Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308187

details

property	value
status	complete
benchmark	PEANO_nosorts_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n124.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.62426 seconds
cpu usage	24.5821
user time	23.0248
system time	1.55736
max virtual memory	1.9276248E7
max residence set size	3838980.0

stage attributes

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

output

24.12/7.41	WORST_CASE(Omega(n^1), O(n^1))
24.12/7.42	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
24.12/7.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
24.12/7.42	
24.12/7.42	
24.12/7.42	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
24.12/7.42	
24.12/7.42	(0) CpxTRS
24.12/7.42	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
24.12/7.42	(2) CpxTRS
24.12/7.42	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
24.12/7.42	    (4) CpxTRS
24.12/7.42	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 61 ms]
24.12/7.42	    (6) BOUNDS(1, n^1)
24.12/7.42	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
24.12/7.42	(8) CpxTRS
24.12/7.42	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
24.12/7.42	    (10) typed CpxTrs
24.12/7.42	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
24.12/7.42	    (12) typed CpxTrs
24.12/7.42	    (13) RewriteLemmaProof [LOWER BOUND(ID), 479 ms]
24.12/7.42	    (14) BEST
24.12/7.42	        (15) proven lower bound
24.12/7.42	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
24.12/7.42	            (17) BOUNDS(n^1, INF)
24.12/7.42	        (18) typed CpxTrs
24.12/7.42	            (19) RewriteLemmaProof [LOWER BOUND(ID), 75 ms]
24.12/7.42	            (20) typed CpxTrs
24.12/7.42	            (21) RewriteLemmaProof [LOWER BOUND(ID), 111 ms]
24.12/7.42	            (22) typed CpxTrs
24.12/7.42	            (23) RewriteLemmaProof [LOWER BOUND(ID), 115 ms]
24.12/7.42	            (24) typed CpxTrs
24.12/7.42	
24.12/7.42	
24.12/7.42	----------------------------------------
24.12/7.42	
24.12/7.42	(0)
24.12/7.42	Obligation:
24.12/7.42	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
24.12/7.42	
24.12/7.42	
24.12/7.42	The TRS R consists of the following rules:
24.12/7.42	
24.12/7.42	   active(U11(tt, M, N)) -> mark(U12(tt, M, N))
24.12/7.42	   active(U12(tt, M, N)) -> mark(s(plus(N, M)))
24.12/7.42	   active(plus(N, 0)) -> mark(N)
24.12/7.42	   active(plus(N, s(M))) -> mark(U11(tt, M, N))
24.12/7.42	   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
24.12/7.42	   active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
24.12/7.42	   active(s(X)) -> s(active(X))
24.12/7.42	   active(plus(X1, X2)) -> plus(active(X1), X2)
24.12/7.42	   active(plus(X1, X2)) -> plus(X1, active(X2))
24.12/7.42	   U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
24.12/7.42	   U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3))
24.12/7.42	   s(mark(X)) -> mark(s(X))
24.12/7.42	   plus(mark(X1), X2) -> mark(plus(X1, X2))
24.12/7.42	   plus(X1, mark(X2)) -> mark(plus(X1, X2))
24.12/7.42	   proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3))
24.12/7.42	   proper(tt) -> ok(tt)
24.12/7.42	   proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3))
24.12/7.42	   proper(s(X)) -> s(proper(X))
24.12/7.42	   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
24.12/7.42	   proper(0) -> ok(0)
24.12/7.42	   U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
24.12/7.42	   U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3))
24.12/7.42	   s(ok(X)) -> ok(s(X))
24.12/7.42	   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
24.12/7.42	   top(mark(X)) -> top(proper(X))
24.12/7.42	   top(ok(X)) -> top(active(X))
24.12/7.42	
24.12/7.42	S is empty.
24.12/7.42	Rewrite Strategy: FULL
24.12/7.42	----------------------------------------
24.12/7.42	
24.12/7.42	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
24.12/7.42	The following defined symbols can occur below the 0th argument of top: proper, active
24.12/7.42	The following defined symbols can occur below the 0th argument of proper: proper, active
24.12/7.42	The following defined symbols can occur below the 0th argument of active: proper, active
24.12/7.42	
24.12/7.42	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
24.12/7.42	active(U11(tt, M, N)) -> mark(U12(tt, M, N))
24.12/7.42	active(U12(tt, M, N)) -> mark(s(plus(N, M)))
24.12/7.42	active(plus(N, 0)) -> mark(N)
24.12/7.42	active(plus(N, s(M))) -> mark(U11(tt, M, N))
24.12/7.42	active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
24.12/7.42	active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
24.12/7.42	active(s(X)) -> s(active(X))
24.12/7.42	active(plus(X1, X2)) -> plus(active(X1), X2)
24.12/7.42	active(plus(X1, X2)) -> plus(X1, active(X2))
24.12/7.42	proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3))
24.12/7.42	proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3))
24.12/7.42	proper(s(X)) -> s(proper(X))
24.12/7.42	proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
24.12/7.42	
24.12/7.42	----------------------------------------
24.12/7.42	
24.12/7.42	(2)
24.12/7.42	Obligation:
24.12/7.42	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
24.12/7.42

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