Runti Compl Inner Rewri 22807 pair #381905088

details

property	value
status	complete
benchmark	2.19.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.13887286186 seconds
cpu usage	17.096622657
max memory	3.718692864E9

stage attributes

key	value
output-size	17132
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

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^2), O(n^2))
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^2, n^2).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 86 ms]
    (6) CdtProblem
    (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 47 ms]
    (8) CdtProblem
    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 45 ms]
    (10) CdtProblem
    (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) BOUNDS(1, 1)
(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(14) CpxTRS
    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) typed CpxTrs
    (17) OrderProof [LOWER BOUND(ID), 0 ms]
    (18) typed CpxTrs
    (19) RewriteLemmaProof [LOWER BOUND(ID), 284 ms]
    (20) BEST
        (21) proven lower bound
            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
            (23) BOUNDS(n^1, INF)
        (24) typed CpxTrs
            (25) RewriteLemmaProof [LOWER BOUND(ID), 80 ms]
            (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 120 ms]
            (28) proven lower bound
            (29) LowerBoundPropagationProof [FINISHED, 0 ms]
            (30) BOUNDS(n^2, INF)


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).


The TRS R consists of the following rules:

   sqr(0) -> 0
   sqr(s(x)) -> +(sqr(x), s(double(x)))
   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   +(x, 0) -> x
   +(x, s(y)) -> s(+(x, y))
   sqr(s(x)) -> s(+(sqr(x), double(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:
   sqr(0) -> 0
   sqr(s(z0)) -> +(sqr(z0), s(double(z0)))
   sqr(s(z0)) -> s(+(sqr(z0), double(z0)))
   double(0) -> 0
   double(s(z0)) -> s(s(double(z0)))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   SQR(0) -> c
   SQR(s(z0)) -> c1(+'(sqr(z0), s(double(z0))), SQR(z0), DOUBLE(z0))
   SQR(s(z0)) -> c2(+'(sqr(z0), double(z0)), SQR(z0), DOUBLE(z0))
   DOUBLE(0) -> c3
   DOUBLE(s(z0)) -> c4(DOUBLE(z0))
   +'(z0, 0) -> c5
   +'(z0, s(z1)) -> c6(+'(z0, z1))
S tuples:
   SQR(0) -> c
   SQR(s(z0)) -> c1(+'(sqr(z0), s(double(z0))), SQR(z0), DOUBLE(z0))
   SQR(s(z0)) -> c2(+'(sqr(z0), double(z0)), SQR(z0), DOUBLE(z0))
   DOUBLE(0) -> c3
   DOUBLE(s(z0)) -> c4(DOUBLE(z0))
   +'(z0, 0) -> c5
   +'(z0, s(z1)) -> c6(+'(z0, z1))
K tuples:none

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