MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          add0#(x,Nil()) -> c_1()
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          goal#(x,y) -> c_3(power#(x,y))
          mult#(x,Nil()) -> c_4()
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          power#(x,Nil()) -> c_6()
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x,Nil()) -> c_1()
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x,Nil()) -> c_4()
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x,Nil()) -> c_6()
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          add0(x,Nil()) -> x
          add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
          mult(x,Nil()) -> Nil()
          mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
          power(x,Nil()) -> Cons(Nil(),Nil())
          power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          add0#(x,Nil()) -> c_1()
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          goal#(x,y) -> c_3(power#(x,y))
          mult#(x,Nil()) -> c_4()
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          power#(x,Nil()) -> c_6()
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x,Nil()) -> c_1()
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x,Nil()) -> c_4()
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x,Nil()) -> c_6()
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,6}
        by application of
          Pre({1,4,6}) = {2,3,5,7}.
        Here rules are labelled as follows:
          1: add0#(x,Nil()) -> c_1()
          2: add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          3: goal#(x,y) -> c_3(power#(x,y))
          4: mult#(x,Nil()) -> c_4()
          5: mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          6: power#(x,Nil()) -> c_6()
          7: power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak DPs:
            add0#(x,Nil()) -> c_1()
            mult#(x,Nil()) -> c_4()
            power#(x,Nil()) -> c_6()
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
             -->_1 add0#(x,Nil()) -> c_1():5
             -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
          
          2:S:goal#(x,y) -> c_3(power#(x,y))
             -->_1 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
             -->_1 power#(x,Nil()) -> c_6():7
          
          3:S:mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
             -->_2 mult#(x,Nil()) -> c_4():6
             -->_1 add0#(x,Nil()) -> c_1():5
             -->_2 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
             -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
          
          4:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x,Nil()) -> c_6():7
             -->_1 mult#(x,Nil()) -> c_4():6
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
             -->_1 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
          
          5:W:add0#(x,Nil()) -> c_1()
             
          
          6:W:mult#(x,Nil()) -> c_4()
             
          
          7:W:power#(x,Nil()) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: mult#(x,Nil()) -> c_4()
          7: power#(x,Nil()) -> c_6()
          5: add0#(x,Nil()) -> c_1()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
           -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
        
        2:S:goal#(x,y) -> c_3(power#(x,y))
           -->_1 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
        
        3:S:mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
           -->_2 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
           -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
        
        4:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
           -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
           -->_1 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
        
        
        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).
        
        [(2,goal#(x,y) -> c_3(power#(x,y)))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
      - Weak TRS:
          add0(x,Nil()) -> x
          add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
          mult(x,Nil()) -> Nil()
          mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
          power(x,Nil()) -> Cons(Nil(),Nil())
          power(x',Cons(x,xs)) -> mult(x',power(x',xs))
      - Signature:
          {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
          ,c_5/2,c_6/0,c_7/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE