WORST_CASE(?,O(n^2)) Solution: --------- "Cons" :: ["__ANY_TYPE__"(0, 0) x "list"(6, 3)] -(3)-> "list"(3, 3) "Cons" :: ["__ANY_TYPE__"(0, 0) x "list"(2, 1)] -(1)-> "list"(1, 1) "Cons" :: ["__ANY_TYPE__"(0, 0) x "list"(2, 0)] -(2)-> "list"(2, 0) "Cons" :: ["__ANY_TYPE__"(0, 0) x "list"(0, 0)] -(0)-> "list"(0, 0) "Nil" :: [] -(0)-> "list"(3, 3) "Nil" :: [] -(0)-> "list"(2, 0) "Nil" :: [] -(0)-> "list"(2, 1) "Nil" :: [] -(0)-> "list"(0, 0) "append#2" :: ["list"(2, 0) x "list"(1, 1)] -(0)-> "list"(0, 0) "main" :: ["list"(3, 3)] -(2)-> "list"(0, 0) "rev#1" :: ["list"(3, 3)] -(1)-> "list"(0, 0) Cost Free Signatures: --------------------- "Cons" :: ["__ANY_TYPE__"_cf(0, 0) x "list"_cf(3, 0)] -(3)-> "list"_cf(3, 0) "Cons" :: ["__ANY_TYPE__"_cf(0, 0) x "list"_cf(0, 0)] -(0)-> "list"_cf(0, 0) "Cons" :: ["__ANY_TYPE__"_cf(0, 0) x "list"_cf(2, 0)] -(2)-> "list"_cf(2, 0) "Cons" :: ["__ANY_TYPE__"_cf(0, 0) x "list"_cf(1, 0)] -(1)-> "list"_cf(1, 0) "Nil" :: [] -(0)-> "list"_cf(3, 0) "Nil" :: [] -(0)-> "list"_cf(2, 1) "Nil" :: [] -(0)-> "list"_cf(2, 0) "Nil" :: [] -(0)-> "list"_cf(0, 0) "Nil" :: [] -(0)-> "list"_cf(1, 1) "append#2" :: ["list"_cf(2, 0) x "list"_cf(0, 0)] -(2)-> "list"_cf(2, 0) "append#2" :: ["list"_cf(0, 0) x "list"_cf(0, 0)] -(1)-> "list"_cf(0, 0) "rev#1" :: ["list"_cf(3, 0)] -(1)-> "list"_cf(2, 0) Used heuristics (no base constructurs) -------------------------------------- Parsed Typed Term Rewrite System: --------------------------------- (STRATEGY INNERMOST) (VAR "v2" "v1" "v6" "v4" "v0") (DATATYPES "list" = µX.< "Nil", "Cons"("__ANY_TYPE__", X) >) (SIGNATURES "rev#1" :: ["list"] --> "list" "append#2" :: ["list" x "list"] --> "list" "main" :: ["list"] --> "list") (RULES "rev#1"("Nil"()) -> "Nil"() "rev#1"("Cons"("v2","v1")) -> "append#2"("rev#1"("v1"),"Cons"("v2","Nil"())) "append#2"("Nil"(),"Cons"("v2","Nil"())) -> "Cons"("v2","Nil"()) "append#2"("Cons"("v6","v4"),"Cons"("v2","Nil"())) -> "Cons"("v6","append#2"("v4","Cons"("v2","Nil"()))) "main"("v0") -> "rev#1"("v0")) WORST_CASE(?,O(n^2))