Derivational Complexity: TRS Innermost pair #487108262

details

property	value
status	complete
benchmark	LengthOfFiniteLists_nokinds_noand_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	rcdcRelativeAlsoLower
runtime (wallclock)	295.646 seconds
cpu usage	1159.26
user time	1147.18
system time	12.0837
max virtual memory	1.917606E7
max residence set size	1.494256E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 673 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 6 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), 436 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), 120 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 151 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 154 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 130 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 144 ms]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 112 ms]
        (28) typed CpxTrs
        (29) RewriteLemmaProof [LOWER BOUND(ID), 137 ms]
        (30) typed CpxTrs
        (31) RewriteLemmaProof [LOWER BOUND(ID), 117 ms]
        (32) typed CpxTrs
        (33) RewriteLemmaProof [LOWER BOUND(ID), 189 ms]
        (34) typed CpxTrs
        (35) RewriteLemmaProof [LOWER BOUND(ID), 170 ms]
        (36) typed CpxTrs
        (37) RewriteLemmaProof [LOWER BOUND(ID), 233 ms]
        (38) 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, L, N)) -> mark(U62(isNat(N), L))
   active(U62(tt, L)) -> mark(s(length(L)))
   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(length(nil)) -> mark(0)
   active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(U11(X)) -> U11(active(X))
   active(U21(X)) -> U21(active(X))
   active(U31(X)) -> U31(active(X))
   active(U41(X1, X2)) -> U41(active(X1), X2)
   active(U42(X)) -> U42(active(X))
   active(U51(X1, X2)) -> U51(active(X1), X2)
   active(U52(X)) -> U52(active(X))
   active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
   active(U62(X1, X2)) -> U62(active(X1), X2)
   active(s(X)) -> s(active(X))
   active(length(X)) -> length(active(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   U11(mark(X)) -> mark(U11(X))
   U21(mark(X)) -> mark(U21(X))
   U31(mark(X)) -> mark(U31(X))
   U41(mark(X1), X2) -> mark(U41(X1, X2))
   U42(mark(X)) -> mark(U42(X))
   U51(mark(X1), X2) -> mark(U51(X1, X2))
   U52(mark(X)) -> mark(U52(X))
   U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3))
   U62(mark(X1), X2) -> mark(U62(X1, X2))
   s(mark(X)) -> mark(s(X))

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