MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            append(l1,l2) -> ifappend(l1,l2,is_empty(l1))
            hd(cons(x,l)) -> x
            ifappend(l1,l2,false()) -> cons(hd(l1),append(tl(l1),l2))
            ifappend(l1,l2,true()) -> l2
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,hd,ifappend,is_empty,tl} and constructors {cons
            ,false,nil,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
          hd#(cons(x,l)) -> c_2()
          ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
          ifappend#(l1,l2,true()) -> c_4()
          is_empty#(cons(x,l)) -> c_5()
          is_empty#(nil()) -> c_6()
          tl#(cons(x,l)) -> c_7()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
            hd#(cons(x,l)) -> c_2()
            ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
            ifappend#(l1,l2,true()) -> c_4()
            is_empty#(cons(x,l)) -> c_5()
            is_empty#(nil()) -> c_6()
            tl#(cons(x,l)) -> c_7()
        - Weak TRS:
            append(l1,l2) -> ifappend(l1,l2,is_empty(l1))
            hd(cons(x,l)) -> x
            ifappend(l1,l2,false()) -> cons(hd(l1),append(tl(l1),l2))
            ifappend(l1,l2,true()) -> l2
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1,append#/2,hd#/1,ifappend#/3,is_empty#/1,tl#/1} / {cons/2,false/0
            ,nil/0,true/0,c_1/2,c_2/0,c_3/3,c_4/0,c_5/0,c_6/0,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append#,hd#,ifappend#,is_empty#
            ,tl#} and constructors {cons,false,nil,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          is_empty(cons(x,l)) -> false()
          is_empty(nil()) -> true()
          tl(cons(x,l)) -> l
          append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
          hd#(cons(x,l)) -> c_2()
          ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
          ifappend#(l1,l2,true()) -> c_4()
          is_empty#(cons(x,l)) -> c_5()
          is_empty#(nil()) -> c_6()
          tl#(cons(x,l)) -> c_7()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
            hd#(cons(x,l)) -> c_2()
            ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
            ifappend#(l1,l2,true()) -> c_4()
            is_empty#(cons(x,l)) -> c_5()
            is_empty#(nil()) -> c_6()
            tl#(cons(x,l)) -> c_7()
        - Weak TRS:
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1,append#/2,hd#/1,ifappend#/3,is_empty#/1,tl#/1} / {cons/2,false/0
            ,nil/0,true/0,c_1/2,c_2/0,c_3/3,c_4/0,c_5/0,c_6/0,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append#,hd#,ifappend#,is_empty#
            ,tl#} and constructors {cons,false,nil,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,4,5,6,7}
        by application of
          Pre({2,4,5,6,7}) = {1,3}.
        Here rules are labelled as follows:
          1: append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
          2: hd#(cons(x,l)) -> c_2()
          3: ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
          4: ifappend#(l1,l2,true()) -> c_4()
          5: is_empty#(cons(x,l)) -> c_5()
          6: is_empty#(nil()) -> c_6()
          7: tl#(cons(x,l)) -> c_7()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
            ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
        - Weak DPs:
            hd#(cons(x,l)) -> c_2()
            ifappend#(l1,l2,true()) -> c_4()
            is_empty#(cons(x,l)) -> c_5()
            is_empty#(nil()) -> c_6()
            tl#(cons(x,l)) -> c_7()
        - Weak TRS:
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1,append#/2,hd#/1,ifappend#/3,is_empty#/1,tl#/1} / {cons/2,false/0
            ,nil/0,true/0,c_1/2,c_2/0,c_3/3,c_4/0,c_5/0,c_6/0,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append#,hd#,ifappend#,is_empty#
            ,tl#} and constructors {cons,false,nil,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
             -->_1 ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1)):2
             -->_2 is_empty#(nil()) -> c_6():6
             -->_2 is_empty#(cons(x,l)) -> c_5():5
             -->_1 ifappend#(l1,l2,true()) -> c_4():4
          
          2:S:ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
             -->_3 tl#(cons(x,l)) -> c_7():7
             -->_1 hd#(cons(x,l)) -> c_2():3
             -->_2 append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1)):1
          
          3:W:hd#(cons(x,l)) -> c_2()
             
          
          4:W:ifappend#(l1,l2,true()) -> c_4()
             
          
          5:W:is_empty#(cons(x,l)) -> c_5()
             
          
          6:W:is_empty#(nil()) -> c_6()
             
          
          7:W:tl#(cons(x,l)) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: ifappend#(l1,l2,true()) -> c_4()
          5: is_empty#(cons(x,l)) -> c_5()
          6: is_empty#(nil()) -> c_6()
          3: hd#(cons(x,l)) -> c_2()
          7: tl#(cons(x,l)) -> c_7()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
            ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
        - Weak TRS:
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1,append#/2,hd#/1,ifappend#/3,is_empty#/1,tl#/1} / {cons/2,false/0
            ,nil/0,true/0,c_1/2,c_2/0,c_3/3,c_4/0,c_5/0,c_6/0,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append#,hd#,ifappend#,is_empty#
            ,tl#} and constructors {cons,false,nil,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1))
             -->_1 ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1)):2
          
          2:S:ifappend#(l1,l2,false()) -> c_3(hd#(l1),append#(tl(l1),l2),tl#(l1))
             -->_2 append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)),is_empty#(l1)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)))
          ifappend#(l1,l2,false()) -> c_3(append#(tl(l1),l2))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          append#(l1,l2) -> c_1(ifappend#(l1,l2,is_empty(l1)))
          ifappend#(l1,l2,false()) -> c_3(append#(tl(l1),l2))
      - Weak TRS:
          is_empty(cons(x,l)) -> false()
          is_empty(nil()) -> true()
          tl(cons(x,l)) -> l
      - Signature:
          {append/2,hd/1,ifappend/3,is_empty/1,tl/1,append#/2,hd#/1,ifappend#/3,is_empty#/1,tl#/1} / {cons/2,false/0
          ,nil/0,true/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {append#,hd#,ifappend#,is_empty#
          ,tl#} and constructors {cons,false,nil,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE