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