Runtime Complexity: TRS Innermost pair #487112596

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	n150.star.cs.uiowa.edu
space	hoca

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.806 seconds
cpu usage	800.738
user time	788.373
system time	12.365
max virtual memory	3.8042508E7
max residence set size	1.300134E7

stage attributes

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

output

WORST_CASE(Omega(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^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), 279 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), 34 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 81 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), 0 ms]
                (22) typed CpxTrs
                (23) RewriteLemmaProof [LOWER BOUND(ID), 3891 ms]
                (24) BOUNDS(1, INF)


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

(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
----------------------------------------

(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
----------------------------------------

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

(4)
Obligation:
Innermost TRS:
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))

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