MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
            msort(nil()) -> nil()
        - Signature:
            {del/2,min/2,msort/1} / {./2,<=/2,=/2,if/3,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del,min,msort} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          del#(x,.(y,z)) -> c_1(del#(x,z))
          del#(x,nil()) -> c_2()
          min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
          min#(x,nil()) -> c_4()
          msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
          msort#(nil()) -> c_6()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,.(y,z)) -> c_1(del#(x,z))
            del#(x,nil()) -> c_2()
            min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
            min#(x,nil()) -> c_4()
            msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
            msort#(nil()) -> c_6()
        - Weak TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
            msort(nil()) -> nil()
        - Signature:
            {del/2,min/2,msort/1,del#/2,min#/2,msort#/1} / {./2,<=/2,=/2,if/3,nil/0,c_1/1,c_2/0,c_3/2,c_4/0,c_5/4,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,min#,msort#} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
          del(x,nil()) -> nil()
          min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
          min(x,nil()) -> x
          del#(x,.(y,z)) -> c_1(del#(x,z))
          del#(x,nil()) -> c_2()
          min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
          min#(x,nil()) -> c_4()
          msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
          msort#(nil()) -> c_6()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,.(y,z)) -> c_1(del#(x,z))
            del#(x,nil()) -> c_2()
            min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
            min#(x,nil()) -> c_4()
            msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
            msort#(nil()) -> c_6()
        - Weak TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
        - Signature:
            {del/2,min/2,msort/1,del#/2,min#/2,msort#/1} / {./2,<=/2,=/2,if/3,nil/0,c_1/1,c_2/0,c_3/2,c_4/0,c_5/4,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,min#,msort#} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,4,6}
        by application of
          Pre({2,4,6}) = {1,3,5}.
        Here rules are labelled as follows:
          1: del#(x,.(y,z)) -> c_1(del#(x,z))
          2: del#(x,nil()) -> c_2()
          3: min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
          4: min#(x,nil()) -> c_4()
          5: msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
          6: msort#(nil()) -> c_6()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,.(y,z)) -> c_1(del#(x,z))
            min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
            msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
        - Weak DPs:
            del#(x,nil()) -> c_2()
            min#(x,nil()) -> c_4()
            msort#(nil()) -> c_6()
        - Weak TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
        - Signature:
            {del/2,min/2,msort/1,del#/2,min#/2,msort#/1} / {./2,<=/2,=/2,if/3,nil/0,c_1/1,c_2/0,c_3/2,c_4/0,c_5/4,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,min#,msort#} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:del#(x,.(y,z)) -> c_1(del#(x,z))
             -->_1 del#(x,nil()) -> c_2():4
             -->_1 del#(x,.(y,z)) -> c_1(del#(x,z)):1
          
          2:S:min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
             -->_2 min#(x,nil()) -> c_4():5
             -->_1 min#(x,nil()) -> c_4():5
             -->_2 min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z)):2
             -->_1 min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z)):2
          
          3:S:msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
             -->_2 msort#(nil()) -> c_6():6
             -->_4 min#(x,nil()) -> c_4():5
             -->_1 min#(x,nil()) -> c_4():5
             -->_2 msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y)):3
             -->_4 min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z)):2
             -->_1 min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z)):2
             -->_3 del#(x,.(y,z)) -> c_1(del#(x,z)):1
          
          4:W:del#(x,nil()) -> c_2()
             
          
          5:W:min#(x,nil()) -> c_4()
             
          
          6:W:msort#(nil()) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: msort#(nil()) -> c_6()
          5: min#(x,nil()) -> c_4()
          4: del#(x,nil()) -> c_2()
* Step 5: NaturalMI MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,.(y,z)) -> c_1(del#(x,z))
            min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
            msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
        - Weak TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
        - Signature:
            {del/2,min/2,msort/1,del#/2,min#/2,msort#/1} / {./2,<=/2,=/2,if/3,nil/0,c_1/1,c_2/0,c_3/2,c_4/0,c_5/4,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,min#,msort#} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_3) = {1,2},
          uargs(c_5) = {1,2,3,4}
        
        Following symbols are considered usable:
          {del,del#,min#,msort#}
        TcT has computed the following interpretation:
               p(.) = [4]                                    
              p(<=) = [0]                                    
               p(=) = [8]                                    
             p(del) = [0]                                    
              p(if) = [0]                                    
             p(min) = [3]                                    
           p(msort) = [1]                                    
             p(nil) = [0]                                    
            p(del#) = [0]                                    
            p(min#) = [0]                                    
          p(msort#) = [1] x1 + [0]                           
             p(c_1) = [8] x1 + [0]                           
             p(c_2) = [0]                                    
             p(c_3) = [2] x1 + [2] x2 + [0]                  
             p(c_4) = [1]                                    
             p(c_5) = [2] x1 + [8] x2 + [4] x3 + [8] x4 + [0]
             p(c_6) = [1]                                    
        
        Following rules are strictly oriented:
        msort#(.(x,y)) = [4]                                                                        
                       > [0]                                                                        
                       = c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        del#(x,.(y,z)) =  [0]                       
                       >= [0]                       
                       =  c_1(del#(x,z))            
        
        min#(x,.(y,z)) =  [0]                       
                       >= [0]                       
                       =  c_3(min#(x,z),min#(y,z))  
        
         del(x,.(y,z)) =  [0]                       
                       >= [0]                       
                       =  if(=(x,y),z,.(y,del(x,z)))
        
          del(x,nil()) =  [0]                       
                       >= [0]                       
                       =  nil()                     
        
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          del#(x,.(y,z)) -> c_1(del#(x,z))
          min#(x,.(y,z)) -> c_3(min#(x,z),min#(y,z))
      - Weak DPs:
          msort#(.(x,y)) -> c_5(min#(x,y),msort#(del(min(x,y),.(x,y))),del#(min(x,y),.(x,y)),min#(x,y))
      - Weak TRS:
          del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
          del(x,nil()) -> nil()
          min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
          min(x,nil()) -> x
      - Signature:
          {del/2,min/2,msort/1,del#/2,min#/2,msort#/1} / {./2,<=/2,=/2,if/3,nil/0,c_1/1,c_2/0,c_3/2,c_4/0,c_5/4,c_6/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {del#,min#,msort#} and constructors {.,<=,=,if,nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE