Runti Compl Full Rewri 10127 pair #381903543

details

property	value
status	complete
benchmark	OvConsOS_nosorts_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	294.564555883 seconds
cpu usage	1137.25531017
max memory	1.5465242624E10

stage attributes

key	value
output-size	72336
starexec-result	WORST_CASE(Omega(n^1), ?)

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^1), ?)
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^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), 509 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), 146 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 96 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 85 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 174 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 202 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 140 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 140 ms]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 211 ms]
        (28) 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(zeros) -> mark(cons(0, zeros))
   active(U11(tt, L)) -> mark(U12(tt, L))
   active(U12(tt, L)) -> mark(s(length(L)))
   active(U21(tt, IL, M, N)) -> mark(U22(tt, IL, M, N))
   active(U22(tt, IL, M, N)) -> mark(U23(tt, IL, M, N))
   active(U23(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
   active(length(nil)) -> mark(0)
   active(length(cons(N, L))) -> mark(U11(tt, L))
   active(take(0, IL)) -> mark(nil)
   active(take(s(M), cons(N, IL))) -> mark(U21(tt, IL, M, N))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(U11(X1, X2)) -> U11(active(X1), X2)
   active(U12(X1, X2)) -> U12(active(X1), X2)
   active(s(X)) -> s(active(X))
   active(length(X)) -> length(active(X))
   active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
   active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
   active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
   active(take(X1, X2)) -> take(active(X1), X2)
   active(take(X1, X2)) -> take(X1, active(X2))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   U11(mark(X1), X2) -> mark(U11(X1, X2))
   U12(mark(X1), X2) -> mark(U12(X1, X2))
   s(mark(X)) -> mark(s(X))
   length(mark(X)) -> mark(length(X))
   U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
   U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
   U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
   take(mark(X1), X2) -> mark(take(X1, X2))
   take(X1, mark(X2)) -> mark(take(X1, X2))
   proper(zeros) -> ok(zeros)
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
   proper(tt) -> ok(tt)
   proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(length(X)) -> length(proper(X))
   proper(U21(X1, X2, X3, X4)) -> U21(proper(X1), proper(X2), proper(X3), proper(X4))
   proper(U22(X1, X2, X3, X4)) -> U22(proper(X1), proper(X2), proper(X3), proper(X4))
   proper(U23(X1, X2, X3, X4)) -> U23(proper(X1), proper(X2), proper(X3), proper(X4))
   proper(take(X1, X2)) -> take(proper(X1), proper(X2))
   proper(nil) -> ok(nil)
   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
   U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
   U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
   s(ok(X)) -> ok(s(X))

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