Runtime Complexity: TRS Innermost pair #487112088

details

property	value
status	complete
benchmark	5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.684 seconds
cpu usage	1110.05
user time	1096.31
system time	13.7324
max virtual memory	3.8369332E7
max residence set size	1.5281904E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^2).

(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) InliningProof [UPPER BOUND(ID), 1412 ms]
    (12) CpxRNTS
    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxRNTS
    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (18) CpxRNTS
    (19) IntTrsBoundProof [UPPER BOUND(ID), 164 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 56 ms]
    (22) CpxRNTS
    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 72 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
    (28) CpxRNTS
    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 251 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 94 ms]
    (34) CpxRNTS
    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 179 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 25 ms]
    (40) CpxRNTS
    (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 1323 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 1733 ms]
    (46) CpxRNTS
    (47) FinalProof [FINISHED, 0 ms]
    (48) BOUNDS(1, n^2)
(49) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(50) CpxTRS
    (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) typed CpxTrs
    (53) OrderProof [LOWER BOUND(ID), 0 ms]
    (54) typed CpxTrs
    (55) RewriteLemmaProof [LOWER BOUND(ID), 233 ms]
    (56) BEST
        (57) proven lower bound
            (58) LowerBoundPropagationProof [FINISHED, 0 ms]
            (59) BOUNDS(n^1, INF)
        (60) 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^2).


The TRS R consists of the following rules:

   cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x))
   and(x, false) -> false
   and(false, x) -> false
   and(true, true) -> true
   even(0) -> true
   even(s(0)) -> false
   even(s(s(x))) -> even(x)
   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
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