MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,from(s(X)))
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2} / {cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
          app#(nil(),YS) -> c_2()
          from#(X) -> c_3(from#(s(X)))
          prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
          zWadr#(XS,nil()) -> c_5()
          zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
          zWadr#(nil(),YS) -> c_7()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
            app#(nil(),YS) -> c_2()
            from#(X) -> c_3(from#(s(X)))
            prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
            zWadr#(XS,nil()) -> c_5()
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
            zWadr#(nil(),YS) -> c_7()
        - Weak TRS:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,from(s(X)))
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/2,nil/0,s/1,c_1/1,c_2/0,c_3/1
            ,c_4/2,c_5/0,c_6/2,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app#,from#,prefix#,zWadr#} and constructors {cons,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          app(cons(X,XS),YS) -> cons(X,app(XS,YS))
          app(nil(),YS) -> YS
          prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
          zWadr(XS,nil()) -> nil()
          zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
          zWadr(nil(),YS) -> nil()
          app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
          app#(nil(),YS) -> c_2()
          from#(X) -> c_3(from#(s(X)))
          prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
          zWadr#(XS,nil()) -> c_5()
          zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
          zWadr#(nil(),YS) -> c_7()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
            app#(nil(),YS) -> c_2()
            from#(X) -> c_3(from#(s(X)))
            prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
            zWadr#(XS,nil()) -> c_5()
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
            zWadr#(nil(),YS) -> c_7()
        - Weak TRS:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/2,nil/0,s/1,c_1/1,c_2/0,c_3/1
            ,c_4/2,c_5/0,c_6/2,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app#,from#,prefix#,zWadr#} and constructors {cons,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,5,7}
        by application of
          Pre({2,5,7}) = {1,4,6}.
        Here rules are labelled as follows:
          1: app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
          2: app#(nil(),YS) -> c_2()
          3: from#(X) -> c_3(from#(s(X)))
          4: prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
          5: zWadr#(XS,nil()) -> c_5()
          6: zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
          7: zWadr#(nil(),YS) -> c_7()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
            from#(X) -> c_3(from#(s(X)))
            prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
        - Weak DPs:
            app#(nil(),YS) -> c_2()
            zWadr#(XS,nil()) -> c_5()
            zWadr#(nil(),YS) -> c_7()
        - Weak TRS:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/2,nil/0,s/1,c_1/1,c_2/0,c_3/1
            ,c_4/2,c_5/0,c_6/2,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app#,from#,prefix#,zWadr#} and constructors {cons,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
             -->_1 app#(nil(),YS) -> c_2():5
             -->_1 app#(cons(X,XS),YS) -> c_1(app#(XS,YS)):1
          
          2:S:from#(X) -> c_3(from#(s(X)))
             -->_1 from#(X) -> c_3(from#(s(X))):2
          
          3:S:prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
             -->_1 zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS)):4
             -->_1 zWadr#(nil(),YS) -> c_7():7
             -->_1 zWadr#(XS,nil()) -> c_5():6
             -->_2 prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L)):3
          
          4:S:zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
             -->_2 zWadr#(nil(),YS) -> c_7():7
             -->_2 zWadr#(XS,nil()) -> c_5():6
             -->_1 app#(nil(),YS) -> c_2():5
             -->_2 zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS)):4
             -->_1 app#(cons(X,XS),YS) -> c_1(app#(XS,YS)):1
          
          5:W:app#(nil(),YS) -> c_2()
             
          
          6:W:zWadr#(XS,nil()) -> c_5()
             
          
          7:W:zWadr#(nil(),YS) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: zWadr#(XS,nil()) -> c_5()
          7: zWadr#(nil(),YS) -> c_7()
          5: app#(nil(),YS) -> c_2()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          app#(cons(X,XS),YS) -> c_1(app#(XS,YS))
          from#(X) -> c_3(from#(s(X)))
          prefix#(L) -> c_4(zWadr#(L,prefix(L)),prefix#(L))
          zWadr#(cons(X,XS),cons(Y,YS)) -> c_6(app#(Y,cons(X,nil())),zWadr#(XS,YS))
      - Weak TRS:
          app(cons(X,XS),YS) -> cons(X,app(XS,YS))
          app(nil(),YS) -> YS
          prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
          zWadr(XS,nil()) -> nil()
          zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
          zWadr(nil(),YS) -> nil()
      - Signature:
          {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/2,nil/0,s/1,c_1/1,c_2/0,c_3/1
          ,c_4/2,c_5/0,c_6/2,c_7/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {app#,from#,prefix#,zWadr#} and constructors {cons,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE