Runtime Complexity: TRS Innermost pair #487112478

details

property	value
status	complete
benchmark	#3.18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.1018 seconds
cpu usage	36.2309
user time	34.1405
system time	2.09041
max virtual memory	1.908036E7
max residence set size	4616188.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxWeightedTrs
    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTypedWeightedTrs
    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
    (6) CpxTypedWeightedCompleteTrs
    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 729 ms]
    (10) BOUNDS(1, n^1)
(11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxTRS
    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) typed CpxTrs
    (15) OrderProof [LOWER BOUND(ID), 0 ms]
    (16) typed CpxTrs
    (17) RewriteLemmaProof [LOWER BOUND(ID), 297 ms]
    (18) BEST
        (19) proven lower bound
            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
            (21) BOUNDS(n^1, INF)
        (22) typed CpxTrs
            (23) RewriteLemmaProof [LOWER BOUND(ID), 96 ms]
            (24) typed CpxTrs
            (25) RewriteLemmaProof [LOWER BOUND(ID), 43 ms]
            (26) BOUNDS(1, INF)


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

(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:

   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   plus(s(x), y) -> plus(x, s(y))
   plus(s(x), y) -> s(plus(minus(x, y), double(y)))

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

(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   double(0) -> 0 [1]
   double(s(x)) -> s(s(double(x))) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   plus(s(x), y) -> plus(x, s(y)) [1]
   plus(s(x), y) -> s(plus(minus(x, y), double(y))) [1]

Rewrite Strategy: INNERMOST
----------------------------------------

(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(4)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   minus(x, 0) -> x [1]
   minus(s(x), s(y)) -> minus(x, y) [1]
   double(0) -> 0 [1]
   double(s(x)) -> s(s(double(x))) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   plus(s(x), y) -> plus(x, s(y)) [1]
   plus(s(x), y) -> s(plus(minus(x, y), double(y))) [1]

The TRS has the following type information:

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