MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            r(xs,ys,zs,nil()) -> xs
            r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
            r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
            r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
        - Signature:
            {r/4} / {cons/2,nil/0,succ/1,zero/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          r#(xs,ys,zs,nil()) -> c_1()
          r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
          r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
          r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            r#(xs,ys,zs,nil()) -> c_1()
            r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
            r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
            r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
        - Strict TRS:
            r(xs,ys,zs,nil()) -> xs
            r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
            r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
            r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
        - Signature:
            {r/4,r#/4} / {cons/2,nil/0,succ/1,zero/0,c_1/0,c_2/1,c_3/1,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r#} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          r#(xs,ys,zs,nil()) -> c_1()
          r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
          r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
          r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            r#(xs,ys,zs,nil()) -> c_1()
            r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
            r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
            r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
        - Signature:
            {r/4,r#/4} / {cons/2,nil/0,succ/1,zero/0,c_1/0,c_2/1,c_3/1,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r#} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {3,4}.
        Here rules are labelled as follows:
          1: r#(xs,ys,zs,nil()) -> c_1()
          2: r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
          3: r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
          4: r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
            r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
            r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
        - Weak DPs:
            r#(xs,ys,zs,nil()) -> c_1()
        - Signature:
            {r/4,r#/4} / {cons/2,nil/0,succ/1,zero/0,c_1/0,c_2/1,c_3/1,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r#} and constructors {cons,nil,succ,zero}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
             -->_1 r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws)):2
             -->_1 r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))):1
          
          2:S:r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
             -->_1 r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws)):3
             -->_1 r#(xs,ys,zs,nil()) -> c_1():4
             -->_1 r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))):1
          
          3:S:r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
             -->_1 r#(xs,ys,zs,nil()) -> c_1():4
             -->_1 r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws)):3
             -->_1 r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))):1
          
          4:W:r#(xs,ys,zs,nil()) -> c_1()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: r#(xs,ys,zs,nil()) -> c_1()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          r#(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> c_2(r#(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))))
          r#(xs,cons(y,ys),nil(),cons(w,ws)) -> c_3(r#(xs,xs,cons(succ(zero()),nil()),ws))
          r#(xs,nil(),zs,cons(w,ws)) -> c_4(r#(xs,xs,cons(succ(zero()),zs),ws))
      - Signature:
          {r/4,r#/4} / {cons/2,nil/0,succ/1,zero/0,c_1/0,c_2/1,c_3/1,c_4/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {r#} and constructors {cons,nil,succ,zero}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE