/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(f(),app(g(),x)) -> app(g(),app(g(),app(f(),x)))
 app(f(),app(g(),x)) -> app(g(),app(g(),app(g(),x)))
 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
   g ==> g0/0 g1/1
   f ==> f0/0 f1/1
   
  uncurry-rules:
   app(f0(),x3) -> f1(x3)
   app(g0(),x5) -> g1(x5)
   app(map1(x7),x8) -> map2(x7,x8)
   app(map0(),x7) -> map1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(filter1(x14),x15) -> filter2(x14,x15)
   app(filter0(),x14) -> filter1(x14)
   app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
   app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
   app(filter21(x17),x18) -> filter22(x17,x18)
   app(filter20(),x17) -> filter21(x17)
  eta-rules:
   
  problem:
   f1(g1(x)) -> g1(g1(f1(x)))
   f1(g1(x)) -> g1(g1(g1(x)))
   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(),x3) -> f1(x3)
   app(g0(),x5) -> g1(x5)
   app(map1(x7),x8) -> map2(x7,x8)
   app(map0(),x7) -> map1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(filter1(x14),x15) -> filter2(x14,x15)
   app(filter0(),x14) -> filter1(x14)
   app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
   app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
   app(filter21(x17),x18) -> filter22(x17,x18)
   app(filter20(),x17) -> filter21(x17)
  DP Processor:
   DPs:
    f{1,#}(g1(x)) -> f{1,#}(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)) -> 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(),x3) -> f{1,#}(x3)
    app#(map1(x7),x8) -> map{2,#}(x7,x8)
    app#(filter1(x14),x15) -> filter{2,#}(x14,x15)
    app#(filter23(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20)
   TRS:
    f1(g1(x)) -> g1(g1(f1(x)))
    f1(g1(x)) -> g1(g1(g1(x)))
    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(),x3) -> f1(x3)
    app(g0(),x5) -> g1(x5)
    app(map1(x7),x8) -> map2(x7,x8)
    app(map0(),x7) -> map1(x7)
    app(cons1(x11),x12) -> cons2(x11,x12)
    app(cons0(),x11) -> cons1(x11)
    app(filter1(x14),x15) -> filter2(x14,x15)
    app(filter0(),x14) -> filter1(x14)
    app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
    app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
    app(filter21(x17),x18) -> filter22(x17,x18)
    app(filter20(),x17) -> filter21(x17)
   TDG Processor:
    DPs:
     f{1,#}(g1(x)) -> f{1,#}(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)) -> 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(),x3) -> f{1,#}(x3)
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     app#(filter1(x14),x15) -> filter{2,#}(x14,x15)
     app#(filter23(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20)
    TRS:
     f1(g1(x)) -> g1(g1(f1(x)))
     f1(g1(x)) -> g1(g1(g1(x)))
     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(),x3) -> f1(x3)
     app(g0(),x5) -> g1(x5)
     app(map1(x7),x8) -> map2(x7,x8)
     app(map0(),x7) -> map1(x7)
     app(cons1(x11),x12) -> cons2(x11,x12)
     app(cons0(),x11) -> cons1(x11)
     app(filter1(x14),x15) -> filter2(x14,x15)
     app(filter0(),x14) -> filter1(x14)
     app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
     app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
     app(filter21(x17),x18) -> filter22(x17,x18)
     app(filter20(),x17) -> filter21(x17)
    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(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x14),x15) -> filter{2,#}(x14,x15)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f0(),x3) -> f{1,#}(x3)
     app#(filter23(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20) ->
     filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter23(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20) ->
     filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter1(x14),x15) -> filter{2,#}(x14,x15) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     app#(filter1(x14),x15) -> filter{2,#}(x14,x15) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     app#(f0(),x3) -> f{1,#}(x3) ->
     f{1,#}(g1(x)) -> f{1,#}(x)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x14),x15) -> filter{2,#}(x14,x15)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f0(),x3) -> f{1,#}(x3)
     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{1,#}(g1(x)) -> f{1,#}(x) -> f{1,#}(g1(x)) -> f{1,#}(x)
    SCC Processor:
     #sccs: 2
     #rules: 10
     #arcs: 24/121
     DPs:
      filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
      filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(map1(x7),x8) -> map{2,#}(x7,x8)
      map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
      map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(filter1(x14),x15) -> filter{2,#}(x14,x15)
      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(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20)
     TRS:
      f1(g1(x)) -> g1(g1(f1(x)))
      f1(g1(x)) -> g1(g1(g1(x)))
      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(),x3) -> f1(x3)
      app(g0(),x5) -> g1(x5)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map0(),x7) -> map1(x7)
      app(cons1(x11),x12) -> cons2(x11,x12)
      app(cons0(),x11) -> cons1(x11)
      app(filter1(x14),x15) -> filter2(x14,x15)
      app(filter0(),x14) -> filter1(x14)
      app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
      app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
      app(filter21(x17),x18) -> filter22(x17,x18)
      app(filter20(),x17) -> filter21(x17)
     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(g1(x)) -> g1(g1(f1(x)))
        f1(g1(x)) -> g1(g1(g1(x)))
        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(),x3) -> f1(x3)
        app(g0(),x5) -> g1(x5)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map0(),x7) -> map1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(filter1(x14),x15) -> filter2(x14,x15)
        app(filter0(),x14) -> filter1(x14)
        app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
        app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
        app(filter21(x17),x18) -> filter22(x17,x18)
        app(filter20(),x17) -> filter21(x17)
      SCC Processor:
       #sccs: 2
       #rules: 4
       #arcs: 20/36
       DPs:
        map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
       TRS:
        f1(g1(x)) -> g1(g1(f1(x)))
        f1(g1(x)) -> g1(g1(g1(x)))
        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(),x3) -> f1(x3)
        app(g0(),x5) -> g1(x5)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map0(),x7) -> map1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(filter1(x14),x15) -> filter2(x14,x15)
        app(filter0(),x14) -> filter1(x14)
        app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
        app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
        app(filter21(x17),x18) -> filter22(x17,x18)
        app(filter20(),x17) -> filter21(x17)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          f1(g1(x)) -> g1(g1(f1(x)))
          f1(g1(x)) -> g1(g1(g1(x)))
          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(),x3) -> f1(x3)
          app(g0(),x5) -> g1(x5)
          app(map1(x7),x8) -> map2(x7,x8)
          app(map0(),x7) -> map1(x7)
          app(cons1(x11),x12) -> cons2(x11,x12)
          app(cons0(),x11) -> cons1(x11)
          app(filter1(x14),x15) -> filter2(x14,x15)
          app(filter0(),x14) -> filter1(x14)
          app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
          app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
          app(filter21(x17),x18) -> filter22(x17,x18)
          app(filter20(),x17) -> filter21(x17)
        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(g1(x)) -> g1(g1(f1(x)))
        f1(g1(x)) -> g1(g1(g1(x)))
        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(),x3) -> f1(x3)
        app(g0(),x5) -> g1(x5)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map0(),x7) -> map1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(filter1(x14),x15) -> filter2(x14,x15)
        app(filter0(),x14) -> filter1(x14)
        app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
        app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
        app(filter21(x17),x18) -> filter22(x17,x18)
        app(filter20(),x17) -> filter21(x17)
       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(g1(x)) -> g1(g1(f1(x)))
          f1(g1(x)) -> g1(g1(g1(x)))
          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(),x3) -> f1(x3)
          app(g0(),x5) -> g1(x5)
          app(map1(x7),x8) -> map2(x7,x8)
          app(map0(),x7) -> map1(x7)
          app(cons1(x11),x12) -> cons2(x11,x12)
          app(cons0(),x11) -> cons1(x11)
          app(filter1(x14),x15) -> filter2(x14,x15)
          app(filter0(),x14) -> filter1(x14)
          app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
          app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
          app(filter21(x17),x18) -> filter22(x17,x18)
          app(filter20(),x17) -> filter21(x17)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/4
         
     
     DPs:
      f{1,#}(g1(x)) -> f{1,#}(x)
     TRS:
      f1(g1(x)) -> g1(g1(f1(x)))
      f1(g1(x)) -> g1(g1(g1(x)))
      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(),x3) -> f1(x3)
      app(g0(),x5) -> g1(x5)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map0(),x7) -> map1(x7)
      app(cons1(x11),x12) -> cons2(x11,x12)
      app(cons0(),x11) -> cons1(x11)
      app(filter1(x14),x15) -> filter2(x14,x15)
      app(filter0(),x14) -> filter1(x14)
      app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
      app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
      app(filter21(x17),x18) -> filter22(x17,x18)
      app(filter20(),x17) -> filter21(x17)
     Subterm Criterion Processor:
      simple projection:
       pi(f{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        f1(g1(x)) -> g1(g1(f1(x)))
        f1(g1(x)) -> g1(g1(g1(x)))
        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(),x3) -> f1(x3)
        app(g0(),x5) -> g1(x5)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map0(),x7) -> map1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(filter1(x14),x15) -> filter2(x14,x15)
        app(filter0(),x14) -> filter1(x14)
        app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
        app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
        app(filter21(x17),x18) -> filter22(x17,x18)
        app(filter20(),x17) -> filter21(x17)
      Qed