Runti Compl Full Rewri 10127 pair #381902060

details

property	value
status	complete
benchmark	thiemann14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.964957952 seconds
cpu usage	322.823740831
max memory	5.59224832E9

stage attributes

key	value
output-size	19754
starexec-result	WORST_CASE(Omega(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^2), ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The Runtime Complexity (full) 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) SlicingProof [LOWER BOUND(ID), 0 ms]
(4) CpxTRS
(5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) typed CpxTrs
(7) OrderProof [LOWER BOUND(ID), 0 ms]
(8) typed CpxTrs
(9) RewriteLemmaProof [LOWER BOUND(ID), 292 ms]
(10) BEST
    (11) proven lower bound
        (12) LowerBoundPropagationProof [FINISHED, 0 ms]
        (13) BOUNDS(n^1, INF)
    (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 657 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 352 ms]
        (18) BEST
            (19) proven lower bound
                (20) LowerBoundPropagationProof [FINISHED, 0 ms]
                (21) BOUNDS(n^2, INF)
            (22) typed CpxTrs


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

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


The TRS R consists of the following rules:

   empty(nil) -> true
   empty(cons(x, y)) -> false
   tail(nil) -> nil
   tail(cons(x, y)) -> y
   head(cons(x, y)) -> x
   zero(0) -> true
   zero(s(x)) -> false
   p(0) -> 0
   p(s(0)) -> 0
   p(s(s(x))) -> s(p(s(x)))
   intlist(x) -> if_intlist(empty(x), x)
   if_intlist(true, x) -> nil
   if_intlist(false, x) -> cons(s(head(x)), intlist(tail(x)))
   int(x, y) -> if_int(zero(x), zero(y), x, y)
   if_int(true, b, x, y) -> if1(b, x, y)
   if_int(false, b, x, y) -> if2(b, x, y)
   if1(true, x, y) -> cons(0, nil)
   if1(false, x, y) -> cons(0, int(s(0), y))
   if2(true, x, y) -> nil
   if2(false, x, y) -> intlist(int(p(x), p(y)))

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^2, INF).


The TRS R consists of the following rules:

   empty(nil) -> true
   empty(cons(x, y)) -> false
   tail(nil) -> nil
   tail(cons(x, y)) -> y
   head(cons(x, y)) -> x
   zero(0') -> true
   zero(s(x)) -> false
   p(0') -> 0'
   p(s(0')) -> 0'
   p(s(s(x))) -> s(p(s(x)))
   intlist(x) -> if_intlist(empty(x), x)
   if_intlist(true, x) -> nil
   if_intlist(false, x) -> cons(s(head(x)), intlist(tail(x)))
   int(x, y) -> if_int(zero(x), zero(y), x, y)
   if_int(true, b, x, y) -> if1(b, x, y)
   if_int(false, b, x, y) -> if2(b, x, y)
   if1(true, x, y) -> cons(0', nil)

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