Runti Compl Inner Rewri 22807 pair #381903981

details

property	value
status	complete
benchmark	tower.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	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.570142984 seconds
cpu usage	1140.40115443
max memory	1.6542912512E10

stage attributes

key	value
output-size	15973
starexec-result	WORST_CASE(Omega(n^3), ?)

output

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


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WORST_CASE(Omega(n^3), ?)
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^3, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) typed CpxTrs
(5) OrderProof [LOWER BOUND(ID), 0 ms]
(6) typed CpxTrs
(7) RewriteLemmaProof [LOWER BOUND(ID), 299 ms]
(8) BEST
    (9) proven lower bound
        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
        (11) BOUNDS(n^1, INF)
    (12) typed CpxTrs
        (13) RewriteLemmaProof [LOWER BOUND(ID), 29 ms]
        (14) BEST
            (15) proven lower bound
                (16) LowerBoundPropagationProof [FINISHED, 0 ms]
                (17) BOUNDS(n^2, INF)
            (18) typed CpxTrs
                (19) RewriteLemmaProof [LOWER BOUND(ID), 38 ms]
                (20) BEST
                    (21) proven lower bound
                        (22) LowerBoundPropagationProof [FINISHED, 0 ms]
                        (23) BOUNDS(n^3, INF)
                    (24) typed CpxTrs
                        (25) RewriteLemmaProof [LOWER BOUND(ID), 509 ms]
                        (26) typed CpxTrs


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF).


The TRS R consists of the following rules:

   plus(0, x) -> x
   plus(s(x), y) -> s(plus(p(s(x)), y))
   times(0, y) -> 0
   times(s(x), y) -> plus(y, times(p(s(x)), y))
   exp(x, 0) -> s(0)
   exp(x, s(y)) -> times(x, exp(x, y))
   p(s(0)) -> 0
   p(s(s(x))) -> s(p(s(x)))
   tower(x, y) -> towerIter(x, y, s(0))
   towerIter(0, y, z) -> z
   towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z))

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

(1) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF).


The TRS R consists of the following rules:

   plus(0', x) -> x
   plus(s(x), y) -> s(plus(p(s(x)), y))
   times(0', y) -> 0'
   times(s(x), y) -> plus(y, times(p(s(x)), y))
   exp(x, 0') -> s(0')
   exp(x, s(y)) -> times(x, exp(x, y))
   p(s(0')) -> 0'
   p(s(s(x))) -> s(p(s(x)))
   tower(x, y) -> towerIter(x, y, s(0'))
   towerIter(0', y, z) -> z
   towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z))

S is empty.
Rewrite Strategy: INNERMOST
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(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
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(4)
Obligation:

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