BEST_CASE(Omega(n^1),?)

Solution:
---------

  "0" :: [] -(0)-> "nat"(1)
  "0" :: [] -(0)-> "nat"(0)
  "Cons" :: ["__ANY_TYPE__"(0) x "list"(0)] -(0)-> "list"(0)
  "Nil" :: [] -(0)-> "list"(0)
  "S" :: ["nat"(1)] -(1)-> "nat"(1)
  "S" :: ["nat"(0)] -(0)-> "nat"(0)
  "main" :: ["nat"(1)] -(1)-> "nat"(0)
  "map#2" :: ["list"(0)] -(1)-> "list"(0)
  "mult#2" :: ["nat"(0) x "nat"(0)] -(1)-> "nat"(0)
  "plus#2" :: ["nat"(0) x "nat"(0)] -(1)-> "nat"(0)
  "sum#1" :: ["list"(0)] -(1)-> "nat"(0)
  "unfoldr#2" :: ["nat"(1)] -(1)-> "list"(0)


Cost Free Signatures:
---------------------



Used heuristics (no base constructurs)
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Parsed Typed Term Rewrite System:
---------------------------------

(STRATEGY
 INNERMOST)
(VAR
 "v2" "v1" "v5" "v4" "v8")
(DATATYPES
   "list" = µX.< "Nil", "Cons"("__ANY_TYPE__", X) >
   "nat" = µX.< "0", "S"(X) >)
(SIGNATURES
   "sum#1" :: ["list"] --> "nat"
   "map#2" :: ["list"] --> "list"
   "unfoldr#2" :: ["nat"] --> "list"
   "mult#2" :: ["nat" x "nat"] --> "nat"
   "plus#2" :: ["nat" x "nat"] --> "nat"
   "main" :: ["nat"] --> "nat")
(RULES
 "sum#1"("Nil"()) -> "0"()
 "sum#1"("Cons"("v2","v1")) -> "plus#2"("v2","sum#1"("v1"))
 "map#2"("Nil"()) -> "Nil"()
 "map#2"("Cons"("v2","v5")) -> "Cons"("mult#2"("v2","v2"),"map#2"("v5"))
 "unfoldr#2"("0"()) -> "Nil"()
 "unfoldr#2"("S"("v2")) -> "Cons"("v2","unfoldr#2"("v2"))
 "mult#2"("0"(),"v2") -> "0"()
 "mult#2"("S"("v4"),"v2") -> "plus#2"("v2","mult#2"("v4","v2"))
 "plus#2"("0"(),"v8") -> "v8"
 "plus#2"("S"("v4"),"v2") -> "S"("plus#2"("v4","v2"))
 "main"("0"()) -> "0"()
 "main"("S"("v1")) -> "sum#1"("map#2"("Cons"("S"("v1"),"unfoldr#2"("S"("v1"))))))


BEST_CASE(Omega(n^1),?)