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


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YES

Problem:
 app(app(app(f(),0()),1()),x) -> app(app(app(f(),app(s(),x)),x),x)
 app(app(app(f(),x),y),app(s(),z)) -> app(s(),app(app(app(f(),0()),1()),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
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   1 ==> 10/0
   0 ==> 00/0
   f ==> f0/0 f1/1 f2/2 f3/3
   
  uncurry-rules:
   app(f2(x5,x6),x7) -> f3(x5,x6,x7)
   app(f1(x5),x6) -> f2(x5,x6)
   app(f0(),x5) -> f1(x5)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
   app(filter1(x20),x21) -> filter2(x20,x21)
   app(filter0(),x20) -> filter1(x20)
   app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
   app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
   app(filter21(x23),x24) -> filter22(x23,x24)
   app(filter20(),x23) -> filter21(x23)
  eta-rules:
   
  problem:
   f3(00(),10(),x) -> f3(s1(x),x,x)
   f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
   app(f1(x5),x6) -> f2(x5,x6)
   app(f0(),x5) -> f1(x5)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
   app(filter1(x20),x21) -> filter2(x20,x21)
   app(filter0(),x20) -> filter1(x20)
   app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
   app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
   app(filter21(x23),x24) -> filter22(x23,x24)
   app(filter20(),x23) -> filter21(x23)
  DP Processor:
   DPs:
    f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
    f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),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#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7)
    app#(map1(x13),x14) -> map{2,#}(x13,x14)
    app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
    app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
   TRS:
    f3(00(),10(),x) -> f3(s1(x),x,x)
    f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
    app(f1(x5),x6) -> f2(x5,x6)
    app(f0(),x5) -> f1(x5)
    app(s0(),x11) -> s1(x11)
    app(map1(x13),x14) -> map2(x13,x14)
    app(map0(),x13) -> map1(x13)
    app(cons1(x17),x18) -> cons2(x17,x18)
    app(cons0(),x17) -> cons1(x17)
    app(filter1(x20),x21) -> filter2(x20,x21)
    app(filter0(),x20) -> filter1(x20)
    app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
    app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
    app(filter21(x23),x24) -> filter22(x23,x24)
    app(filter20(),x23) -> filter21(x23)
   TDG Processor:
    DPs:
     f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
     f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),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#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7)
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
    TRS:
     f3(00(),10(),x) -> f3(s1(x),x,x)
     f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
     app(f1(x5),x6) -> f2(x5,x6)
     app(f0(),x5) -> f1(x5)
     app(s0(),x11) -> s1(x11)
     app(map1(x13),x14) -> map2(x13,x14)
     app(map0(),x13) -> map1(x13)
     app(cons1(x17),x18) -> cons2(x17,x18)
     app(cons0(),x17) -> cons1(x17)
     app(filter1(x20),x21) -> filter2(x20,x21)
     app(filter0(),x20) -> filter1(x20)
     app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
     app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
     app(filter21(x23),x24) -> filter22(x23,x24)
     app(filter20(),x23) -> filter21(x23)
    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(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7)
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26) ->
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26) ->
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x13),x14) -> map{2,#}(x13,x14) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x13),x14) -> map{2,#}(x13,x14) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     app#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7) ->
     f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z)
     app#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7) ->
     f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7)
     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)
     f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x) ->
     f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z)
     f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x) ->
     f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
     f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z) ->
     f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z)
     f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z) -> f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
    SCC Processor:
     #sccs: 2
     #rules: 11
     #arcs: 28/144
     DPs:
      filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
      filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(map1(x13),x14) -> map{2,#}(x13,x14)
      map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
      map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
      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(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
     TRS:
      f3(00(),10(),x) -> f3(s1(x),x,x)
      f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
      app(f1(x5),x6) -> f2(x5,x6)
      app(f0(),x5) -> f1(x5)
      app(s0(),x11) -> s1(x11)
      app(map1(x13),x14) -> map2(x13,x14)
      app(map0(),x13) -> map1(x13)
      app(cons1(x17),x18) -> cons2(x17,x18)
      app(cons0(),x17) -> cons1(x17)
      app(filter1(x20),x21) -> filter2(x20,x21)
      app(filter0(),x20) -> filter1(x20)
      app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
      app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
      app(filter21(x23),x24) -> filter22(x23,x24)
      app(filter20(),x23) -> filter21(x23)
     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:
        f3(00(),10(),x) -> f3(s1(x),x,x)
        f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
        app(f1(x5),x6) -> f2(x5,x6)
        app(f0(),x5) -> f1(x5)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
        app(filter1(x20),x21) -> filter2(x20,x21)
        app(filter0(),x20) -> filter1(x20)
        app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
        app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
        app(filter21(x23),x24) -> filter22(x23,x24)
        app(filter20(),x23) -> filter21(x23)
      SCC Processor:
       #sccs: 2
       #rules: 4
       #arcs: 20/36
       DPs:
        map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
       TRS:
        f3(00(),10(),x) -> f3(s1(x),x,x)
        f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
        app(f1(x5),x6) -> f2(x5,x6)
        app(f0(),x5) -> f1(x5)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
        app(filter1(x20),x21) -> filter2(x20,x21)
        app(filter0(),x20) -> filter1(x20)
        app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
        app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
        app(filter21(x23),x24) -> filter22(x23,x24)
        app(filter20(),x23) -> filter21(x23)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          f3(00(),10(),x) -> f3(s1(x),x,x)
          f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
          app(f1(x5),x6) -> f2(x5,x6)
          app(f0(),x5) -> f1(x5)
          app(s0(),x11) -> s1(x11)
          app(map1(x13),x14) -> map2(x13,x14)
          app(map0(),x13) -> map1(x13)
          app(cons1(x17),x18) -> cons2(x17,x18)
          app(cons0(),x17) -> cons1(x17)
          app(filter1(x20),x21) -> filter2(x20,x21)
          app(filter0(),x20) -> filter1(x20)
          app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
          app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
          app(filter21(x23),x24) -> filter22(x23,x24)
          app(filter20(),x23) -> filter21(x23)
        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:
        f3(00(),10(),x) -> f3(s1(x),x,x)
        f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
        app(f1(x5),x6) -> f2(x5,x6)
        app(f0(),x5) -> f1(x5)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
        app(filter1(x20),x21) -> filter2(x20,x21)
        app(filter0(),x20) -> filter1(x20)
        app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
        app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
        app(filter21(x23),x24) -> filter22(x23,x24)
        app(filter20(),x23) -> filter21(x23)
       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:
          f3(00(),10(),x) -> f3(s1(x),x,x)
          f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
          app(f1(x5),x6) -> f2(x5,x6)
          app(f0(),x5) -> f1(x5)
          app(s0(),x11) -> s1(x11)
          app(map1(x13),x14) -> map2(x13,x14)
          app(map0(),x13) -> map1(x13)
          app(cons1(x17),x18) -> cons2(x17,x18)
          app(cons0(),x17) -> cons1(x17)
          app(filter1(x20),x21) -> filter2(x20,x21)
          app(filter0(),x20) -> filter1(x20)
          app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
          app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
          app(filter21(x23),x24) -> filter22(x23,x24)
          app(filter20(),x23) -> filter21(x23)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/4
         
     
     DPs:
      f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
      f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z)
     TRS:
      f3(00(),10(),x) -> f3(s1(x),x,x)
      f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
      app(f1(x5),x6) -> f2(x5,x6)
      app(f0(),x5) -> f1(x5)
      app(s0(),x11) -> s1(x11)
      app(map1(x13),x14) -> map2(x13,x14)
      app(map0(),x13) -> map1(x13)
      app(cons1(x17),x18) -> cons2(x17,x18)
      app(cons0(),x17) -> cons1(x17)
      app(filter1(x20),x21) -> filter2(x20,x21)
      app(filter0(),x20) -> filter1(x20)
      app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
      app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
      app(filter21(x23),x24) -> filter22(x23,x24)
      app(filter20(),x23) -> filter21(x23)
     Subterm Criterion Processor:
      simple projection:
       pi(f{3,#}) = 2
      problem:
       DPs:
        f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
       TRS:
        f3(00(),10(),x) -> f3(s1(x),x,x)
        f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
        app(f1(x5),x6) -> f2(x5,x6)
        app(f0(),x5) -> f1(x5)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
        app(filter1(x20),x21) -> filter2(x20,x21)
        app(filter0(),x20) -> filter1(x20)
        app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
        app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
        app(filter21(x23),x24) -> filter22(x23,x24)
        app(filter20(),x23) -> filter21(x23)
      EDG Processor:
       DPs:
        f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
       TRS:
        f3(00(),10(),x) -> f3(s1(x),x,x)
        f3(x,y,s1(z)) -> s1(f3(00(),10(),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(f2(x5,x6),x7) -> f3(x5,x6,x7)
        app(f1(x5),x6) -> f2(x5,x6)
        app(f0(),x5) -> f1(x5)
        app(s0(),x11) -> s1(x11)
        app(map1(x13),x14) -> map2(x13,x14)
        app(map0(),x13) -> map1(x13)
        app(cons1(x17),x18) -> cons2(x17,x18)
        app(cons0(),x17) -> cons1(x17)
        app(filter1(x20),x21) -> filter2(x20,x21)
        app(filter0(),x20) -> filter1(x20)
        app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
        app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
        app(filter21(x23),x24) -> filter22(x23,x24)
        app(filter20(),x23) -> filter21(x23)
       graph:
        
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 0/1