Runtime Complexity: TRS pair #487109722

details

property	value
status	complete
benchmark	Ex9_BLR02_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.773 seconds
cpu usage	329.779
user time	324.884
system time	4.89448
max virtual memory	1.8279408E7
max residence set size	8398796.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?)
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^1, 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), 417 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), 126 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 46 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 77 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 73 ms]
        (20) typed CpxTrs


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(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M)))
   active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M)))
   active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y)))
   active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N))))
   active(nats(N)) -> mark(cons(N, nats(s(N))))
   active(zprimes) -> mark(sieve(nats(s(s(0)))))
   active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3)
   active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3)
   active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(s(X)) -> s(active(X))
   active(sieve(X)) -> sieve(active(X))
   active(nats(X)) -> nats(active(X))
   filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3))
   filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3))
   filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   s(mark(X)) -> mark(s(X))
   sieve(mark(X)) -> mark(sieve(X))
   nats(mark(X)) -> mark(nats(X))
   proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3))
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(s(X)) -> s(proper(X))
   proper(sieve(X)) -> sieve(proper(X))
   proper(nats(X)) -> nats(proper(X))
   proper(zprimes) -> ok(zprimes)
   filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3))
   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
   s(ok(X)) -> ok(s(X))
   sieve(ok(X)) -> ok(sieve(X))
   nats(ok(X)) -> ok(nats(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

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^1, INF).


The TRS R consists of the following rules:

   active(filter(cons(X, Y), 0', M)) -> mark(cons(0', filter(Y, M, M)))
   active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M)))
   active(sieve(cons(0', Y))) -> mark(cons(0', sieve(Y)))
   active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N))))
   active(nats(N)) -> mark(cons(N, nats(s(N))))
   active(zprimes) -> mark(sieve(nats(s(s(0')))))
   active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3)
   active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3)
   active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(s(X)) -> s(active(X))

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