/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(rev(),nil()) -> nil()
 app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
 app(app(rev1(),0()),nil()) -> 0()
 app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
 app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
 app(app(rev2(),x),nil()) -> nil()
 app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
 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
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   rev2 ==> rev20/0 rev21/1 rev22/2
   rev1 ==> rev10/0 rev11/1 rev12/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   rev ==> rev0/0 rev1/1
   
  uncurry-rules:
   app(rev0(),x5) -> rev1(x5)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(rev11(x11),x12) -> rev12(x11,x12)
   app(rev10(),x11) -> rev11(x11)
   app(rev21(x14),x15) -> rev22(x14,x15)
   app(rev20(),x14) -> rev21(x14)
   app(s0(),x18) -> s1(x18)
   app(map1(x20),x21) -> map2(x20,x21)
   app(map0(),x20) -> map1(x20)
   app(filter1(x23),x24) -> filter2(x23,x24)
   app(filter0(),x23) -> filter1(x23)
   app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
   app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
   app(filter21(x26),x27) -> filter22(x26,x27)
   app(filter20(),x26) -> filter21(x26)
  eta-rules:
   
  problem:
   rev1(nil0()) -> nil0()
   rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
   rev12(00(),nil0()) -> 00()
   rev12(s1(x),nil0()) -> s1(x)
   rev12(x,cons2(y,l)) -> rev12(y,l)
   rev22(x,nil0()) -> nil0()
   rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
   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(rev0(),x5) -> rev1(x5)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(rev11(x11),x12) -> rev12(x11,x12)
   app(rev10(),x11) -> rev11(x11)
   app(rev21(x14),x15) -> rev22(x14,x15)
   app(rev20(),x14) -> rev21(x14)
   app(s0(),x18) -> s1(x18)
   app(map1(x20),x21) -> map2(x20,x21)
   app(map0(),x20) -> map1(x20)
   app(filter1(x23),x24) -> filter2(x23,x24)
   app(filter0(),x23) -> filter1(x23)
   app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
   app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
   app(filter21(x26),x27) -> filter22(x26,x27)
   app(filter20(),x26) -> filter21(x26)
  DP Processor:
   DPs:
    rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l)
    rev{1,#}(cons2(x,l)) -> rev1{2,#}(x,l)
    rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l)
    rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l)
    rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
    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#(rev0(),x5) -> rev{1,#}(x5)
    app#(rev11(x11),x12) -> rev1{2,#}(x11,x12)
    app#(rev21(x14),x15) -> rev2{2,#}(x14,x15)
    app#(map1(x20),x21) -> map{2,#}(x20,x21)
    app#(filter1(x23),x24) -> filter{2,#}(x23,x24)
    app#(filter23(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29)
   TRS:
    rev1(nil0()) -> nil0()
    rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
    rev12(00(),nil0()) -> 00()
    rev12(s1(x),nil0()) -> s1(x)
    rev12(x,cons2(y,l)) -> rev12(y,l)
    rev22(x,nil0()) -> nil0()
    rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
    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(rev0(),x5) -> rev1(x5)
    app(cons1(x8),x9) -> cons2(x8,x9)
    app(cons0(),x8) -> cons1(x8)
    app(rev11(x11),x12) -> rev12(x11,x12)
    app(rev10(),x11) -> rev11(x11)
    app(rev21(x14),x15) -> rev22(x14,x15)
    app(rev20(),x14) -> rev21(x14)
    app(s0(),x18) -> s1(x18)
    app(map1(x20),x21) -> map2(x20,x21)
    app(map0(),x20) -> map1(x20)
    app(filter1(x23),x24) -> filter2(x23,x24)
    app(filter0(),x23) -> filter1(x23)
    app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
    app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
    app(filter21(x26),x27) -> filter22(x26,x27)
    app(filter20(),x26) -> filter21(x26)
   TDG Processor:
    DPs:
     rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l)
     rev{1,#}(cons2(x,l)) -> rev1{2,#}(x,l)
     rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l)
     rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l)
     rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
     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#(rev0(),x5) -> rev{1,#}(x5)
     app#(rev11(x11),x12) -> rev1{2,#}(x11,x12)
     app#(rev21(x14),x15) -> rev2{2,#}(x14,x15)
     app#(map1(x20),x21) -> map{2,#}(x20,x21)
     app#(filter1(x23),x24) -> filter{2,#}(x23,x24)
     app#(filter23(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29)
    TRS:
     rev1(nil0()) -> nil0()
     rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
     rev12(00(),nil0()) -> 00()
     rev12(s1(x),nil0()) -> s1(x)
     rev12(x,cons2(y,l)) -> rev12(y,l)
     rev22(x,nil0()) -> nil0()
     rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
     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(rev0(),x5) -> rev1(x5)
     app(cons1(x8),x9) -> cons2(x8,x9)
     app(cons0(),x8) -> cons1(x8)
     app(rev11(x11),x12) -> rev12(x11,x12)
     app(rev10(),x11) -> rev11(x11)
     app(rev21(x14),x15) -> rev22(x14,x15)
     app(rev20(),x14) -> rev21(x14)
     app(s0(),x18) -> s1(x18)
     app(map1(x20),x21) -> map2(x20,x21)
     app(map0(),x20) -> map1(x20)
     app(filter1(x23),x24) -> filter2(x23,x24)
     app(filter0(),x23) -> filter1(x23)
     app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
     app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
     app(filter21(x26),x27) -> filter22(x26,x27)
     app(filter20(),x26) -> filter21(x26)
    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(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x23),x24) -> filter{2,#}(x23,x24)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x20),x21) -> map{2,#}(x20,x21)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(rev21(x14),x15) -> rev2{2,#}(x14,x15)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(rev11(x11),x12) -> rev1{2,#}(x11,x12)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(rev0(),x5) -> rev{1,#}(x5)
     app#(filter23(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29) ->
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29) ->
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x23),x24) -> filter{2,#}(x23,x24) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x23),x24) -> filter{2,#}(x23,x24) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x20),x21) -> map{2,#}(x20,x21) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x20),x21) -> map{2,#}(x20,x21) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(rev21(x14),x15) -> rev2{2,#}(x14,x15) ->
     rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
     app#(rev21(x14),x15) -> rev2{2,#}(x14,x15) ->
     rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l)
     app#(rev11(x11),x12) -> rev1{2,#}(x11,x12) ->
     rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l)
     app#(rev0(),x5) -> rev{1,#}(x5) ->
     rev{1,#}(cons2(x,l)) -> rev1{2,#}(x,l)
     app#(rev0(),x5) -> rev{1,#}(x5) ->
     rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x23),x24) -> filter{2,#}(x23,x24)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x20),x21) -> map{2,#}(x20,x21)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(rev21(x14),x15) -> rev2{2,#}(x14,x15)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(rev11(x11),x12) -> rev1{2,#}(x11,x12)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(rev0(),x5) -> rev{1,#}(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)
     rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l) ->
     rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l)
     rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l) ->
     rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
     rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l) ->
     rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l)
     rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l))) ->
     rev{1,#}(cons2(x,l)) -> rev1{2,#}(x,l)
     rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l))) ->
     rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l)
     rev{1,#}(cons2(x,l)) -> rev1{2,#}(x,l) ->
     rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l)
     rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l) ->
     rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
     rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l) -> rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l)
    SCC Processor:
     #sccs: 3
     #rules: 13
     #arcs: 39/289
     DPs:
      filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x20),x21) -> map{2,#}(x20,x21)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x23),x24) -> filter{2,#}(x23,x24)
      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(x26,x27,x28),x29) -> filter2{4,#}(x26,x27,x28,x29)
     TRS:
      rev1(nil0()) -> nil0()
      rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
      rev12(00(),nil0()) -> 00()
      rev12(s1(x),nil0()) -> s1(x)
      rev12(x,cons2(y,l)) -> rev12(y,l)
      rev22(x,nil0()) -> nil0()
      rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
      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(rev0(),x5) -> rev1(x5)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(rev11(x11),x12) -> rev12(x11,x12)
      app(rev10(),x11) -> rev11(x11)
      app(rev21(x14),x15) -> rev22(x14,x15)
      app(rev20(),x14) -> rev21(x14)
      app(s0(),x18) -> s1(x18)
      app(map1(x20),x21) -> map2(x20,x21)
      app(map0(),x20) -> map1(x20)
      app(filter1(x23),x24) -> filter2(x23,x24)
      app(filter0(),x23) -> filter1(x23)
      app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
      app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
      app(filter21(x26),x27) -> filter22(x26,x27)
      app(filter20(),x26) -> filter21(x26)
     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:
        rev1(nil0()) -> nil0()
        rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
        rev12(00(),nil0()) -> 00()
        rev12(s1(x),nil0()) -> s1(x)
        rev12(x,cons2(y,l)) -> rev12(y,l)
        rev22(x,nil0()) -> nil0()
        rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
        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(rev0(),x5) -> rev1(x5)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(rev11(x11),x12) -> rev12(x11,x12)
        app(rev10(),x11) -> rev11(x11)
        app(rev21(x14),x15) -> rev22(x14,x15)
        app(rev20(),x14) -> rev21(x14)
        app(s0(),x18) -> s1(x18)
        app(map1(x20),x21) -> map2(x20,x21)
        app(map0(),x20) -> map1(x20)
        app(filter1(x23),x24) -> filter2(x23,x24)
        app(filter0(),x23) -> filter1(x23)
        app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
        app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
        app(filter21(x26),x27) -> filter22(x26,x27)
        app(filter20(),x26) -> filter21(x26)
      SCC Processor:
       #sccs: 2
       #rules: 4
       #arcs: 20/36
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
       TRS:
        rev1(nil0()) -> nil0()
        rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
        rev12(00(),nil0()) -> 00()
        rev12(s1(x),nil0()) -> s1(x)
        rev12(x,cons2(y,l)) -> rev12(y,l)
        rev22(x,nil0()) -> nil0()
        rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
        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(rev0(),x5) -> rev1(x5)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(rev11(x11),x12) -> rev12(x11,x12)
        app(rev10(),x11) -> rev11(x11)
        app(rev21(x14),x15) -> rev22(x14,x15)
        app(rev20(),x14) -> rev21(x14)
        app(s0(),x18) -> s1(x18)
        app(map1(x20),x21) -> map2(x20,x21)
        app(map0(),x20) -> map1(x20)
        app(filter1(x23),x24) -> filter2(x23,x24)
        app(filter0(),x23) -> filter1(x23)
        app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
        app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
        app(filter21(x26),x27) -> filter22(x26,x27)
        app(filter20(),x26) -> filter21(x26)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          rev1(nil0()) -> nil0()
          rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
          rev12(00(),nil0()) -> 00()
          rev12(s1(x),nil0()) -> s1(x)
          rev12(x,cons2(y,l)) -> rev12(y,l)
          rev22(x,nil0()) -> nil0()
          rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
          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(rev0(),x5) -> rev1(x5)
          app(cons1(x8),x9) -> cons2(x8,x9)
          app(cons0(),x8) -> cons1(x8)
          app(rev11(x11),x12) -> rev12(x11,x12)
          app(rev10(),x11) -> rev11(x11)
          app(rev21(x14),x15) -> rev22(x14,x15)
          app(rev20(),x14) -> rev21(x14)
          app(s0(),x18) -> s1(x18)
          app(map1(x20),x21) -> map2(x20,x21)
          app(map0(),x20) -> map1(x20)
          app(filter1(x23),x24) -> filter2(x23,x24)
          app(filter0(),x23) -> filter1(x23)
          app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
          app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
          app(filter21(x26),x27) -> filter22(x26,x27)
          app(filter20(),x26) -> filter21(x26)
        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:
        rev1(nil0()) -> nil0()
        rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
        rev12(00(),nil0()) -> 00()
        rev12(s1(x),nil0()) -> s1(x)
        rev12(x,cons2(y,l)) -> rev12(y,l)
        rev22(x,nil0()) -> nil0()
        rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
        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(rev0(),x5) -> rev1(x5)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(rev11(x11),x12) -> rev12(x11,x12)
        app(rev10(),x11) -> rev11(x11)
        app(rev21(x14),x15) -> rev22(x14,x15)
        app(rev20(),x14) -> rev21(x14)
        app(s0(),x18) -> s1(x18)
        app(map1(x20),x21) -> map2(x20,x21)
        app(map0(),x20) -> map1(x20)
        app(filter1(x23),x24) -> filter2(x23,x24)
        app(filter0(),x23) -> filter1(x23)
        app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
        app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
        app(filter21(x26),x27) -> filter22(x26,x27)
        app(filter20(),x26) -> filter21(x26)
       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:
          rev1(nil0()) -> nil0()
          rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
          rev12(00(),nil0()) -> 00()
          rev12(s1(x),nil0()) -> s1(x)
          rev12(x,cons2(y,l)) -> rev12(y,l)
          rev22(x,nil0()) -> nil0()
          rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
          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(rev0(),x5) -> rev1(x5)
          app(cons1(x8),x9) -> cons2(x8,x9)
          app(cons0(),x8) -> cons1(x8)
          app(rev11(x11),x12) -> rev12(x11,x12)
          app(rev10(),x11) -> rev11(x11)
          app(rev21(x14),x15) -> rev22(x14,x15)
          app(rev20(),x14) -> rev21(x14)
          app(s0(),x18) -> s1(x18)
          app(map1(x20),x21) -> map2(x20,x21)
          app(map0(),x20) -> map1(x20)
          app(filter1(x23),x24) -> filter2(x23,x24)
          app(filter0(),x23) -> filter1(x23)
          app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
          app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
          app(filter21(x26),x27) -> filter22(x26,x27)
          app(filter20(),x26) -> filter21(x26)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/4
         
     
     DPs:
      rev{1,#}(cons2(x,l)) -> rev2{2,#}(x,l)
      rev2{2,#}(x,cons2(y,l)) -> rev2{2,#}(y,l)
      rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
     TRS:
      rev1(nil0()) -> nil0()
      rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
      rev12(00(),nil0()) -> 00()
      rev12(s1(x),nil0()) -> s1(x)
      rev12(x,cons2(y,l)) -> rev12(y,l)
      rev22(x,nil0()) -> nil0()
      rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
      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(rev0(),x5) -> rev1(x5)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(rev11(x11),x12) -> rev12(x11,x12)
      app(rev10(),x11) -> rev11(x11)
      app(rev21(x14),x15) -> rev22(x14,x15)
      app(rev20(),x14) -> rev21(x14)
      app(s0(),x18) -> s1(x18)
      app(map1(x20),x21) -> map2(x20,x21)
      app(map0(),x20) -> map1(x20)
      app(filter1(x23),x24) -> filter2(x23,x24)
      app(filter0(),x23) -> filter1(x23)
      app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
      app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
      app(filter21(x26),x27) -> filter22(x26,x27)
      app(filter20(),x26) -> filter21(x26)
     Subterm Criterion Processor:
      simple projection:
       pi(rev1) = 0
       pi(cons1) = [0,0]
       pi(cons2) = [1,1]
       pi(rev11) = [0,0]
       pi(rev21) = [0,0]
       pi(rev22) = 1
       pi(map1) = [0,0]
       pi(filter22) = [1,1]
       pi(rev{1,#}) = [0,0]
       pi(rev2{2,#}) = [1,1]
      problem:
       DPs:
        rev2{2,#}(x,cons2(y,l)) -> rev{1,#}(cons2(x,rev22(y,l)))
       TRS:
        rev1(nil0()) -> nil0()
        rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
        rev12(00(),nil0()) -> 00()
        rev12(s1(x),nil0()) -> s1(x)
        rev12(x,cons2(y,l)) -> rev12(y,l)
        rev22(x,nil0()) -> nil0()
        rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
        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(rev0(),x5) -> rev1(x5)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(rev11(x11),x12) -> rev12(x11,x12)
        app(rev10(),x11) -> rev11(x11)
        app(rev21(x14),x15) -> rev22(x14,x15)
        app(rev20(),x14) -> rev21(x14)
        app(s0(),x18) -> s1(x18)
        app(map1(x20),x21) -> map2(x20,x21)
        app(map0(),x20) -> map1(x20)
        app(filter1(x23),x24) -> filter2(x23,x24)
        app(filter0(),x23) -> filter1(x23)
        app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
        app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
        app(filter21(x26),x27) -> filter22(x26,x27)
        app(filter20(),x26) -> filter21(x26)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 5/1
       
     
     DPs:
      rev1{2,#}(x,cons2(y,l)) -> rev1{2,#}(y,l)
     TRS:
      rev1(nil0()) -> nil0()
      rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
      rev12(00(),nil0()) -> 00()
      rev12(s1(x),nil0()) -> s1(x)
      rev12(x,cons2(y,l)) -> rev12(y,l)
      rev22(x,nil0()) -> nil0()
      rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
      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(rev0(),x5) -> rev1(x5)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(rev11(x11),x12) -> rev12(x11,x12)
      app(rev10(),x11) -> rev11(x11)
      app(rev21(x14),x15) -> rev22(x14,x15)
      app(rev20(),x14) -> rev21(x14)
      app(s0(),x18) -> s1(x18)
      app(map1(x20),x21) -> map2(x20,x21)
      app(map0(),x20) -> map1(x20)
      app(filter1(x23),x24) -> filter2(x23,x24)
      app(filter0(),x23) -> filter1(x23)
      app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
      app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
      app(filter21(x26),x27) -> filter22(x26,x27)
      app(filter20(),x26) -> filter21(x26)
     Subterm Criterion Processor:
      simple projection:
       pi(rev1{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        rev1(nil0()) -> nil0()
        rev1(cons2(x,l)) -> cons2(rev12(x,l),rev22(x,l))
        rev12(00(),nil0()) -> 00()
        rev12(s1(x),nil0()) -> s1(x)
        rev12(x,cons2(y,l)) -> rev12(y,l)
        rev22(x,nil0()) -> nil0()
        rev22(x,cons2(y,l)) -> rev1(cons2(x,rev22(y,l)))
        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(rev0(),x5) -> rev1(x5)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(rev11(x11),x12) -> rev12(x11,x12)
        app(rev10(),x11) -> rev11(x11)
        app(rev21(x14),x15) -> rev22(x14,x15)
        app(rev20(),x14) -> rev21(x14)
        app(s0(),x18) -> s1(x18)
        app(map1(x20),x21) -> map2(x20,x21)
        app(map0(),x20) -> map1(x20)
        app(filter1(x23),x24) -> filter2(x23,x24)
        app(filter0(),x23) -> filter1(x23)
        app(filter23(x26,x27,x28),x29) -> filter24(x26,x27,x28,x29)
        app(filter22(x26,x27),x28) -> filter23(x26,x27,x28)
        app(filter21(x26),x27) -> filter22(x26,x27)
        app(filter20(),x26) -> filter21(x26)
      Qed