BEST_CASE(Omega(n^1),?)

Solution:
---------

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


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



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

(STRATEGY
 INNERMOST)
(VAR
 "v8" "v12" "v14" "v2" "v6" "v4" "v5")
(DATATYPES
   "list" = µX.< "Nil", "Cons"("__ANY_TYPE__", X) >
   "nat" = µX.< "0", "S"(X), "plus_x"(X) >)
(SIGNATURES
   "plus_x#1" :: ["nat" x "nat"] --> "nat"
   "map#2" :: ["nat" x "list"] --> "list"
   "main" :: ["list" x "nat"] --> "list")
(RULES
 "plus_x#1"("0"(),"v8") -> "v8"
 "plus_x#1"("S"("v12"),"v14") -> "S"("plus_x#1"("v12","v14"))
 "map#2"("plus_x"("v2"),"Nil"()) -> "Nil"()
 "map#2"("plus_x"("v6"),"Cons"("v4","v2")) -> "Cons"("plus_x#1"("v6","v4"),"map#2"("plus_x"("v6"),"v2"))
 "main"("v5","v12") -> "map#2"("plus_x"("v12"),"v5"))


BEST_CASE(Omega(n^1),?)