/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 app(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   false ==> false0/0
   true ==> true0/0
   filter2 ==> filter20/0 filter21/1 filter22/2 filter23/3 filter24/4
   filter ==> filter0/0 filter1/1 filter2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   + ==> +0/0 +1/1 +2/2
   * ==> *0/0 *1/1 *2/2
   
  uncurry-rules:
   app(*1(x5),x6) -> *2(x5,x6)
   app(*0(),x5) -> *1(x5)
   app(+1(x8),x9) -> +2(x8,x9)
   app(+0(),x8) -> +1(x8)
   app(map1(x11),x12) -> map2(x11,x12)
   app(map0(),x11) -> map1(x11)
   app(cons1(x15),x16) -> cons2(x15,x16)
   app(cons0(),x15) -> cons1(x15)
   app(filter1(x18),x19) -> filter2(x18,x19)
   app(filter0(),x18) -> filter1(x18)
   app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
   app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
   app(filter21(x21),x22) -> filter22(x21,x22)
   app(filter20(),x21) -> filter21(x21)
  eta-rules:
   
  problem:
   *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   filter2(f,nil0()) -> nil0()
   filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
   filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
   filter24(false0(),f,x,xs) -> filter2(f,xs)
   app(*1(x5),x6) -> *2(x5,x6)
   app(*0(),x5) -> *1(x5)
   app(+1(x8),x9) -> +2(x8,x9)
   app(+0(),x8) -> +1(x8)
   app(map1(x11),x12) -> map2(x11,x12)
   app(map0(),x11) -> map1(x11)
   app(cons1(x15),x16) -> cons2(x15,x16)
   app(cons0(),x15) -> cons1(x15)
   app(filter1(x18),x19) -> filter2(x18,x19)
   app(filter0(),x18) -> filter1(x18)
   app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
   app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
   app(filter21(x21),x22) -> filter22(x21,x22)
   app(filter20(),x21) -> filter21(x21)
  DP Processor:
   DPs:
    *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
    *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
    filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
    filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
    app#(*1(x5),x6) -> *{2,#}(x5,x6)
    app#(map1(x11),x12) -> map{2,#}(x11,x12)
    app#(filter1(x18),x19) -> filter{2,#}(x18,x19)
    app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24)
   TRS:
    *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    filter2(f,nil0()) -> nil0()
    filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
    filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
    filter24(false0(),f,x,xs) -> filter2(f,xs)
    app(*1(x5),x6) -> *2(x5,x6)
    app(*0(),x5) -> *1(x5)
    app(+1(x8),x9) -> +2(x8,x9)
    app(+0(),x8) -> +1(x8)
    app(map1(x11),x12) -> map2(x11,x12)
    app(map0(),x11) -> map1(x11)
    app(cons1(x15),x16) -> cons2(x15,x16)
    app(cons0(),x15) -> cons1(x15)
    app(filter1(x18),x19) -> filter2(x18,x19)
    app(filter0(),x18) -> filter1(x18)
    app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
    app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
    app(filter21(x21),x22) -> filter22(x21,x22)
    app(filter20(),x21) -> filter21(x21)
   TDG Processor:
    DPs:
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(*1(x5),x6) -> *{2,#}(x5,x6)
     app#(map1(x11),x12) -> map{2,#}(x11,x12)
     app#(filter1(x18),x19) -> filter{2,#}(x18,x19)
     app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24)
    TRS:
     *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     filter2(f,nil0()) -> nil0()
     filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
     filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
     filter24(false0(),f,x,xs) -> filter2(f,xs)
     app(*1(x5),x6) -> *2(x5,x6)
     app(*0(),x5) -> *1(x5)
     app(+1(x8),x9) -> +2(x8,x9)
     app(+0(),x8) -> +1(x8)
     app(map1(x11),x12) -> map2(x11,x12)
     app(map0(),x11) -> map1(x11)
     app(cons1(x15),x16) -> cons2(x15,x16)
     app(cons0(),x15) -> cons1(x15)
     app(filter1(x18),x19) -> filter2(x18,x19)
     app(filter0(),x18) -> filter1(x18)
     app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
     app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
     app(filter21(x21),x22) -> filter22(x21,x22)
     app(filter20(),x21) -> filter21(x21)
    graph:
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) ->
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) ->
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x18),x19) -> filter{2,#}(x18,x19)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x11),x12) -> map{2,#}(x11,x12)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(*1(x5),x6) -> *{2,#}(x5,x6)
     app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24) ->
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24) ->
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x18),x19) -> filter{2,#}(x18,x19) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x18),x19) -> filter{2,#}(x18,x19) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x11),x12) -> map{2,#}(x11,x12) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x11),x12) -> map{2,#}(x11,x12) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(*1(x5),x6) -> *{2,#}(x5,x6) ->
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
     app#(*1(x5),x6) -> *{2,#}(x5,x6) ->
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x18),x19) -> filter{2,#}(x18,x19)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x11),x12) -> map{2,#}(x11,x12)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(*1(x5),x6) -> *{2,#}(x5,x6)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,z) ->
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,z) ->
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,y) ->
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
     *{2,#}(x,+2(y,z)) -> *{2,#}(x,y) -> *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
    SCC Processor:
     #sccs: 2
     #rules: 11
     #arcs: 28/144
     DPs:
      filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x11),x12) -> map{2,#}(x11,x12)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x18),x19) -> filter{2,#}(x18,x19)
      filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
      filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
      app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24)
     TRS:
      *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil0()) -> nil0()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false0(),f,x,xs) -> filter2(f,xs)
      app(*1(x5),x6) -> *2(x5,x6)
      app(*0(),x5) -> *1(x5)
      app(+1(x8),x9) -> +2(x8,x9)
      app(+0(),x8) -> +1(x8)
      app(map1(x11),x12) -> map2(x11,x12)
      app(map0(),x11) -> map1(x11)
      app(cons1(x15),x16) -> cons2(x15,x16)
      app(cons0(),x15) -> cons1(x15)
      app(filter1(x18),x19) -> filter2(x18,x19)
      app(filter0(),x18) -> filter1(x18)
      app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
      app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
      app(filter21(x21),x22) -> filter22(x21,x22)
      app(filter20(),x21) -> filter21(x21)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 0
       pi(app#) = 0
       pi(filter{2,#}) = 0
       pi(filter2{4,#}) = 1
      problem:
       DPs:
        filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
        filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
        map{2,#}(f,cons2(x,xs)) -> app#(f,x)
        filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
        filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
       TRS:
        *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false0(),f,x,xs) -> filter2(f,xs)
        app(*1(x5),x6) -> *2(x5,x6)
        app(*0(),x5) -> *1(x5)
        app(+1(x8),x9) -> +2(x8,x9)
        app(+0(),x8) -> +1(x8)
        app(map1(x11),x12) -> map2(x11,x12)
        app(map0(),x11) -> map1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(filter1(x18),x19) -> filter2(x18,x19)
        app(filter0(),x18) -> filter1(x18)
        app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
        app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
        app(filter21(x21),x22) -> filter22(x21,x22)
        app(filter20(),x21) -> filter21(x21)
      SCC Processor:
       #sccs: 2
       #rules: 4
       #arcs: 20/36
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
       TRS:
        *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false0(),f,x,xs) -> filter2(f,xs)
        app(*1(x5),x6) -> *2(x5,x6)
        app(*0(),x5) -> *1(x5)
        app(+1(x8),x9) -> +2(x8,x9)
        app(+0(),x8) -> +1(x8)
        app(map1(x11),x12) -> map2(x11,x12)
        app(map0(),x11) -> map1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(filter1(x18),x19) -> filter2(x18,x19)
        app(filter0(),x18) -> filter1(x18)
        app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
        app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
        app(filter21(x21),x22) -> filter22(x21,x22)
        app(filter20(),x21) -> filter21(x21)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
          map2(f,nil0()) -> nil0()
          map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
          filter2(f,nil0()) -> nil0()
          filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
          filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
          filter24(false0(),f,x,xs) -> filter2(f,xs)
          app(*1(x5),x6) -> *2(x5,x6)
          app(*0(),x5) -> *1(x5)
          app(+1(x8),x9) -> +2(x8,x9)
          app(+0(),x8) -> +1(x8)
          app(map1(x11),x12) -> map2(x11,x12)
          app(map0(),x11) -> map1(x11)
          app(cons1(x15),x16) -> cons2(x15,x16)
          app(cons0(),x15) -> cons1(x15)
          app(filter1(x18),x19) -> filter2(x18,x19)
          app(filter0(),x18) -> filter1(x18)
          app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
          app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
          app(filter21(x21),x22) -> filter22(x21,x22)
          app(filter20(),x21) -> filter21(x21)
        Qed
       
       DPs:
        filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
        filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
        filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
       TRS:
        *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false0(),f,x,xs) -> filter2(f,xs)
        app(*1(x5),x6) -> *2(x5,x6)
        app(*0(),x5) -> *1(x5)
        app(+1(x8),x9) -> +2(x8,x9)
        app(+0(),x8) -> +1(x8)
        app(map1(x11),x12) -> map2(x11,x12)
        app(map0(),x11) -> map1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(filter1(x18),x19) -> filter2(x18,x19)
        app(filter0(),x18) -> filter1(x18)
        app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
        app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
        app(filter21(x21),x22) -> filter22(x21,x22)
        app(filter20(),x21) -> filter21(x21)
       Subterm Criterion Processor:
        simple projection:
         pi(filter{2,#}) = 1
         pi(filter2{4,#}) = 3
        problem:
         DPs:
          filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
          filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
         TRS:
          *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
          map2(f,nil0()) -> nil0()
          map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
          filter2(f,nil0()) -> nil0()
          filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
          filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
          filter24(false0(),f,x,xs) -> filter2(f,xs)
          app(*1(x5),x6) -> *2(x5,x6)
          app(*0(),x5) -> *1(x5)
          app(+1(x8),x9) -> +2(x8,x9)
          app(+0(),x8) -> +1(x8)
          app(map1(x11),x12) -> map2(x11,x12)
          app(map0(),x11) -> map1(x11)
          app(cons1(x15),x16) -> cons2(x15,x16)
          app(cons0(),x15) -> cons1(x15)
          app(filter1(x18),x19) -> filter2(x18,x19)
          app(filter0(),x18) -> filter1(x18)
          app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
          app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
          app(filter21(x21),x22) -> filter22(x21,x22)
          app(filter20(),x21) -> filter21(x21)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/4
         
     
     DPs:
      *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
      *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
     TRS:
      *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil0()) -> nil0()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false0(),f,x,xs) -> filter2(f,xs)
      app(*1(x5),x6) -> *2(x5,x6)
      app(*0(),x5) -> *1(x5)
      app(+1(x8),x9) -> +2(x8,x9)
      app(+0(),x8) -> +1(x8)
      app(map1(x11),x12) -> map2(x11,x12)
      app(map0(),x11) -> map1(x11)
      app(cons1(x15),x16) -> cons2(x15,x16)
      app(cons0(),x15) -> cons1(x15)
      app(filter1(x18),x19) -> filter2(x18,x19)
      app(filter0(),x18) -> filter1(x18)
      app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
      app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
      app(filter21(x21),x22) -> filter22(x21,x22)
      app(filter20(),x21) -> filter21(x21)
     Subterm Criterion Processor:
      simple projection:
       pi(*{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false0(),f,x,xs) -> filter2(f,xs)
        app(*1(x5),x6) -> *2(x5,x6)
        app(*0(),x5) -> *1(x5)
        app(+1(x8),x9) -> +2(x8,x9)
        app(+0(),x8) -> +1(x8)
        app(map1(x11),x12) -> map2(x11,x12)
        app(map0(),x11) -> map1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(filter1(x18),x19) -> filter2(x18,x19)
        app(filter0(),x18) -> filter1(x18)
        app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
        app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
        app(filter21(x21),x22) -> filter22(x21,x22)
        app(filter20(),x21) -> filter21(x21)
      Qed