Runtime Complexity: TRS pair #487110176

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	n143.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	293.165 seconds
cpu usage	1146.44
user time	1131.76
system time	14.6749
max virtual memory	3.8447084E7
max residence set size	1.5028052E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 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), 10 ms]
(6) typed CpxTrs
(7) RewriteLemmaProof [LOWER BOUND(ID), 454 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), 120 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 88 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 61 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 102 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 109 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 82 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 186 ms]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 252 ms]
        (28) typed CpxTrs
        (29) RewriteLemmaProof [LOWER BOUND(ID), 125 ms]
        (30) typed CpxTrs
        (31) RewriteLemmaProof [LOWER BOUND(ID), 82 ms]
        (32) typed CpxTrs
        (33) RewriteLemmaProof [LOWER BOUND(ID), 108 ms]
        (34) typed CpxTrs
        (35) RewriteLemmaProof [LOWER BOUND(ID), 103 ms]
        (36) typed CpxTrs
        (37) RewriteLemmaProof [LOWER BOUND(ID), 145 ms]
        (38) typed CpxTrs
        (39) RewriteLemmaProof [LOWER BOUND(ID), 134 ms]
        (40) typed CpxTrs
        (41) RewriteLemmaProof [LOWER BOUND(ID), 157 ms]
        (42) typed CpxTrs
        (43) RewriteLemmaProof [LOWER BOUND(ID), 165 ms]
        (44) typed CpxTrs
        (45) RewriteLemmaProof [LOWER BOUND(ID), 114 ms]
        (46) typed CpxTrs
        (47) RewriteLemmaProof [LOWER BOUND(ID), 240 ms]
        (48) typed CpxTrs


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

(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)) -> 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))
   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))

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