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	n151.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	22.7012 seconds
cpu usage	56.8712
user time	54.6148
system time	2.25636
max virtual memory	3.7754952E7
max residence set size	4525552.0

stage attributes

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

output

WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 1149 ms] (14) BOUNDS(1, n^2) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxTRS (17) SlicingProof [LOWER BOUND(ID), 0 ms] (18) CpxTRS (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) typed CpxTrs (21) OrderProof [LOWER BOUND(ID), 0 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 214 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 799 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 683 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 53 ms] (34) proven lower bound (35) LowerBoundPropagationProof [FINISHED, 0 ms] (36) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s) Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s) Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s) Frozen(m, Sum_term_var(xi), n, s) -> Case(Term_sub(m, s), xi, Term_sub(n, s)) Term_sub(Term_app(m, n), s) -> Term_app(Term_sub(m, s), Term_sub(n, s)) Term_sub(Term_pair(m, n), s) -> Term_pair(Term_sub(m, s), Term_sub(n, s)) Term_sub(Term_inl(m), s) -> Term_inl(Term_sub(m, s)) Term_sub(Term_inr(m), s) -> Term_inr(Term_sub(m, s)) Term_sub(Term_var(x), Id) -> Term_var(x) Term_sub(Term_var(x), Cons_usual(y, m, s)) -> m Term_sub(Term_var(x), Cons_usual(y, m, s)) -> Term_sub(Term_var(x), s) Term_sub(Term_var(x), Cons_sum(xi, k, s)) -> Term_sub(Term_var(x), s) Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t)) Sum_sub(xi, Id) -> Sum_term_var(xi) Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_constant(k) Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_sub(xi, s) Sum_sub(xi, Cons_usual(y, m, s)) -> Sum_sub(xi, s) Concat(Concat(s, t), u) -> Concat(s, Concat(t, u)) Concat(Cons_usual(x, m, s), t) -> Cons_usual(x, Term_sub(m, t), Concat(s, t)) Concat(Cons_sum(xi, k, s), t) -> Cons_sum(xi, k, Concat(s, t)) Concat(Id, s) -> s S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 1th argument of Frozen: Sum_sub Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t)) Concat(Concat(s, t), u) -> Concat(s, Concat(t, u)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s) Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s) Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s) popout

output may be truncated. 'popout' for the full output.

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actions

all output return to Runtime Complexity: TRS