Runtime Complexity: TRS Innermost pair #487112084

details

property	value
status	complete
benchmark	22.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	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.67835 seconds
cpu usage	29.7603
user time	27.837
system time	1.92329
max virtual memory	3.7717332E7
max residence set size	4169460.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) 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) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (10) CpxRNTS
    (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxRNTS
    (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxRNTS
    (15) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
    (16) CpxRNTS
    (17) IntTrsBoundProof [UPPER BOUND(ID), 895 ms]
    (18) CpxRNTS
    (19) IntTrsBoundProof [UPPER BOUND(ID), 607 ms]
    (20) CpxRNTS
    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 59 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 101 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 115 ms]
    (32) CpxRNTS
    (33) FinalProof [FINISHED, 0 ms]
    (34) BOUNDS(1, n^1)
(35) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(36) CpxTRS
    (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) typed CpxTrs
    (39) OrderProof [LOWER BOUND(ID), 0 ms]
    (40) typed CpxTrs
    (41) RewriteLemmaProof [LOWER BOUND(ID), 285 ms]
    (42) BEST
        (43) proven lower bound
            (44) LowerBoundPropagationProof [FINISHED, 0 ms]
            (45) BOUNDS(n^1, INF)
        (46) typed CpxTrs


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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:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y))
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x

S is empty.
Rewrite Strategy: INNERMOST
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(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:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y)) [1]
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]

Rewrite Strategy: INNERMOST
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