/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 app(f(),app(app(cons(),nil()),y)) -> y
 app(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app(app(app(copy(),n()),y),z)
 app(app(app(copy(),0()),y),z) -> app(f(),z)
 app(app(app(copy(),app(s(),x)),y),z) -> app(app(app(copy(),x),y),app(app(cons(),app(f(),y)),z))
 app(app(map(),fun),nil()) -> nil()
 app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
 app(app(filter(),fun),nil()) -> nil()
 app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
 app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
 app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),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
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   n ==> n0/0
   copy ==> copy0/0 copy1/1 copy2/2 copy3/3
   nil ==> nil0/0
   cons ==> cons0/0 cons1/1 cons2/2
   f ==> f0/0 f1/1
   
  uncurry-rules:
   app(f0(),x5) -> f1(x5)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
   app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
   app(copy1(x11),x12) -> copy2(x11,x12)
   app(copy0(),x11) -> copy1(x11)
   app(s0(),x17) -> s1(x17)
   app(map1(x19),x20) -> map2(x19,x20)
   app(map0(),x19) -> map1(x19)
   app(filter1(x22),x23) -> filter2(x22,x23)
   app(filter0(),x22) -> filter1(x22)
   app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
   app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
   app(filter21(x25),x26) -> filter22(x25,x26)
   app(filter20(),x25) -> filter21(x25)
  eta-rules:
   
  problem:
   f1(cons2(nil0(),y)) -> y
   f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
   copy3(00(),y,z) -> f1(z)
   copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
   map2(fun,nil0()) -> nil0()
   map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
   filter2(fun,nil0()) -> nil0()
   filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
   filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
   filter24(false0(),fun,x,xs) -> filter2(fun,xs)
   app(f0(),x5) -> f1(x5)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
   app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
   app(copy1(x11),x12) -> copy2(x11,x12)
   app(copy0(),x11) -> copy1(x11)
   app(s0(),x17) -> s1(x17)
   app(map1(x19),x20) -> map2(x19,x20)
   app(map0(),x19) -> map1(x19)
   app(filter1(x22),x23) -> filter2(x22,x23)
   app(filter0(),x22) -> filter1(x22)
   app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
   app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
   app(filter21(x25),x26) -> filter22(x25,x26)
   app(filter20(),x25) -> filter21(x25)
  DP Processor:
   DPs:
    f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
    copy{3,#}(00(),y,z) -> f{1,#}(z)
    copy{3,#}(s1(x),y,z) -> f{1,#}(y)
    copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
    map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
    map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
    filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
    filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
    filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
    filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
    app#(f0(),x5) -> f{1,#}(x5)
    app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13)
    app#(map1(x19),x20) -> map{2,#}(x19,x20)
    app#(filter1(x22),x23) -> filter{2,#}(x22,x23)
    app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28)
   TRS:
    f1(cons2(nil0(),y)) -> y
    f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
    copy3(00(),y,z) -> f1(z)
    copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
    map2(fun,nil0()) -> nil0()
    map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
    filter2(fun,nil0()) -> nil0()
    filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
    filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
    filter24(false0(),fun,x,xs) -> filter2(fun,xs)
    app(f0(),x5) -> f1(x5)
    app(cons1(x7),x8) -> cons2(x7,x8)
    app(cons0(),x7) -> cons1(x7)
    app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
    app(copy1(x11),x12) -> copy2(x11,x12)
    app(copy0(),x11) -> copy1(x11)
    app(s0(),x17) -> s1(x17)
    app(map1(x19),x20) -> map2(x19,x20)
    app(map0(),x19) -> map1(x19)
    app(filter1(x22),x23) -> filter2(x22,x23)
    app(filter0(),x22) -> filter1(x22)
    app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
    app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
    app(filter21(x25),x26) -> filter22(x25,x26)
    app(filter20(),x25) -> filter21(x25)
   TDG Processor:
    DPs:
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
     copy{3,#}(00(),y,z) -> f{1,#}(z)
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(f0(),x5) -> f{1,#}(x5)
     app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13)
     app#(map1(x19),x20) -> map{2,#}(x19,x20)
     app#(filter1(x22),x23) -> filter{2,#}(x22,x23)
     app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28)
    TRS:
     f1(cons2(nil0(),y)) -> y
     f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
     copy3(00(),y,z) -> f1(z)
     copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
     map2(fun,nil0()) -> nil0()
     map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
     filter2(fun,nil0()) -> nil0()
     filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
     filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
     filter24(false0(),fun,x,xs) -> filter2(fun,xs)
     app(f0(),x5) -> f1(x5)
     app(cons1(x7),x8) -> cons2(x7,x8)
     app(cons0(),x7) -> cons1(x7)
     app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
     app(copy1(x11),x12) -> copy2(x11,x12)
     app(copy0(),x11) -> copy1(x11)
     app(s0(),x17) -> s1(x17)
     app(map1(x19),x20) -> map2(x19,x20)
     app(map0(),x19) -> map1(x19)
     app(filter1(x22),x23) -> filter2(x22,x23)
     app(filter0(),x22) -> filter1(x22)
     app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
     app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
     app(filter21(x25),x26) -> filter22(x25,x26)
     app(filter20(),x25) -> filter21(x25)
    graph:
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs) ->
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs) ->
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x22),x23) -> filter{2,#}(x22,x23)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x19),x20) -> map{2,#}(x19,x20)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f0(),x5) -> f{1,#}(x5)
     app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28) ->
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28) ->
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter1(x22),x23) -> filter{2,#}(x22,x23) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     app#(filter1(x22),x23) -> filter{2,#}(x22,x23) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x19),x20) -> map{2,#}(x19,x20) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x19),x20) -> map{2,#}(x19,x20) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13) ->
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13) ->
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13) ->
     copy{3,#}(00(),y,z) -> f{1,#}(z)
     app#(f0(),x5) -> f{1,#}(x5) ->
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x22),x23) -> filter{2,#}(x22,x23)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x19),x20) -> map{2,#}(x19,x20)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f0(),x5) -> f{1,#}(x5)
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
     copy{3,#}(00(),y,z) -> f{1,#}(z)
     copy{3,#}(s1(x),y,z) -> f{1,#}(y) ->
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
     copy{3,#}(00(),y,z) -> f{1,#}(z) ->
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z) ->
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z) ->
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z) ->
     copy{3,#}(00(),y,z) -> f{1,#}(z)
    SCC Processor:
     #sccs: 2
     #rules: 13
     #arcs: 36/225
     DPs:
      filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
      filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(map1(x19),x20) -> map{2,#}(x19,x20)
      map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
      map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(filter1(x22),x23) -> filter{2,#}(x22,x23)
      filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
      filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
      app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28)
     TRS:
      f1(cons2(nil0(),y)) -> y
      f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
      copy3(00(),y,z) -> f1(z)
      copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
      map2(fun,nil0()) -> nil0()
      map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
      filter2(fun,nil0()) -> nil0()
      filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
      filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
      filter24(false0(),fun,x,xs) -> filter2(fun,xs)
      app(f0(),x5) -> f1(x5)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons0(),x7) -> cons1(x7)
      app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
      app(copy1(x11),x12) -> copy2(x11,x12)
      app(copy0(),x11) -> copy1(x11)
      app(s0(),x17) -> s1(x17)
      app(map1(x19),x20) -> map2(x19,x20)
      app(map0(),x19) -> map1(x19)
      app(filter1(x22),x23) -> filter2(x22,x23)
      app(filter0(),x22) -> filter1(x22)
      app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
      app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
      app(filter21(x25),x26) -> filter22(x25,x26)
      app(filter20(),x25) -> filter21(x25)
     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(),fun,x,xs) -> filter{2,#}(fun,xs)
        filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
        map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
        map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
        filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
        filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
       TRS:
        f1(cons2(nil0(),y)) -> y
        f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
        copy3(00(),y,z) -> f1(z)
        copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
        map2(fun,nil0()) -> nil0()
        map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
        filter2(fun,nil0()) -> nil0()
        filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
        filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
        filter24(false0(),fun,x,xs) -> filter2(fun,xs)
        app(f0(),x5) -> f1(x5)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons0(),x7) -> cons1(x7)
        app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
        app(copy1(x11),x12) -> copy2(x11,x12)
        app(copy0(),x11) -> copy1(x11)
        app(s0(),x17) -> s1(x17)
        app(map1(x19),x20) -> map2(x19,x20)
        app(map0(),x19) -> map1(x19)
        app(filter1(x22),x23) -> filter2(x22,x23)
        app(filter0(),x22) -> filter1(x22)
        app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
        app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
        app(filter21(x25),x26) -> filter22(x25,x26)
        app(filter20(),x25) -> filter21(x25)
      SCC Processor:
       #sccs: 2
       #rules: 4
       #arcs: 20/36
       DPs:
        map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
       TRS:
        f1(cons2(nil0(),y)) -> y
        f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
        copy3(00(),y,z) -> f1(z)
        copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
        map2(fun,nil0()) -> nil0()
        map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
        filter2(fun,nil0()) -> nil0()
        filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
        filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
        filter24(false0(),fun,x,xs) -> filter2(fun,xs)
        app(f0(),x5) -> f1(x5)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons0(),x7) -> cons1(x7)
        app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
        app(copy1(x11),x12) -> copy2(x11,x12)
        app(copy0(),x11) -> copy1(x11)
        app(s0(),x17) -> s1(x17)
        app(map1(x19),x20) -> map2(x19,x20)
        app(map0(),x19) -> map1(x19)
        app(filter1(x22),x23) -> filter2(x22,x23)
        app(filter0(),x22) -> filter1(x22)
        app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
        app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
        app(filter21(x25),x26) -> filter22(x25,x26)
        app(filter20(),x25) -> filter21(x25)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          f1(cons2(nil0(),y)) -> y
          f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
          copy3(00(),y,z) -> f1(z)
          copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
          map2(fun,nil0()) -> nil0()
          map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
          filter2(fun,nil0()) -> nil0()
          filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
          filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
          filter24(false0(),fun,x,xs) -> filter2(fun,xs)
          app(f0(),x5) -> f1(x5)
          app(cons1(x7),x8) -> cons2(x7,x8)
          app(cons0(),x7) -> cons1(x7)
          app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
          app(copy1(x11),x12) -> copy2(x11,x12)
          app(copy0(),x11) -> copy1(x11)
          app(s0(),x17) -> s1(x17)
          app(map1(x19),x20) -> map2(x19,x20)
          app(map0(),x19) -> map1(x19)
          app(filter1(x22),x23) -> filter2(x22,x23)
          app(filter0(),x22) -> filter1(x22)
          app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
          app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
          app(filter21(x25),x26) -> filter22(x25,x26)
          app(filter20(),x25) -> filter21(x25)
        Qed
       
       DPs:
        filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
        filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
        filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
       TRS:
        f1(cons2(nil0(),y)) -> y
        f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
        copy3(00(),y,z) -> f1(z)
        copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
        map2(fun,nil0()) -> nil0()
        map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
        filter2(fun,nil0()) -> nil0()
        filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
        filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
        filter24(false0(),fun,x,xs) -> filter2(fun,xs)
        app(f0(),x5) -> f1(x5)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons0(),x7) -> cons1(x7)
        app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
        app(copy1(x11),x12) -> copy2(x11,x12)
        app(copy0(),x11) -> copy1(x11)
        app(s0(),x17) -> s1(x17)
        app(map1(x19),x20) -> map2(x19,x20)
        app(map0(),x19) -> map1(x19)
        app(filter1(x22),x23) -> filter2(x22,x23)
        app(filter0(),x22) -> filter1(x22)
        app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
        app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
        app(filter21(x25),x26) -> filter22(x25,x26)
        app(filter20(),x25) -> filter21(x25)
       Subterm Criterion Processor:
        simple projection:
         pi(filter{2,#}) = 1
         pi(filter2{4,#}) = 3
        problem:
         DPs:
          filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
          filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
         TRS:
          f1(cons2(nil0(),y)) -> y
          f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
          copy3(00(),y,z) -> f1(z)
          copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
          map2(fun,nil0()) -> nil0()
          map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
          filter2(fun,nil0()) -> nil0()
          filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
          filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
          filter24(false0(),fun,x,xs) -> filter2(fun,xs)
          app(f0(),x5) -> f1(x5)
          app(cons1(x7),x8) -> cons2(x7,x8)
          app(cons0(),x7) -> cons1(x7)
          app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
          app(copy1(x11),x12) -> copy2(x11,x12)
          app(copy0(),x11) -> copy1(x11)
          app(s0(),x17) -> s1(x17)
          app(map1(x19),x20) -> map2(x19,x20)
          app(map0(),x19) -> map1(x19)
          app(filter1(x22),x23) -> filter2(x22,x23)
          app(filter0(),x22) -> filter1(x22)
          app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
          app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
          app(filter21(x25),x26) -> filter22(x25,x26)
          app(filter20(),x25) -> filter21(x25)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/4
         
     
     DPs:
      f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
      copy{3,#}(00(),y,z) -> f{1,#}(z)
      copy{3,#}(s1(x),y,z) -> f{1,#}(y)
      copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     TRS:
      f1(cons2(nil0(),y)) -> y
      f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
      copy3(00(),y,z) -> f1(z)
      copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
      map2(fun,nil0()) -> nil0()
      map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
      filter2(fun,nil0()) -> nil0()
      filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
      filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
      filter24(false0(),fun,x,xs) -> filter2(fun,xs)
      app(f0(),x5) -> f1(x5)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons0(),x7) -> cons1(x7)
      app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
      app(copy1(x11),x12) -> copy2(x11,x12)
      app(copy0(),x11) -> copy1(x11)
      app(s0(),x17) -> s1(x17)
      app(map1(x19),x20) -> map2(x19,x20)
      app(map0(),x19) -> map1(x19)
      app(filter1(x22),x23) -> filter2(x22,x23)
      app(filter0(),x22) -> filter1(x22)
      app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
      app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
      app(filter21(x25),x26) -> filter22(x25,x26)
      app(filter20(),x25) -> filter21(x25)
     EDG Processor:
      DPs:
       f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
       copy{3,#}(00(),y,z) -> f{1,#}(z)
       copy{3,#}(s1(x),y,z) -> f{1,#}(y)
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
      TRS:
       f1(cons2(nil0(),y)) -> y
       f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
       copy3(00(),y,z) -> f1(z)
       copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
       map2(fun,nil0()) -> nil0()
       map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
       filter2(fun,nil0()) -> nil0()
       filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
       filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
       filter24(false0(),fun,x,xs) -> filter2(fun,xs)
       app(f0(),x5) -> f1(x5)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons0(),x7) -> cons1(x7)
       app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
       app(copy1(x11),x12) -> copy2(x11,x12)
       app(copy0(),x11) -> copy1(x11)
       app(s0(),x17) -> s1(x17)
       app(map1(x19),x20) -> map2(x19,x20)
       app(map0(),x19) -> map1(x19)
       app(filter1(x22),x23) -> filter2(x22,x23)
       app(filter0(),x22) -> filter1(x22)
       app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
       app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
       app(filter21(x25),x26) -> filter22(x25,x26)
       app(filter20(),x25) -> filter21(x25)
      graph:
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
       copy{3,#}(00(),y,z) -> f{1,#}(z)
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
       copy{3,#}(s1(x),y,z) -> f{1,#}(y)
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
       copy{3,#}(s1(x),y,z) -> f{1,#}(y) ->
       f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
       copy{3,#}(00(),y,z) -> f{1,#}(z) ->
       f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 5/16
       DPs:
        copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
       TRS:
        f1(cons2(nil0(),y)) -> y
        f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
        copy3(00(),y,z) -> f1(z)
        copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
        map2(fun,nil0()) -> nil0()
        map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
        filter2(fun,nil0()) -> nil0()
        filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
        filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
        filter24(false0(),fun,x,xs) -> filter2(fun,xs)
        app(f0(),x5) -> f1(x5)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons0(),x7) -> cons1(x7)
        app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
        app(copy1(x11),x12) -> copy2(x11,x12)
        app(copy0(),x11) -> copy1(x11)
        app(s0(),x17) -> s1(x17)
        app(map1(x19),x20) -> map2(x19,x20)
        app(map0(),x19) -> map1(x19)
        app(filter1(x22),x23) -> filter2(x22,x23)
        app(filter0(),x22) -> filter1(x22)
        app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
        app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
        app(filter21(x25),x26) -> filter22(x25,x26)
        app(filter20(),x25) -> filter21(x25)
       Size-Change Termination Processor:
        DPs:
         
        TRS:
         f1(cons2(nil0(),y)) -> y
         f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
         copy3(00(),y,z) -> f1(z)
         copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
         map2(fun,nil0()) -> nil0()
         map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
         filter2(fun,nil0()) -> nil0()
         filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
         filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
         filter24(false0(),fun,x,xs) -> filter2(fun,xs)
         app(f0(),x5) -> f1(x5)
         app(cons1(x7),x8) -> cons2(x7,x8)
         app(cons0(),x7) -> cons1(x7)
         app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
         app(copy1(x11),x12) -> copy2(x11,x12)
         app(copy0(),x11) -> copy1(x11)
         app(s0(),x17) -> s1(x17)
         app(map1(x19),x20) -> map2(x19,x20)
         app(map0(),x19) -> map1(x19)
         app(filter1(x22),x23) -> filter2(x22,x23)
         app(filter0(),x22) -> filter1(x22)
         app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
         app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
         app(filter21(x25),x26) -> filter22(x25,x26)
         app(filter20(),x25) -> filter21(x25)
        The DP: copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) has the edges:
          0 >   0
          1 >=  1
        Qed