Runti Compl Inner Rewri 22807 pair #381904170

details

property	value
status	complete
benchmark	cade16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n036.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.861064911 seconds
cpu usage	1140.25757323
max memory	1.4004342784E10

stage attributes

key	value
output-size	22010
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

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^1), O(n^2))
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 370 ms]
    (10) BOUNDS(1, n^2)
(11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxTRS
    (13) SlicingProof [LOWER BOUND(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), 257 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), 51 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^1, n^2).


The TRS R consists of the following rules:

   nthtail(n, l) -> cond(ge(n, length(l)), n, l)
   cond(true, n, l) -> l
   cond(false, n, l) -> tail(nthtail(s(n), l))
   tail(nil) -> nil
   tail(cons(x, l)) -> l
   length(nil) -> 0
   length(cons(x, l)) -> s(length(l))
   ge(u, 0) -> true
   ge(0, s(v)) -> false
   ge(s(u), s(v)) -> ge(u, v)

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


The TRS R consists of the following rules:

   nthtail(n, l) -> cond(ge(n, length(l)), n, l) [1]
   cond(true, n, l) -> l [1]
   cond(false, n, l) -> tail(nthtail(s(n), l)) [1]
   tail(nil) -> nil [1]
   tail(cons(x, l)) -> l [1]
   length(nil) -> 0 [1]
   length(cons(x, l)) -> s(length(l)) [1]
   ge(u, 0) -> true [1]
   ge(0, s(v)) -> false [1]
   ge(s(u), s(v)) -> ge(u, v) [1]

Rewrite Strategy: INNERMOST
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(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
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(4)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

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