Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307636

details

property	value
status	complete
benchmark	lse.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	24.2577 seconds
cpu usage	59.4553
user time	56.4391
system time	3.01615
max virtual memory	1.9369308E7
max residence set size	4499376.0

stage attributes

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

output

59.24/24.19	WORST_CASE(Omega(n^2), O(n^2))
59.24/24.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
59.24/24.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
59.24/24.21	
59.24/24.21	
59.24/24.21	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).
59.24/24.21	
59.24/24.21	(0) CpxTRS
59.24/24.21	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
59.24/24.21	(2) CpxTRS
59.24/24.21	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
59.24/24.21	    (4) CpxTRS
59.24/24.21	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms]
59.24/24.21	    (6) CpxWeightedTrs
59.24/24.21	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
59.24/24.21	    (8) CpxTypedWeightedTrs
59.24/24.21	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
59.24/24.21	    (10) CpxTypedWeightedCompleteTrs
59.24/24.21	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
59.24/24.21	    (12) CpxRNTS
59.24/24.21	    (13) CompleteCoflocoProof [FINISHED, 1155 ms]
59.24/24.21	    (14) BOUNDS(1, n^2)
59.24/24.21	(15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
59.24/24.21	(16) CpxTRS
59.24/24.21	    (17) SlicingProof [LOWER BOUND(ID), 0 ms]
59.24/24.21	    (18) CpxTRS
59.24/24.21	    (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
59.24/24.21	    (20) typed CpxTrs
59.24/24.21	    (21) OrderProof [LOWER BOUND(ID), 0 ms]
59.24/24.21	    (22) typed CpxTrs
59.24/24.21	    (23) RewriteLemmaProof [LOWER BOUND(ID), 226 ms]
59.24/24.21	    (24) BEST
59.24/24.21	        (25) proven lower bound
59.24/24.21	            (26) LowerBoundPropagationProof [FINISHED, 0 ms]
59.24/24.21	            (27) BOUNDS(n^1, INF)
59.24/24.21	        (28) typed CpxTrs
59.24/24.21	            (29) RewriteLemmaProof [LOWER BOUND(ID), 811 ms]
59.24/24.21	            (30) typed CpxTrs
59.24/24.21	            (31) RewriteLemmaProof [LOWER BOUND(ID), 715 ms]
59.24/24.21	            (32) typed CpxTrs
59.24/24.21	            (33) RewriteLemmaProof [LOWER BOUND(ID), 0 ms]
59.24/24.21	            (34) proven lower bound
59.24/24.21	            (35) LowerBoundPropagationProof [FINISHED, 0 ms]
59.24/24.21	            (36) BOUNDS(n^2, INF)
59.24/24.21	
59.24/24.21	
59.24/24.21	----------------------------------------
59.24/24.21	
59.24/24.21	(0)
59.24/24.21	Obligation:
59.24/24.21	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).
59.24/24.21	
59.24/24.21	
59.24/24.21	The TRS R consists of the following rules:
59.24/24.21	
59.24/24.21	   Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s)
59.24/24.21	   Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s)
59.24/24.21	   Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s)
59.24/24.21	   Frozen(m, Sum_term_var(xi), n, s) -> Case(Term_sub(m, s), xi, Term_sub(n, s))
59.24/24.21	   Term_sub(Term_app(m, n), s) -> Term_app(Term_sub(m, s), Term_sub(n, s))
59.24/24.21	   Term_sub(Term_pair(m, n), s) -> Term_pair(Term_sub(m, s), Term_sub(n, s))
59.24/24.21	   Term_sub(Term_inl(m), s) -> Term_inl(Term_sub(m, s))
59.24/24.21	   Term_sub(Term_inr(m), s) -> Term_inr(Term_sub(m, s))
59.24/24.21	   Term_sub(Term_var(x), Id) -> Term_var(x)
59.24/24.21	   Term_sub(Term_var(x), Cons_usual(y, m, s)) -> m
59.24/24.21	   Term_sub(Term_var(x), Cons_usual(y, m, s)) -> Term_sub(Term_var(x), s)
59.24/24.21	   Term_sub(Term_var(x), Cons_sum(xi, k, s)) -> Term_sub(Term_var(x), s)
59.24/24.21	   Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t))
59.24/24.21	   Sum_sub(xi, Id) -> Sum_term_var(xi)
59.24/24.21	   Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_constant(k)
59.24/24.21	   Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_sub(xi, s)
59.24/24.21	   Sum_sub(xi, Cons_usual(y, m, s)) -> Sum_sub(xi, s)
59.24/24.21	   Concat(Concat(s, t), u) -> Concat(s, Concat(t, u))
59.24/24.21	   Concat(Cons_usual(x, m, s), t) -> Cons_usual(x, Term_sub(m, t), Concat(s, t))
59.24/24.21	   Concat(Cons_sum(xi, k, s), t) -> Cons_sum(xi, k, Concat(s, t))
59.24/24.21	   Concat(Id, s) -> s
59.24/24.21	
59.24/24.21	S is empty.
59.24/24.21	Rewrite Strategy: FULL
59.24/24.21	----------------------------------------
59.24/24.21	
59.24/24.21	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
59.24/24.21	The following defined symbols can occur below the 1th argument of Frozen: Sum_sub
59.24/24.21	
59.24/24.21	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
59.24/24.21	Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t))
59.24/24.21	Concat(Concat(s, t), u) -> Concat(s, Concat(t, u))
59.24/24.21	
59.24/24.21	----------------------------------------
59.24/24.21	
59.24/24.21	(2)
59.24/24.21	Obligation:
59.24/24.21	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2).
59.24/24.21	
59.24/24.21	
59.24/24.21	The TRS R consists of the following rules:
59.24/24.21	
59.24/24.21	   Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s)
59.24/24.21	   Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s)
59.24/24.21	   Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s)

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11