WORST_CASE(?,O(n^1))
* Step 1: Ara WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a__eq(X,Y) -> false()
a__eq(X1,X2) -> eq(X1,X2)
a__eq(0(),0()) -> true()
a__eq(s(X),s(Y)) -> a__eq(X,Y)
a__inf(X) -> cons(X,inf(s(X)))
a__inf(X) -> inf(X)
a__length(X) -> length(X)
a__length(cons(X,L)) -> s(length(L))
a__length(nil()) -> 0()
a__take(X1,X2) -> take(X1,X2)
a__take(0(),X) -> nil()
a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
mark(0()) -> 0()
mark(cons(X1,X2)) -> cons(X1,X2)
mark(eq(X1,X2)) -> a__eq(X1,X2)
mark(false()) -> false()
mark(inf(X)) -> a__inf(mark(X))
mark(length(X)) -> a__length(mark(X))
mark(nil()) -> nil()
mark(s(X)) -> s(X)
mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
mark(true()) -> true()
- Signature:
{a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0
,cons,eq,false,inf,length,nil,s,take,true}
+ Applied Processor:
Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
+ Details:
Signatures used:
----------------
0 :: [] -(0)-> "A"(1)
0 :: [] -(0)-> "A"(0)
0 :: [] -(0)-> "A"(15)
0 :: [] -(0)-> "A"(7)
a__eq :: ["A"(1) x "A"(0)] -(8)-> "A"(0)
a__inf :: ["A"(0)] -(8)-> "A"(0)
a__length :: ["A"(0)] -(12)-> "A"(0)
a__take :: ["A"(0) x "A"(0)] -(8)-> "A"(0)
cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
cons :: ["A"(0) x "A"(15)] -(0)-> "A"(15)
cons :: ["A"(0) x "A"(10)] -(0)-> "A"(10)
eq :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
eq :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
false :: [] -(0)-> "A"(15)
false :: [] -(0)-> "A"(7)
inf :: ["A"(15)] -(15)-> "A"(15)
inf :: ["A"(0)] -(0)-> "A"(0)
length :: ["A"(15)] -(15)-> "A"(15)
length :: ["A"(0)] -(0)-> "A"(0)
mark :: ["A"(15)] -(1)-> "A"(0)
nil :: [] -(0)-> "A"(0)
nil :: [] -(0)-> "A"(15)
nil :: [] -(0)-> "A"(7)
s :: ["A"(1)] -(1)-> "A"(1)
s :: ["A"(0)] -(0)-> "A"(0)
s :: ["A"(15)] -(15)-> "A"(15)
s :: ["A"(8)] -(8)-> "A"(8)
take :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
take :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
true :: [] -(0)-> "A"(15)
true :: [] -(0)-> "A"(7)
Cost-free Signatures used:
--------------------------
Base Constructor Signatures used:
---------------------------------
"0_A" :: [] -(0)-> "A"(1)
"cons_A" :: ["A"(0) x "A"(1)] -(0)-> "A"(1)
"eq_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
"false_A" :: [] -(0)-> "A"(1)
"inf_A" :: ["A"(1)] -(1)-> "A"(1)
"length_A" :: ["A"(1)] -(1)-> "A"(1)
"nil_A" :: [] -(0)-> "A"(1)
"s_A" :: ["A"(1)] -(1)-> "A"(1)
"take_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
"true_A" :: [] -(0)-> "A"(1)
WORST_CASE(?,O(n^1))