Runtime Complexity: TRS Innermost pair #487112324

details

property	value
status	complete
benchmark	Ex1_GL02a_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.45164 seconds
cpu usage	14.4871
user time	13.5402
system time	0.946929
max virtual memory	1.9042028E7
max residence set size	3324240.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 64 ms]
    (10) CdtProblem
    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms]
    (12) CdtProblem
    (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) BOUNDS(1, 1)
(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), 273 ms]
    (24) BEST
        (25) proven lower bound
            (26) LowerBoundPropagationProof [FINISHED, 0 ms]
            (27) BOUNDS(n^1, INF)
        (28) typed CpxTrs


----------------------------------------

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).


The TRS R consists of the following rules:

   a__eq(0, 0) -> true
   a__eq(s(X), s(Y)) -> a__eq(X, Y)
   a__eq(X, Y) -> false
   a__inf(X) -> cons(X, inf(s(X)))
   a__take(0, X) -> nil
   a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L))
   a__length(nil) -> 0
   a__length(cons(X, L)) -> s(length(L))
   mark(eq(X1, X2)) -> a__eq(X1, X2)
   mark(inf(X)) -> a__inf(mark(X))
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(length(X)) -> a__length(mark(X))
   mark(0) -> 0
   mark(true) -> true
   mark(s(X)) -> s(X)
   mark(false) -> false
   mark(cons(X1, X2)) -> cons(X1, X2)
   mark(nil) -> nil
   a__eq(X1, X2) -> eq(X1, X2)
   a__inf(X) -> inf(X)
   a__take(X1, X2) -> take(X1, X2)
   a__length(X) -> length(X)

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS to CDT
----------------------------------------

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__eq(0, 0) -> true
   a__eq(s(z0), s(z1)) -> a__eq(z0, z1)
   a__eq(z0, z1) -> false
   a__eq(z0, z1) -> eq(z0, z1)
   a__inf(z0) -> cons(z0, inf(s(z0)))
   a__inf(z0) -> inf(z0)
   a__take(0, z0) -> nil
   a__take(s(z0), cons(z1, z2)) -> cons(z1, take(z0, z2))
   a__take(z0, z1) -> take(z0, z1)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> s(length(z1))
   a__length(z0) -> length(z0)
   mark(eq(z0, z1)) -> a__eq(z0, z1)
   mark(inf(z0)) -> a__inf(mark(z0))
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(length(z0)) -> a__length(mark(z0))
   mark(0) -> 0

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