOWER BOUND(ID), 558 ms]
44.21/13.29	    (14) BEST
44.21/13.29	        (15) proven lower bound
44.21/13.29	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
44.21/13.29	            (17) BOUNDS(n^1, INF)
44.21/13.29	        (18) typed CpxTrs
44.21/13.29	            (19) RewriteLemmaProof [LOWER BOUND(ID), 148 ms]
44.21/13.29	            (20) typed CpxTrs
44.21/13.29	            (21) RewriteLemmaProof [LOWER BOUND(ID), 99 ms]
44.21/13.29	            (22) typed CpxTrs
44.21/13.29	            (23) RewriteLemmaProof [LOWER BOUND(ID), 103 ms]
44.21/13.29	            (24) typed CpxTrs
44.21/13.29	            (25) RewriteLemmaProof [LOWER BOUND(ID), 83 ms]
44.21/13.29	            (26) typed CpxTrs
44.21/13.29	            (27) RewriteLemmaProof [LOWER BOUND(ID), 37 ms]
44.21/13.29	            (28) typed CpxTrs
44.21/13.29	            (29) RewriteLemmaProof [LOWER BOUND(ID), 75 ms]
44.21/13.29	            (30) typed CpxTrs
44.21/13.29	            (31) RewriteLemmaProof [LOWER BOUND(ID), 58 ms]
44.21/13.29	            (32) typed CpxTrs
44.21/13.29	
44.21/13.29	
44.21/13.29	----------------------------------------
44.21/13.29	
44.21/13.29	(0)
44.21/13.29	Obligation:
44.21/13.29	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
44.21/13.29	
44.21/13.29	
44.21/13.29	The TRS R consists of the following rules:
44.21/13.29	
44.21/13.29	   active(dbl(0)) -> mark(0)
44.21/13.29	   active(dbl(s(X))) -> mark(s(s(dbl(X))))
44.21/13.29	   active(dbls(nil)) -> mark(nil)
44.21/13.29	   active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
44.21/13.29	   active(sel(0, cons(X, Y))) -> mark(X)
44.21/13.29	   active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
44.21/13.29	   active(indx(nil, X)) -> mark(nil)
44.21/13.29	   active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
44.21/13.29	   active(from(X)) -> mark(cons(X, from(s(X))))
44.21/13.29	   active(dbl1(0)) -> mark(01)
44.21/13.29	   active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
44.21/13.29	   active(sel1(0, cons(X, Y))) -> mark(X)
44.21/13.29	   active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
44.21/13.29	   active(quote(0)) -> mark(01)
44.21/13.29	   active(quote(s(X))) -> mark(s1(quote(X)))
44.21/13.29	   active(quote(dbl(X))) -> mark(dbl1(X))
44.21/13.29	   active(quote(sel(X, Y))) -> mark(sel1(X, Y))
44.21/13.29	   active(dbl(X)) -> dbl(active(X))
44.21/13.29	   active(dbls(X)) -> dbls(active(X))
44.21/13.29	   active(sel(X1, X2)) -> sel(active(X1), X2)
44.21/13.29	   active(sel(X1, X2)) -> sel(X1, active(X2))
44.21/13.29	   active(indx(X1, X2)) -> indx(active(X1), X2)
44.21/13.29	   active(dbl1(X)) -> dbl1(active(X))
44.21/13.29	   active(s1(X)) -> s1(active(X))
44.21/13.29	   active(sel1(X1, X2)) -> sel1(active(X1), X2)
44.21/13.29	   active(sel1(X1, X2)) -> sel1(X1, active(X2))
44.21/13.29	   active(quote(X)) -> quote(active(X))
44.21/13.29	   dbl(mark(X)) -> mark(dbl(X))
44.21/13.29	   dbls(mark(X)) -> mark(dbls(X))
44.21/13.29	   sel(mark(X1), X2) -> mark(sel(X1, X2))
44.21/13.29	   sel(X1, mark(X2)) -> mark(sel(X1, X2))
44.21/13.29	   indx(mark(X1), X2) -> mark(indx(X1, X2))
44.21/13.29	   dbl1(mark(X)) -> mark(dbl1(X))
44.21/13.29	   s1(mark(X)) -> mark(s1(X))
44.21/13.29	   sel1(mark(X1), X2) -> mark(sel1(X1, X2))
44.21/13.29	   sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
44.21/13.29	   quote(mark(X)) -> mark(quote(X))
44.21/13.29	   proper(dbl(X)) -> dbl(proper(X))
44.21/13.29	   proper(0) -> ok(0)
44.21/13.29	   proper(s(X)) -> s(proper(X))
44.21/13.29	   proper(dbls(X)) -> dbls(proper(X))
44.21/13.29	   proper(nil) -> ok(nil)
44.21/13.29	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
44.21/13.29	   proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
44.21/13.29	   proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
44.21/13.29	   proper(from(X)) -> from(proper(X))
44.21/13.29	   proper(dbl1(X)) -> dbl1(proper(X))
44.21/13.29	   proper(01) -> ok(01)
44.21/13.29	   proper(s1(X)) -> s1(proper(X))

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