Runti Compl Inner Rewri 22807 pair #381904425

details

property	value
status	complete
benchmark	sum_sqs3.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	hoca

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.503144026 seconds
cpu usage	803.378049834
max memory	1.3593116672E10

stage attributes

key	value
output-size	16944
starexec-result	WORST_CASE(Omega(n^2), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^2), ?)
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^2, 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), 298 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), 32 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 65 ms]
        (16) BEST
            (17) proven lower bound
                (18) LowerBoundPropagationProof [FINISHED, 0 ms]
                (19) BOUNDS(n^2, INF)
            (20) typed CpxTrs
                (21) RewriteLemmaProof [LOWER BOUND(ID), 29 ms]
                (22) typed CpxTrs
                (23) RewriteLemmaProof [LOWER BOUND(ID), 3759 ms]
                (24) BOUNDS(1, INF)


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).


The TRS R consists of the following rules:

   sum#1(Nil) -> 0
   sum#1(Cons(x2, x1)) -> plus#2(x2, sum#1(x1))
   map#2(Nil) -> Nil
   map#2(Cons(x2, x5)) -> Cons(mult#2(x2, x2), map#2(x5))
   unfoldr#2(0) -> Nil
   unfoldr#2(S(x2)) -> Cons(x2, unfoldr#2(x2))
   mult#2(0, x2) -> 0
   mult#2(S(x4), x2) -> plus#2(x2, mult#2(x4, x2))
   plus#2(0, x8) -> x8
   plus#2(S(x4), x2) -> S(plus#2(x4, x2))
   main(0) -> 0
   main(S(x1)) -> sum#1(map#2(Cons(S(x1), unfoldr#2(S(x1)))))

S is empty.
Rewrite Strategy: INNERMOST
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(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^2, INF).


The TRS R consists of the following rules:

   sum#1(Nil) -> 0'
   sum#1(Cons(x2, x1)) -> plus#2(x2, sum#1(x1))
   map#2(Nil) -> Nil
   map#2(Cons(x2, x5)) -> Cons(mult#2(x2, x2), map#2(x5))
   unfoldr#2(0') -> Nil
   unfoldr#2(S(x2)) -> Cons(x2, unfoldr#2(x2))
   mult#2(0', x2) -> 0'
   mult#2(S(x4), x2) -> plus#2(x2, mult#2(x4, x2))
   plus#2(0', x8) -> x8
   plus#2(S(x4), x2) -> S(plus#2(x4, x2))
   main(0') -> 0'
   main(S(x1)) -> sum#1(map#2(Cons(S(x1), unfoldr#2(S(x1)))))

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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