MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            check(free(x)) -> free(check(x))
            check(new(x)) -> new(check(x))
            check(old(x)) -> old(x)
            check(old(x)) -> old(check(x))
            new(free(x)) -> free(new(x))
            new(serve()) -> free(serve())
            old(free(x)) -> free(old(x))
            old(serve()) -> free(serve())
            top(free(x)) -> top(check(new(x)))
        - Signature:
            {check/1,new/1,old/1,top/1} / {free/1,serve/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {check,new,old,top} and constructors {free,serve}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          check#(free(x)) -> c_1(check#(x))
          check#(new(x)) -> c_2(new#(check(x)),check#(x))
          check#(old(x)) -> c_3(old#(x))
          check#(old(x)) -> c_4(old#(check(x)),check#(x))
          new#(free(x)) -> c_5(new#(x))
          new#(serve()) -> c_6()
          old#(free(x)) -> c_7(old#(x))
          old#(serve()) -> c_8()
          top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            check#(free(x)) -> c_1(check#(x))
            check#(new(x)) -> c_2(new#(check(x)),check#(x))
            check#(old(x)) -> c_3(old#(x))
            check#(old(x)) -> c_4(old#(check(x)),check#(x))
            new#(free(x)) -> c_5(new#(x))
            new#(serve()) -> c_6()
            old#(free(x)) -> c_7(old#(x))
            old#(serve()) -> c_8()
            top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
        - Weak TRS:
            check(free(x)) -> free(check(x))
            check(new(x)) -> new(check(x))
            check(old(x)) -> old(x)
            check(old(x)) -> old(check(x))
            new(free(x)) -> free(new(x))
            new(serve()) -> free(serve())
            old(free(x)) -> free(old(x))
            old(serve()) -> free(serve())
            top(free(x)) -> top(check(new(x)))
        - Signature:
            {check/1,new/1,old/1,top/1,check#/1,new#/1,old#/1,top#/1} / {free/1,serve/0,c_1/1,c_2/2,c_3/1,c_4/2,c_5/1
            ,c_6/0,c_7/1,c_8/0,c_9/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {check#,new#,old#,top#} and constructors {free,serve}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          check(free(x)) -> free(check(x))
          check(new(x)) -> new(check(x))
          check(old(x)) -> old(x)
          check(old(x)) -> old(check(x))
          new(free(x)) -> free(new(x))
          new(serve()) -> free(serve())
          old(free(x)) -> free(old(x))
          old(serve()) -> free(serve())
          check#(free(x)) -> c_1(check#(x))
          check#(new(x)) -> c_2(new#(check(x)),check#(x))
          check#(old(x)) -> c_3(old#(x))
          check#(old(x)) -> c_4(old#(check(x)),check#(x))
          new#(free(x)) -> c_5(new#(x))
          new#(serve()) -> c_6()
          old#(free(x)) -> c_7(old#(x))
          old#(serve()) -> c_8()
          top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            check#(free(x)) -> c_1(check#(x))
            check#(new(x)) -> c_2(new#(check(x)),check#(x))
            check#(old(x)) -> c_3(old#(x))
            check#(old(x)) -> c_4(old#(check(x)),check#(x))
            new#(free(x)) -> c_5(new#(x))
            new#(serve()) -> c_6()
            old#(free(x)) -> c_7(old#(x))
            old#(serve()) -> c_8()
            top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
        - Weak TRS:
            check(free(x)) -> free(check(x))
            check(new(x)) -> new(check(x))
            check(old(x)) -> old(x)
            check(old(x)) -> old(check(x))
            new(free(x)) -> free(new(x))
            new(serve()) -> free(serve())
            old(free(x)) -> free(old(x))
            old(serve()) -> free(serve())
        - Signature:
            {check/1,new/1,old/1,top/1,check#/1,new#/1,old#/1,top#/1} / {free/1,serve/0,c_1/1,c_2/2,c_3/1,c_4/2,c_5/1
            ,c_6/0,c_7/1,c_8/0,c_9/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {check#,new#,old#,top#} and constructors {free,serve}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {6,8}
        by application of
          Pre({6,8}) = {2,3,4,5,7,9}.
        Here rules are labelled as follows:
          1: check#(free(x)) -> c_1(check#(x))
          2: check#(new(x)) -> c_2(new#(check(x)),check#(x))
          3: check#(old(x)) -> c_3(old#(x))
          4: check#(old(x)) -> c_4(old#(check(x)),check#(x))
          5: new#(free(x)) -> c_5(new#(x))
          6: new#(serve()) -> c_6()
          7: old#(free(x)) -> c_7(old#(x))
          8: old#(serve()) -> c_8()
          9: top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            check#(free(x)) -> c_1(check#(x))
            check#(new(x)) -> c_2(new#(check(x)),check#(x))
            check#(old(x)) -> c_3(old#(x))
            check#(old(x)) -> c_4(old#(check(x)),check#(x))
            new#(free(x)) -> c_5(new#(x))
            old#(free(x)) -> c_7(old#(x))
            top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
        - Weak DPs:
            new#(serve()) -> c_6()
            old#(serve()) -> c_8()
        - Weak TRS:
            check(free(x)) -> free(check(x))
            check(new(x)) -> new(check(x))
            check(old(x)) -> old(x)
            check(old(x)) -> old(check(x))
            new(free(x)) -> free(new(x))
            new(serve()) -> free(serve())
            old(free(x)) -> free(old(x))
            old(serve()) -> free(serve())
        - Signature:
            {check/1,new/1,old/1,top/1,check#/1,new#/1,old#/1,top#/1} / {free/1,serve/0,c_1/1,c_2/2,c_3/1,c_4/2,c_5/1
            ,c_6/0,c_7/1,c_8/0,c_9/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {check#,new#,old#,top#} and constructors {free,serve}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:check#(free(x)) -> c_1(check#(x))
             -->_1 check#(old(x)) -> c_4(old#(check(x)),check#(x)):4
             -->_1 check#(old(x)) -> c_3(old#(x)):3
             -->_1 check#(new(x)) -> c_2(new#(check(x)),check#(x)):2
             -->_1 check#(free(x)) -> c_1(check#(x)):1
          
          2:S:check#(new(x)) -> c_2(new#(check(x)),check#(x))
             -->_1 new#(free(x)) -> c_5(new#(x)):5
             -->_2 check#(old(x)) -> c_4(old#(check(x)),check#(x)):4
             -->_2 check#(old(x)) -> c_3(old#(x)):3
             -->_1 new#(serve()) -> c_6():8
             -->_2 check#(new(x)) -> c_2(new#(check(x)),check#(x)):2
             -->_2 check#(free(x)) -> c_1(check#(x)):1
          
          3:S:check#(old(x)) -> c_3(old#(x))
             -->_1 old#(free(x)) -> c_7(old#(x)):6
             -->_1 old#(serve()) -> c_8():9
          
          4:S:check#(old(x)) -> c_4(old#(check(x)),check#(x))
             -->_1 old#(free(x)) -> c_7(old#(x)):6
             -->_1 old#(serve()) -> c_8():9
             -->_2 check#(old(x)) -> c_4(old#(check(x)),check#(x)):4
             -->_2 check#(old(x)) -> c_3(old#(x)):3
             -->_2 check#(new(x)) -> c_2(new#(check(x)),check#(x)):2
             -->_2 check#(free(x)) -> c_1(check#(x)):1
          
          5:S:new#(free(x)) -> c_5(new#(x))
             -->_1 new#(serve()) -> c_6():8
             -->_1 new#(free(x)) -> c_5(new#(x)):5
          
          6:S:old#(free(x)) -> c_7(old#(x))
             -->_1 old#(serve()) -> c_8():9
             -->_1 old#(free(x)) -> c_7(old#(x)):6
          
          7:S:top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
             -->_3 new#(serve()) -> c_6():8
             -->_1 top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x)):7
             -->_3 new#(free(x)) -> c_5(new#(x)):5
             -->_2 check#(old(x)) -> c_4(old#(check(x)),check#(x)):4
             -->_2 check#(old(x)) -> c_3(old#(x)):3
             -->_2 check#(new(x)) -> c_2(new#(check(x)),check#(x)):2
             -->_2 check#(free(x)) -> c_1(check#(x)):1
          
          8:W:new#(serve()) -> c_6()
             
          
          9:W:old#(serve()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: new#(serve()) -> c_6()
          9: old#(serve()) -> c_8()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          check#(free(x)) -> c_1(check#(x))
          check#(new(x)) -> c_2(new#(check(x)),check#(x))
          check#(old(x)) -> c_3(old#(x))
          check#(old(x)) -> c_4(old#(check(x)),check#(x))
          new#(free(x)) -> c_5(new#(x))
          old#(free(x)) -> c_7(old#(x))
          top#(free(x)) -> c_9(top#(check(new(x))),check#(new(x)),new#(x))
      - Weak TRS:
          check(free(x)) -> free(check(x))
          check(new(x)) -> new(check(x))
          check(old(x)) -> old(x)
          check(old(x)) -> old(check(x))
          new(free(x)) -> free(new(x))
          new(serve()) -> free(serve())
          old(free(x)) -> free(old(x))
          old(serve()) -> free(serve())
      - Signature:
          {check/1,new/1,old/1,top/1,check#/1,new#/1,old#/1,top#/1} / {free/1,serve/0,c_1/1,c_2/2,c_3/1,c_4/2,c_5/1
          ,c_6/0,c_7/1,c_8/0,c_9/3}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {check#,new#,old#,top#} and constructors {free,serve}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE