*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        app(cons(X),YS) -> cons(X)
        app(nil(),YS) -> YS
        from(X) -> cons(X)
        prefix(L) -> cons(nil())
        zWadr(XS,nil()) -> nil()
        zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
        zWadr(nil(),YS) -> nil()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {app/2,from/1,prefix/1,zWadr/2} / {cons/1,nil/0}
      Obligation:
        Full
        basic terms: {app,from,prefix,zWadr}/{cons,nil}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        app(cons(X),YS) -> cons(X)
        app(nil(),YS) -> YS
        from(X) -> cons(X)
        prefix(L) -> cons(nil())
        zWadr(XS,nil()) -> nil()
        zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
        zWadr(nil(),YS) -> nil()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {app/2,from/1,prefix/1,zWadr/2} / {cons/1,nil/0}
      Obligation:
        Innermost
        basic terms: {app,from,prefix,zWadr}/{cons,nil}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following dependency tuples:
      
      Strict DPs
        app#(cons(X),YS) -> c_1()
        app#(nil(),YS) -> c_2()
        from#(X) -> c_3()
        prefix#(L) -> c_4()
        zWadr#(XS,nil()) -> c_5()
        zWadr#(cons(X),cons(Y)) -> c_6(app#(Y,cons(X)))
        zWadr#(nil(),YS) -> c_7()
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        app#(cons(X),YS) -> c_1()
        app#(nil(),YS) -> c_2()
        from#(X) -> c_3()
        prefix#(L) -> c_4()
        zWadr#(XS,nil()) -> c_5()
        zWadr#(cons(X),cons(Y)) -> c_6(app#(Y,cons(X)))
        zWadr#(nil(),YS) -> c_7()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        app(cons(X),YS) -> cons(X)
        app(nil(),YS) -> YS
        from(X) -> cons(X)
        prefix(L) -> cons(nil())
        zWadr(XS,nil()) -> nil()
        zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X)))
        zWadr(nil(),YS) -> nil()
      Signature:
        {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/1,nil/0,c_1/0,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0}
      Obligation:
        Innermost
        basic terms: {app#,from#,prefix#,zWadr#}/{cons,nil}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        app#(cons(X),YS) -> c_1()
        app#(nil(),YS) -> c_2()
        from#(X) -> c_3()
        prefix#(L) -> c_4()
        zWadr#(XS,nil()) -> c_5()
        zWadr#(cons(X),cons(Y)) -> c_6(app#(Y,cons(X)))
        zWadr#(nil(),YS) -> c_7()
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        app#(cons(X),YS) -> c_1()
        app#(nil(),YS) -> c_2()
        from#(X) -> c_3()
        prefix#(L) -> c_4()
        zWadr#(XS,nil()) -> c_5()
        zWadr#(cons(X),cons(Y)) -> c_6(app#(Y,cons(X)))
        zWadr#(nil(),YS) -> c_7()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/1,nil/0,c_1/0,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0}
      Obligation:
        Innermost
        basic terms: {app#,from#,prefix#,zWadr#}/{cons,nil}
    Applied Processor:
      Trivial
    Proof:
      Consider the dependency graph
        1:S:app#(cons(X),YS) -> c_1()
           
        
        2:S:app#(nil(),YS) -> c_2()
           
        
        3:S:from#(X) -> c_3()
           
        
        4:S:prefix#(L) -> c_4()
           
        
        5:S:zWadr#(XS,nil()) -> c_5()
           
        
        6:S:zWadr#(cons(X),cons(Y)) -> c_6(app#(Y,cons(X)))
           -->_1 app#(nil(),YS) -> c_2():2
           -->_1 app#(cons(X),YS) -> c_1():1
        
        7:S:zWadr#(nil(),YS) -> c_7()
           
        
      The dependency graph contains no loops, we remove all dependency pairs.
*** 1.1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {app/2,from/1,prefix/1,zWadr/2,app#/2,from#/1,prefix#/1,zWadr#/2} / {cons/1,nil/0,c_1/0,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0}
      Obligation:
        Innermost
        basic terms: {app#,from#,prefix#,zWadr#}/{cons,nil}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).