Runtime Complexity: TRS pair #487110672

details

property	value
status	complete
benchmark	factorial1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.48 seconds
cpu usage	332.291
user time	329.843
system time	2.44776
max virtual memory	1.8279408E7
max residence set size	5812172.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^4), ?)

output

WORST_CASE(Omega(n^4), ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^4, 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), 254 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), 24 ms]
        (14) BEST
            (15) proven lower bound
                (16) LowerBoundPropagationProof [FINISHED, 0 ms]
                (17) BOUNDS(n^2, INF)
            (18) typed CpxTrs
                (19) RewriteLemmaProof [LOWER BOUND(ID), 18 ms]
                (20) BEST
                    (21) proven lower bound
                        (22) LowerBoundPropagationProof [FINISHED, 0 ms]
                        (23) BOUNDS(n^3, INF)
                    (24) typed CpxTrs
                        (25) RewriteLemmaProof [LOWER BOUND(ID), 1131 ms]
                        (26) proven lower bound
                        (27) LowerBoundPropagationProof [FINISHED, 0 ms]
                        (28) BOUNDS(n^4, INF)


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

(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^4, INF).


The TRS R consists of the following rules:

   plus(0, x) -> x
   plus(s(x), y) -> s(plus(p(s(x)), y))
   times(0, y) -> 0
   times(s(x), y) -> plus(y, times(p(s(x)), y))
   p(s(0)) -> 0
   p(s(s(x))) -> s(p(s(x)))
   fac(0, x) -> x
   fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
   factorial(x) -> fac(x, s(0))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(2)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^4, INF).


The TRS R consists of the following rules:

   plus(0', x) -> x
   plus(s(x), y) -> s(plus(p(s(x)), y))
   times(0', y) -> 0'
   times(s(x), y) -> plus(y, times(p(s(x)), y))
   p(s(0')) -> 0'
   p(s(s(x))) -> s(p(s(x)))
   fac(0', x) -> x
   fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
   factorial(x) -> fac(x, s(0'))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

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

(4)
Obligation:
TRS:
Rules:
plus(0', x) -> x
plus(s(x), y) -> s(plus(p(s(x)), y))
times(0', y) -> 0'
times(s(x), y) -> plus(y, times(p(s(x)), y))
p(s(0')) -> 0'
p(s(s(x))) -> s(p(s(x)))

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