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)
  "comp_f_g" :: ["nat"(0) x "nat"(0)] -(0)-> "nat"(0)
  "comp_f_g#1" :: ["nat"(0) x "nat"(0)] -(1)-> "nat"(0)
  "foldr#3" :: ["list"(0)] -(1)-> "nat"(0)
  "foldr_f#3" :: ["list"(0)] -(1)-> "nat"(0)
  "id" :: [] -(0)-> "nat"(0)
  "main" :: ["list"(1)] -(1)-> "nat"(0)
  "map#2" :: ["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)
--------------------------------------


Parsed Typed Term Rewrite System:
---------------------------------

(STRATEGY
 INNERMOST)
(VAR
 "v3" "v2" "v1" "v16" "v6" "v8" "v10")
(DATATYPES
   "list" = µX.< "Nil", "Cons"("__ANY_TYPE__", X) >
   "nat" = µX.< "plus_x"(X), "comp_f_g"(X, X), "id", "0", "S"(X) >)
(SIGNATURES
   "comp_f_g#1" :: ["nat" x "nat"] --> "nat"
   "map#2" :: ["list"] --> "list"
   "plus_x#1" :: ["nat" x "nat"] --> "nat"
   "foldr_f#3" :: ["list"] --> "nat"
   "foldr#3" :: ["list"] --> "nat"
   "main" :: ["list"] --> "nat")
(RULES
 "comp_f_g#1"("plus_x"("v3"),"comp_f_g"("plus_x"("v2"),"v1")) -> "plus_x#1"("v3","comp_f_g#1"("plus_x"("v2"),"v1"))
 "comp_f_g#1"("plus_x"("v3"),"id"()) -> "plus_x#1"("v3","0"())
 "map#2"("Nil"()) -> "Nil"()
 "map#2"("Cons"("v16","v6")) -> "Cons"("plus_x"("v16"),"map#2"("v6"))
 "plus_x#1"("0"(),"v6") -> "v6"
 "plus_x#1"("S"("v8"),"v10") -> "S"("plus_x#1"("v8","v10"))
 "foldr_f#3"("Nil"()) -> "0"()
 "foldr_f#3"("Cons"("plus_x"("v2"),"v1")) -> "comp_f_g#1"("plus_x"("v2"),"foldr#3"("v1"))
 "foldr#3"("Nil"()) -> "id"()
 "foldr#3"("Cons"("plus_x"("v2"),"v1")) -> "comp_f_g"("plus_x"("v2"),"foldr#3"("v1"))
 "main"("v3") -> "foldr_f#3"("map#2"("v3")))


BEST_CASE(Omega(n^1),?)