MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            goal(x,y) -> letexp(x,y)
            letexp(x,y) -> letexp(Cons(Cons(Nil(),Nil()),x),y)
        - Signature:
            {goal/2,letexp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,letexp} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          goal#(x,y) -> c_1(letexp#(x,y))
          letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x,y) -> c_1(letexp#(x,y))
            letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y))
        - Weak TRS:
            goal(x,y) -> letexp(x,y)
            letexp(x,y) -> letexp(Cons(Cons(Nil(),Nil()),x),y)
        - Signature:
            {goal/2,letexp/2,goal#/2,letexp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,letexp#} and constructors {Cons,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          goal#(x,y) -> c_1(letexp#(x,y))
          letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y))
* Step 3: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x,y) -> c_1(letexp#(x,y))
            letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y))
        - Signature:
            {goal/2,letexp/2,goal#/2,letexp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,letexp#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:goal#(x,y) -> c_1(letexp#(x,y))
           -->_1 letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y)):2
        
        2:S:letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y))
           -->_1 letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y)):2
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(1,goal#(x,y) -> c_1(letexp#(x,y)))]
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          letexp#(x,y) -> c_2(letexp#(Cons(Cons(Nil(),Nil()),x),y))
      - Signature:
          {goal/2,letexp/2,goal#/2,letexp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {goal#,letexp#} and constructors {Cons,Nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE