Derivational Complexity: TRS Innermost pair #487109026

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	n148.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.614 seconds
cpu usage	1139.25
user time	1129.43
system time	9.81732
max virtual memory	1.9282972E7
max residence set size	1.4932976E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 794 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) typed CpxTrs
(9) OrderProof [LOWER BOUND(ID), 0 ms]
(10) typed CpxTrs
(11) RewriteLemmaProof [LOWER BOUND(ID), 410 ms]
(12) BEST
    (13) proven lower bound
        (14) LowerBoundPropagationProof [FINISHED, 0 ms]
        (15) BOUNDS(n^1, INF)
    (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 152 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 93 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 105 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 212 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 183 ms]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 103 ms]
        (28) typed CpxTrs
        (29) RewriteLemmaProof [LOWER BOUND(ID), 84 ms]
        (30) typed CpxTrs
        (31) RewriteLemmaProof [LOWER BOUND(ID), 239 ms]
        (32) typed CpxTrs


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

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs 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))
   length(ok(X)) -> ok(length(X))
   U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))

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actions all output return to Derivational Complexity: TRS Innermost