/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(\(),x),x) -> e()
 app(app(\(),e()),x) -> x
 app(app(\(),x),app(app(.(),x),y)) -> y
 app(app(\(),app(app(/(),x),y)),x) -> y
 app(app(/(),x),x) -> e()
 app(app(/(),x),e()) -> x
 app(app(/(),app(app(.(),y),x)),x) -> y
 app(app(/(),x),app(app(\(),y),x)) -> y
 app(app(.(),e()),x) -> x
 app(app(.(),x),e()) -> x
 app(app(.(),x),app(app(\(),x),y)) -> y
 app(app(.(),app(app(/(),y),x)),x) -> y
 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
   e ==> e0/0
   \ ==> \0/0 \1/1 \2/2
   
  uncurry-rules:
   app(\1(x4),x5) -> \2(x4,x5)
   app(\0(),x4) -> \1(x4)
   app(.1(x8),x9) -> .2(x8,x9)
   app(.0(),x8) -> .1(x8)
   app(/1(x11),x12) -> /2(x11,x12)
   app(/0(),x11) -> /1(x11)
   app(map1(x14),x15) -> map2(x14,x15)
   app(map0(),x14) -> map1(x14)
   app(cons1(x18),x19) -> cons2(x18,x19)
   app(cons0(),x18) -> cons1(x18)
   app(filter1(x21),x22) -> filter2(x21,x22)
   app(filter0(),x21) -> filter1(x21)
   app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
   app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
   app(filter21(x24),x25) -> filter22(x24,x25)
   app(filter20(),x24) -> filter21(x24)
  eta-rules:
   
  problem:
   \2(x,x) -> e0()
   \2(e0(),x) -> x
   \2(x,.2(x,y)) -> y
   \2(/2(x,y),x) -> y
   /2(x,x) -> e0()
   /2(x,e0()) -> x
   /2(.2(y,x),x) -> y
   /2(x,\2(y,x)) -> y
   .2(e0(),x) -> x
   .2(x,e0()) -> x
   .2(x,\2(x,y)) -> y
   .2(/2(y,x),x) -> y
   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(x4),x5) -> \2(x4,x5)
   app(\0(),x4) -> \1(x4)
   app(.1(x8),x9) -> .2(x8,x9)
   app(.0(),x8) -> .1(x8)
   app(/1(x11),x12) -> /2(x11,x12)
   app(/0(),x11) -> /1(x11)
   app(map1(x14),x15) -> map2(x14,x15)
   app(map0(),x14) -> map1(x14)
   app(cons1(x18),x19) -> cons2(x18,x19)
   app(cons0(),x18) -> cons1(x18)
   app(filter1(x21),x22) -> filter2(x21,x22)
   app(filter0(),x21) -> filter1(x21)
   app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
   app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
   app(filter21(x24),x25) -> filter22(x24,x25)
   app(filter20(),x24) -> filter21(x24)
  DP Processor:
   DPs:
    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(x4),x5) -> \{2,#}(x4,x5)
    app#(.1(x8),x9) -> .{2,#}(x8,x9)
    app#(/1(x11),x12) -> /{2,#}(x11,x12)
    app#(map1(x14),x15) -> map{2,#}(x14,x15)
    app#(filter1(x21),x22) -> filter{2,#}(x21,x22)
    app#(filter23(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27)
   TRS:
    \2(x,x) -> e0()
    \2(e0(),x) -> x
    \2(x,.2(x,y)) -> y
    \2(/2(x,y),x) -> y
    /2(x,x) -> e0()
    /2(x,e0()) -> x
    /2(.2(y,x),x) -> y
    /2(x,\2(y,x)) -> y
    .2(e0(),x) -> x
    .2(x,e0()) -> x
    .2(x,\2(x,y)) -> y
    .2(/2(y,x),x) -> y
    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(x4),x5) -> \2(x4,x5)
    app(\0(),x4) -> \1(x4)
    app(.1(x8),x9) -> .2(x8,x9)
    app(.0(),x8) -> .1(x8)
    app(/1(x11),x12) -> /2(x11,x12)
    app(/0(),x11) -> /1(x11)
    app(map1(x14),x15) -> map2(x14,x15)
    app(map0(),x14) -> map1(x14)
    app(cons1(x18),x19) -> cons2(x18,x19)
    app(cons0(),x18) -> cons1(x18)
    app(filter1(x21),x22) -> filter2(x21,x22)
    app(filter0(),x21) -> filter1(x21)
    app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
    app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
    app(filter21(x24),x25) -> filter22(x24,x25)
    app(filter20(),x24) -> filter21(x24)
   TDG Processor:
    DPs:
     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(x4),x5) -> \{2,#}(x4,x5)
     app#(.1(x8),x9) -> .{2,#}(x8,x9)
     app#(/1(x11),x12) -> /{2,#}(x11,x12)
     app#(map1(x14),x15) -> map{2,#}(x14,x15)
     app#(filter1(x21),x22) -> filter{2,#}(x21,x22)
     app#(filter23(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27)
    TRS:
     \2(x,x) -> e0()
     \2(e0(),x) -> x
     \2(x,.2(x,y)) -> y
     \2(/2(x,y),x) -> y
     /2(x,x) -> e0()
     /2(x,e0()) -> x
     /2(.2(y,x),x) -> y
     /2(x,\2(y,x)) -> y
     .2(e0(),x) -> x
     .2(x,e0()) -> x
     .2(x,\2(x,y)) -> y
     .2(/2(y,x),x) -> y
     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(x4),x5) -> \2(x4,x5)
     app(\0(),x4) -> \1(x4)
     app(.1(x8),x9) -> .2(x8,x9)
     app(.0(),x8) -> .1(x8)
     app(/1(x11),x12) -> /2(x11,x12)
     app(/0(),x11) -> /1(x11)
     app(map1(x14),x15) -> map2(x14,x15)
     app(map0(),x14) -> map1(x14)
     app(cons1(x18),x19) -> cons2(x18,x19)
     app(cons0(),x18) -> cons1(x18)
     app(filter1(x21),x22) -> filter2(x21,x22)
     app(filter0(),x21) -> filter1(x21)
     app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
     app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
     app(filter21(x24),x25) -> filter22(x24,x25)
     app(filter20(),x24) -> filter21(x24)
    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(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x21),x22) -> filter{2,#}(x21,x22)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x14),x15) -> map{2,#}(x14,x15)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(/1(x11),x12) -> /{2,#}(x11,x12)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(.1(x8),x9) -> .{2,#}(x8,x9)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(\1(x4),x5) -> \{2,#}(x4,x5)
     app#(filter23(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27) ->
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27) ->
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x21),x22) -> filter{2,#}(x21,x22) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x21),x22) -> filter{2,#}(x21,x22) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x21),x22) -> filter{2,#}(x21,x22)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x14),x15) -> map{2,#}(x14,x15)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(/1(x11),x12) -> /{2,#}(x11,x12)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(.1(x8),x9) -> .{2,#}(x8,x9)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(\1(x4),x5) -> \{2,#}(x4,x5)
     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)
    SCC Processor:
     #sccs: 1
     #rules: 9
     #arcs: 26/144
     DPs:
      filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x14),x15) -> map{2,#}(x14,x15)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x21),x22) -> filter{2,#}(x21,x22)
      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(x24,x25,x26),x27) -> filter2{4,#}(x24,x25,x26,x27)
     TRS:
      \2(x,x) -> e0()
      \2(e0(),x) -> x
      \2(x,.2(x,y)) -> y
      \2(/2(x,y),x) -> y
      /2(x,x) -> e0()
      /2(x,e0()) -> x
      /2(.2(y,x),x) -> y
      /2(x,\2(y,x)) -> y
      .2(e0(),x) -> x
      .2(x,e0()) -> x
      .2(x,\2(x,y)) -> y
      .2(/2(y,x),x) -> y
      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(x4),x5) -> \2(x4,x5)
      app(\0(),x4) -> \1(x4)
      app(.1(x8),x9) -> .2(x8,x9)
      app(.0(),x8) -> .1(x8)
      app(/1(x11),x12) -> /2(x11,x12)
      app(/0(),x11) -> /1(x11)
      app(map1(x14),x15) -> map2(x14,x15)
      app(map0(),x14) -> map1(x14)
      app(cons1(x18),x19) -> cons2(x18,x19)
      app(cons0(),x18) -> cons1(x18)
      app(filter1(x21),x22) -> filter2(x21,x22)
      app(filter0(),x21) -> filter1(x21)
      app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
      app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
      app(filter21(x24),x25) -> filter22(x24,x25)
      app(filter20(),x24) -> filter21(x24)
     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,x) -> e0()
        \2(e0(),x) -> x
        \2(x,.2(x,y)) -> y
        \2(/2(x,y),x) -> y
        /2(x,x) -> e0()
        /2(x,e0()) -> x
        /2(.2(y,x),x) -> y
        /2(x,\2(y,x)) -> y
        .2(e0(),x) -> x
        .2(x,e0()) -> x
        .2(x,\2(x,y)) -> y
        .2(/2(y,x),x) -> y
        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(x4),x5) -> \2(x4,x5)
        app(\0(),x4) -> \1(x4)
        app(.1(x8),x9) -> .2(x8,x9)
        app(.0(),x8) -> .1(x8)
        app(/1(x11),x12) -> /2(x11,x12)
        app(/0(),x11) -> /1(x11)
        app(map1(x14),x15) -> map2(x14,x15)
        app(map0(),x14) -> map1(x14)
        app(cons1(x18),x19) -> cons2(x18,x19)
        app(cons0(),x18) -> cons1(x18)
        app(filter1(x21),x22) -> filter2(x21,x22)
        app(filter0(),x21) -> filter1(x21)
        app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
        app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
        app(filter21(x24),x25) -> filter22(x24,x25)
        app(filter20(),x24) -> filter21(x24)
      SCC Processor:
       #sccs: 2
       #rules: 4
       #arcs: 20/36
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
       TRS:
        \2(x,x) -> e0()
        \2(e0(),x) -> x
        \2(x,.2(x,y)) -> y
        \2(/2(x,y),x) -> y
        /2(x,x) -> e0()
        /2(x,e0()) -> x
        /2(.2(y,x),x) -> y
        /2(x,\2(y,x)) -> y
        .2(e0(),x) -> x
        .2(x,e0()) -> x
        .2(x,\2(x,y)) -> y
        .2(/2(y,x),x) -> y
        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(x4),x5) -> \2(x4,x5)
        app(\0(),x4) -> \1(x4)
        app(.1(x8),x9) -> .2(x8,x9)
        app(.0(),x8) -> .1(x8)
        app(/1(x11),x12) -> /2(x11,x12)
        app(/0(),x11) -> /1(x11)
        app(map1(x14),x15) -> map2(x14,x15)
        app(map0(),x14) -> map1(x14)
        app(cons1(x18),x19) -> cons2(x18,x19)
        app(cons0(),x18) -> cons1(x18)
        app(filter1(x21),x22) -> filter2(x21,x22)
        app(filter0(),x21) -> filter1(x21)
        app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
        app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
        app(filter21(x24),x25) -> filter22(x24,x25)
        app(filter20(),x24) -> filter21(x24)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          \2(x,x) -> e0()
          \2(e0(),x) -> x
          \2(x,.2(x,y)) -> y
          \2(/2(x,y),x) -> y
          /2(x,x) -> e0()
          /2(x,e0()) -> x
          /2(.2(y,x),x) -> y
          /2(x,\2(y,x)) -> y
          .2(e0(),x) -> x
          .2(x,e0()) -> x
          .2(x,\2(x,y)) -> y
          .2(/2(y,x),x) -> y
          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(x4),x5) -> \2(x4,x5)
          app(\0(),x4) -> \1(x4)
          app(.1(x8),x9) -> .2(x8,x9)
          app(.0(),x8) -> .1(x8)
          app(/1(x11),x12) -> /2(x11,x12)
          app(/0(),x11) -> /1(x11)
          app(map1(x14),x15) -> map2(x14,x15)
          app(map0(),x14) -> map1(x14)
          app(cons1(x18),x19) -> cons2(x18,x19)
          app(cons0(),x18) -> cons1(x18)
          app(filter1(x21),x22) -> filter2(x21,x22)
          app(filter0(),x21) -> filter1(x21)
          app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
          app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
          app(filter21(x24),x25) -> filter22(x24,x25)
          app(filter20(),x24) -> filter21(x24)
        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,x) -> e0()
        \2(e0(),x) -> x
        \2(x,.2(x,y)) -> y
        \2(/2(x,y),x) -> y
        /2(x,x) -> e0()
        /2(x,e0()) -> x
        /2(.2(y,x),x) -> y
        /2(x,\2(y,x)) -> y
        .2(e0(),x) -> x
        .2(x,e0()) -> x
        .2(x,\2(x,y)) -> y
        .2(/2(y,x),x) -> y
        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(x4),x5) -> \2(x4,x5)
        app(\0(),x4) -> \1(x4)
        app(.1(x8),x9) -> .2(x8,x9)
        app(.0(),x8) -> .1(x8)
        app(/1(x11),x12) -> /2(x11,x12)
        app(/0(),x11) -> /1(x11)
        app(map1(x14),x15) -> map2(x14,x15)
        app(map0(),x14) -> map1(x14)
        app(cons1(x18),x19) -> cons2(x18,x19)
        app(cons0(),x18) -> cons1(x18)
        app(filter1(x21),x22) -> filter2(x21,x22)
        app(filter0(),x21) -> filter1(x21)
        app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
        app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
        app(filter21(x24),x25) -> filter22(x24,x25)
        app(filter20(),x24) -> filter21(x24)
       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,x) -> e0()
          \2(e0(),x) -> x
          \2(x,.2(x,y)) -> y
          \2(/2(x,y),x) -> y
          /2(x,x) -> e0()
          /2(x,e0()) -> x
          /2(.2(y,x),x) -> y
          /2(x,\2(y,x)) -> y
          .2(e0(),x) -> x
          .2(x,e0()) -> x
          .2(x,\2(x,y)) -> y
          .2(/2(y,x),x) -> y
          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(x4),x5) -> \2(x4,x5)
          app(\0(),x4) -> \1(x4)
          app(.1(x8),x9) -> .2(x8,x9)
          app(.0(),x8) -> .1(x8)
          app(/1(x11),x12) -> /2(x11,x12)
          app(/0(),x11) -> /1(x11)
          app(map1(x14),x15) -> map2(x14,x15)
          app(map0(),x14) -> map1(x14)
          app(cons1(x18),x19) -> cons2(x18,x19)
          app(cons0(),x18) -> cons1(x18)
          app(filter1(x21),x22) -> filter2(x21,x22)
          app(filter0(),x21) -> filter1(x21)
          app(filter23(x24,x25,x26),x27) -> filter24(x24,x25,x26,x27)
          app(filter22(x24,x25),x26) -> filter23(x24,x25,x26)
          app(filter21(x24),x25) -> filter22(x24,x25)
          app(filter20(),x24) -> filter21(x24)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/4