Runti Compl Inner Rewri 22807 pair #381905293

details

property	value
status	complete
benchmark	Ex4_7_56_Bor03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.19790101051 seconds
cpu usage	13.826225276
max memory	3.488288768E9

stage attributes

key	value
output-size	8608
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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)), 54 ms]
    (10) CdtProblem
    (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) BOUNDS(1, 1)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
    (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (16) BEST
        (17) proven lower bound
            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
            (19) BOUNDS(n^1, INF)
        (20) TRS for Loop Detection


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(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:

   from(X) -> cons(X, n__from(s(X)))
   after(0, XS) -> XS
   after(s(N), cons(X, XS)) -> after(N, activate(XS))
   from(X) -> n__from(X)
   activate(n__from(X)) -> from(X)
   activate(X) -> 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:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   after(0, z0) -> z0
   after(s(z0), cons(z1, z2)) -> after(z0, activate(z2))
   activate(n__from(z0)) -> from(z0)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   AFTER(0, z0) -> c2
   AFTER(s(z0), cons(z1, z2)) -> c3(AFTER(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__from(z0)) -> c4(FROM(z0))
   ACTIVATE(z0) -> c5
S tuples:
   FROM(z0) -> c
   FROM(z0) -> c1
   AFTER(0, z0) -> c2
   AFTER(s(z0), cons(z1, z2)) -> c3(AFTER(z0, activate(z2)), ACTIVATE(z2))
   ACTIVATE(n__from(z0)) -> c4(FROM(z0))
   ACTIVATE(z0) -> c5
K tuples:none
Defined Rule Symbols:   from_1, after_2, activate_1

Defined Pair Symbols:   FROM_1, AFTER_2, ACTIVATE_1

Compound Symbols:   c, c1, c2, c3_2, c4_1, c5


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(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   FROM(z0) -> c1
   ACTIVATE(z0) -> c5
   ACTIVATE(n__from(z0)) -> c4(FROM(z0))

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