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