MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
            bsort(nil()) -> nil()
            bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
            bubble(.(x,nil())) -> .(x,nil())
            bubble(nil()) -> nil()
            butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
            butlast(.(x,nil())) -> nil()
            butlast(nil()) -> nil()
            last(.(x,.(y,z))) -> last(.(y,z))
            last(.(x,nil())) -> x
            last(nil()) -> 0()
        - Signature:
            {bsort/1,bubble/1,butlast/1,last/1} / {./2,0/0,<=/2,if/3,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {bsort,bubble,butlast,last} and constructors {.,0,<=,if
            ,nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                               ,bubble#(.(x,y))
                               ,bsort#(butlast(bubble(.(x,y))))
                               ,butlast#(bubble(.(x,y)))
                               ,bubble#(.(x,y)))
          bsort#(nil()) -> c_2()
          bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
          bubble#(.(x,nil())) -> c_4()
          bubble#(nil()) -> c_5()
          butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
          butlast#(.(x,nil())) -> c_7()
          butlast#(nil()) -> c_8()
          last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
          last#(.(x,nil())) -> c_10()
          last#(nil()) -> c_11()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                                 ,bubble#(.(x,y))
                                 ,bsort#(butlast(bubble(.(x,y))))
                                 ,butlast#(bubble(.(x,y)))
                                 ,bubble#(.(x,y)))
            bsort#(nil()) -> c_2()
            bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
            bubble#(.(x,nil())) -> c_4()
            bubble#(nil()) -> c_5()
            butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
            butlast#(.(x,nil())) -> c_7()
            butlast#(nil()) -> c_8()
            last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
            last#(.(x,nil())) -> c_10()
            last#(nil()) -> c_11()
        - Weak TRS:
            bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
            bsort(nil()) -> nil()
            bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
            bubble(.(x,nil())) -> .(x,nil())
            bubble(nil()) -> nil()
            butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
            butlast(.(x,nil())) -> nil()
            butlast(nil()) -> nil()
            last(.(x,.(y,z))) -> last(.(y,z))
            last(.(x,nil())) -> x
            last(nil()) -> 0()
        - Signature:
            {bsort/1,bubble/1,butlast/1,last/1,bsort#/1,bubble#/1,butlast#/1,last#/1} / {./2,0/0,<=/2,if/3,nil/0,c_1/5
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {bsort#,bubble#,butlast#,last#} and constructors {.,0,<=
            ,if,nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
          bsort(nil()) -> nil()
          bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
          bubble(.(x,nil())) -> .(x,nil())
          butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
          butlast(.(x,nil())) -> nil()
          butlast(nil()) -> nil()
          last(.(x,.(y,z))) -> last(.(y,z))
          last(.(x,nil())) -> x
          bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                               ,bubble#(.(x,y))
                               ,bsort#(butlast(bubble(.(x,y))))
                               ,butlast#(bubble(.(x,y)))
                               ,bubble#(.(x,y)))
          bsort#(nil()) -> c_2()
          bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
          bubble#(.(x,nil())) -> c_4()
          bubble#(nil()) -> c_5()
          butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
          butlast#(.(x,nil())) -> c_7()
          butlast#(nil()) -> c_8()
          last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
          last#(.(x,nil())) -> c_10()
          last#(nil()) -> c_11()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                                 ,bubble#(.(x,y))
                                 ,bsort#(butlast(bubble(.(x,y))))
                                 ,butlast#(bubble(.(x,y)))
                                 ,bubble#(.(x,y)))
            bsort#(nil()) -> c_2()
            bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
            bubble#(.(x,nil())) -> c_4()
            bubble#(nil()) -> c_5()
            butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
            butlast#(.(x,nil())) -> c_7()
            butlast#(nil()) -> c_8()
            last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
            last#(.(x,nil())) -> c_10()
            last#(nil()) -> c_11()
        - Weak TRS:
            bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
            bsort(nil()) -> nil()
            bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
            bubble(.(x,nil())) -> .(x,nil())
            butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
            butlast(.(x,nil())) -> nil()
            butlast(nil()) -> nil()
            last(.(x,.(y,z))) -> last(.(y,z))
            last(.(x,nil())) -> x
        - Signature:
            {bsort/1,bubble/1,butlast/1,last/1,bsort#/1,bubble#/1,butlast#/1,last#/1} / {./2,0/0,<=/2,if/3,nil/0,c_1/5
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {bsort#,bubble#,butlast#,last#} and constructors {.,0,<=
            ,if,nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,4,5,7,8,10,11}
        by application of
          Pre({2,4,5,7,8,10,11}) = {1,3,6,9}.
        Here rules are labelled as follows:
          1: bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                                  ,bubble#(.(x,y))
                                  ,bsort#(butlast(bubble(.(x,y))))
                                  ,butlast#(bubble(.(x,y)))
                                  ,bubble#(.(x,y)))
          2: bsort#(nil()) -> c_2()
          3: bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
          4: bubble#(.(x,nil())) -> c_4()
          5: bubble#(nil()) -> c_5()
          6: butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
          7: butlast#(.(x,nil())) -> c_7()
          8: butlast#(nil()) -> c_8()
          9: last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
          10: last#(.(x,nil())) -> c_10()
          11: last#(nil()) -> c_11()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                                 ,bubble#(.(x,y))
                                 ,bsort#(butlast(bubble(.(x,y))))
                                 ,butlast#(bubble(.(x,y)))
                                 ,bubble#(.(x,y)))
            bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
            butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
            last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
        - Weak DPs:
            bsort#(nil()) -> c_2()
            bubble#(.(x,nil())) -> c_4()
            bubble#(nil()) -> c_5()
            butlast#(.(x,nil())) -> c_7()
            butlast#(nil()) -> c_8()
            last#(.(x,nil())) -> c_10()
            last#(nil()) -> c_11()
        - Weak TRS:
            bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
            bsort(nil()) -> nil()
            bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
            bubble(.(x,nil())) -> .(x,nil())
            butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
            butlast(.(x,nil())) -> nil()
            butlast(nil()) -> nil()
            last(.(x,.(y,z))) -> last(.(y,z))
            last(.(x,nil())) -> x
        - Signature:
            {bsort/1,bubble/1,butlast/1,last/1,bsort#/1,bubble#/1,butlast#/1,last#/1} / {./2,0/0,<=/2,if/3,nil/0,c_1/5
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {bsort#,bubble#,butlast#,last#} and constructors {.,0,<=
            ,if,nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                                   ,bubble#(.(x,y))
                                   ,bsort#(butlast(bubble(.(x,y))))
                                   ,butlast#(bubble(.(x,y)))
                                   ,bubble#(.(x,y)))
             -->_1 last#(.(x,.(y,z))) -> c_9(last#(.(y,z))):4
             -->_4 butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z))):3
             -->_5 bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z))):2
             -->_2 bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z))):2
             -->_1 last#(.(x,nil())) -> c_10():10
             -->_4 butlast#(nil()) -> c_8():9
             -->_4 butlast#(.(x,nil())) -> c_7():8
             -->_5 bubble#(.(x,nil())) -> c_4():6
             -->_2 bubble#(.(x,nil())) -> c_4():6
             -->_3 bsort#(nil()) -> c_2():5
             -->_3 bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                                        ,bubble#(.(x,y))
                                        ,bsort#(butlast(bubble(.(x,y))))
                                        ,butlast#(bubble(.(x,y)))
                                        ,bubble#(.(x,y))):1
          
          2:S:bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
             -->_2 bubble#(.(x,nil())) -> c_4():6
             -->_1 bubble#(.(x,nil())) -> c_4():6
             -->_2 bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z))):2
             -->_1 bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z))):2
          
          3:S:butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
             -->_1 butlast#(.(x,nil())) -> c_7():8
             -->_1 butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z))):3
          
          4:S:last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
             -->_1 last#(.(x,nil())) -> c_10():10
             -->_1 last#(.(x,.(y,z))) -> c_9(last#(.(y,z))):4
          
          5:W:bsort#(nil()) -> c_2()
             
          
          6:W:bubble#(.(x,nil())) -> c_4()
             
          
          7:W:bubble#(nil()) -> c_5()
             
          
          8:W:butlast#(.(x,nil())) -> c_7()
             
          
          9:W:butlast#(nil()) -> c_8()
             
          
          10:W:last#(.(x,nil())) -> c_10()
             
          
          11:W:last#(nil()) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          11: last#(nil()) -> c_11()
          7: bubble#(nil()) -> c_5()
          5: bsort#(nil()) -> c_2()
          9: butlast#(nil()) -> c_8()
          6: bubble#(.(x,nil())) -> c_4()
          8: butlast#(.(x,nil())) -> c_7()
          10: last#(.(x,nil())) -> c_10()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          bsort#(.(x,y)) -> c_1(last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
                               ,bubble#(.(x,y))
                               ,bsort#(butlast(bubble(.(x,y))))
                               ,butlast#(bubble(.(x,y)))
                               ,bubble#(.(x,y)))
          bubble#(.(x,.(y,z))) -> c_3(bubble#(.(x,z)),bubble#(.(y,z)))
          butlast#(.(x,.(y,z))) -> c_6(butlast#(.(y,z)))
          last#(.(x,.(y,z))) -> c_9(last#(.(y,z)))
      - Weak TRS:
          bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
          bsort(nil()) -> nil()
          bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
          bubble(.(x,nil())) -> .(x,nil())
          butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
          butlast(.(x,nil())) -> nil()
          butlast(nil()) -> nil()
          last(.(x,.(y,z))) -> last(.(y,z))
          last(.(x,nil())) -> x
      - Signature:
          {bsort/1,bubble/1,butlast/1,last/1,bsort#/1,bubble#/1,butlast#/1,last#/1} / {./2,0/0,<=/2,if/3,nil/0,c_1/5
          ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {bsort#,bubble#,butlast#,last#} and constructors {.,0,<=
          ,if,nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE