Derivational Complexity: TRS Innermost pair #487108548

details

property	value
status	complete
benchmark	OvConsOS_nokinds_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.822 seconds
cpu usage	1166.18
user time	1155.04
system time	11.1434
max virtual memory	1.9212116E7
max residence set size	1.5105604E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 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), 809 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 13 ms]
(8) typed CpxTrs
(9) OrderProof [LOWER BOUND(ID), 0 ms]
(10) typed CpxTrs
(11) RewriteLemmaProof [LOWER BOUND(ID), 444 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), 159 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 131 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 132 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 198 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 148 ms]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 111 ms]
        (28) typed CpxTrs
        (29) RewriteLemmaProof [LOWER BOUND(ID), 284 ms]
        (30) typed CpxTrs
        (31) RewriteLemmaProof [LOWER BOUND(ID), 263 ms]
        (32) typed CpxTrs
        (33) RewriteLemmaProof [LOWER BOUND(ID), 141 ms]
        (34) typed CpxTrs
        (35) RewriteLemmaProof [LOWER BOUND(ID), 77 ms]
        (36) typed CpxTrs
        (37) RewriteLemmaProof [LOWER BOUND(ID), 115 ms]
        (38) typed CpxTrs
        (39) RewriteLemmaProof [LOWER BOUND(ID), 104 ms]
        (40) typed CpxTrs
        (41) RewriteLemmaProof [LOWER BOUND(ID), 143 ms]
        (42) typed CpxTrs
        (43) RewriteLemmaProof [LOWER BOUND(ID), 178 ms]
        (44) typed CpxTrs
        (45) RewriteLemmaProof [LOWER BOUND(ID), 153 ms]
        (46) typed CpxTrs
        (47) RewriteLemmaProof [LOWER BOUND(ID), 256 ms]
        (48) typed CpxTrs
        (49) RewriteLemmaProof [LOWER BOUND(ID), 87 ms]
        (50) typed CpxTrs
        (51) RewriteLemmaProof [LOWER BOUND(ID), 353 ms]
        (52) 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)) -> mark(tt)
   active(U21(tt)) -> mark(tt)
   active(U31(tt)) -> mark(tt)
   active(U41(tt, V2)) -> mark(U42(isNatIList(V2)))
   active(U42(tt)) -> mark(tt)
   active(U51(tt, V2)) -> mark(U52(isNatList(V2)))
   active(U52(tt)) -> mark(tt)
   active(U61(tt, V2)) -> mark(U62(isNatIList(V2)))
   active(U62(tt)) -> mark(tt)
   active(U71(tt, L, N)) -> mark(U72(isNat(N), L))
   active(U72(tt, L)) -> mark(s(length(L)))
   active(U81(tt)) -> mark(nil)
   active(U91(tt, IL, M, N)) -> mark(U92(isNat(M), IL, M, N))
   active(U92(tt, IL, M, N)) -> mark(U93(isNat(N), IL, M, N))
   active(U93(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
   active(isNat(0)) -> mark(tt)
   active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
   active(isNat(s(V1))) -> mark(U21(isNat(V1)))
   active(isNatIList(V)) -> mark(U31(isNatList(V)))
   active(isNatIList(zeros)) -> mark(tt)
   active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2))
   active(isNatList(nil)) -> mark(tt)
   active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2))
   active(isNatList(take(V1, V2))) -> mark(U61(isNat(V1), V2))
   active(length(nil)) -> mark(0)
   active(length(cons(N, L))) -> mark(U71(isNatList(L), L, N))
   active(take(0, IL)) -> mark(U81(isNatIList(IL)))
   active(take(s(M), cons(N, IL))) -> mark(U91(isNatIList(IL), IL, M, N))

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