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


--------------------------------------------------------------------------------


YES

Problem:
 app(not(),app(not(),x)) -> x
 app(not(),app(app(or(),x),y)) -> app(app(and(),app(not(),x)),app(not(),y))
 app(not(),app(app(and(),x),y)) -> app(app(or(),app(not(),x)),app(not(),y))
 app(app(and(),x),app(app(or(),y),z)) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
 app(app(and(),app(app(or(),y),z)),x) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
 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
   and ==> and0/0 and1/1 and2/2
   or ==> or0/0 or1/1 or2/2
   not ==> not0/0 not1/1
   
  uncurry-rules:
   app(not0(),x5) -> not1(x5)
   app(or1(x7),x8) -> or2(x7,x8)
   app(or0(),x7) -> or1(x7)
   app(and1(x10),x11) -> and2(x10,x11)
   app(and0(),x10) -> and1(x10)
   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:
   not1(not1(x)) -> x
   not1(or2(x,y)) -> and2(not1(x),not1(y))
   not1(and2(x,y)) -> or2(not1(x),not1(y))
   and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
   and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
   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(not0(),x5) -> not1(x5)
   app(or1(x7),x8) -> or2(x7,x8)
   app(or0(),x7) -> or1(x7)
   app(and1(x10),x11) -> and2(x10,x11)
   app(and0(),x10) -> and1(x10)
   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:
    not{1,#}(or2(x,y)) -> not{1,#}(y)
    not{1,#}(or2(x,y)) -> not{1,#}(x)
    not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
    not{1,#}(and2(x,y)) -> not{1,#}(y)
    not{1,#}(and2(x,y)) -> not{1,#}(x)
    and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
    and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
    and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
    and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
    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#(not0(),x5) -> not{1,#}(x5)
    app#(and1(x10),x11) -> and{2,#}(x10,x11)
    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:
    not1(not1(x)) -> x
    not1(or2(x,y)) -> and2(not1(x),not1(y))
    not1(and2(x,y)) -> or2(not1(x),not1(y))
    and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
    and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
    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(not0(),x5) -> not1(x5)
    app(or1(x7),x8) -> or2(x7,x8)
    app(or0(),x7) -> or1(x7)
    app(and1(x10),x11) -> and2(x10,x11)
    app(and0(),x10) -> and1(x10)
    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:
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     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#(not0(),x5) -> not{1,#}(x5)
     app#(and1(x10),x11) -> and{2,#}(x10,x11)
     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:
     not1(not1(x)) -> x
     not1(or2(x,y)) -> and2(not1(x),not1(y))
     not1(and2(x,y)) -> or2(not1(x),not1(y))
     and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
     and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
     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(not0(),x5) -> not1(x5)
     app(or1(x7),x8) -> or2(x7,x8)
     app(or0(),x7) -> or1(x7)
     app(and1(x10),x11) -> and2(x10,x11)
     app(and0(),x10) -> and1(x10)
     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(),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(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(and1(x10),x11) -> and{2,#}(x10,x11)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(not0(),x5) -> not{1,#}(x5)
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26) ->
     filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26) ->
     filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x13),x14) -> map{2,#}(x13,x14) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x13),x14) -> map{2,#}(x13,x14) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(and1(x10),x11) -> and{2,#}(x10,x11) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     app#(and1(x10),x11) -> and{2,#}(x10,x11) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     app#(and1(x10),x11) -> and{2,#}(x10,x11) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     app#(and1(x10),x11) -> and{2,#}(x10,x11) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     app#(not0(),x5) -> not{1,#}(x5) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     app#(not0(),x5) -> not{1,#}(x5) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     app#(not0(),x5) -> not{1,#}(x5) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     app#(not0(),x5) -> not{1,#}(x5) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     app#(not0(),x5) -> not{1,#}(x5) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(and1(x10),x11) -> and{2,#}(x10,x11)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(not0(),x5) -> not{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)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(x) -> not{1,#}(or2(x,y)) -> not{1,#}(y)
    SCC Processor:
     #sccs: 3
     #rules: 17
     #arcs: 73/400
     DPs:
      filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x13),x14) -> map{2,#}(x13,x14)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
      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(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
     TRS:
      not1(not1(x)) -> x
      not1(or2(x,y)) -> and2(not1(x),not1(y))
      not1(and2(x,y)) -> or2(not1(x),not1(y))
      and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
      and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
      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(not0(),x5) -> not1(x5)
      app(or1(x7),x8) -> or2(x7,x8)
      app(or0(),x7) -> or1(x7)
      app(and1(x10),x11) -> and2(x10,x11)
      app(and0(),x10) -> and1(x10)
      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(),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:
        not1(not1(x)) -> x
        not1(or2(x,y)) -> and2(not1(x),not1(y))
        not1(and2(x,y)) -> or2(not1(x),not1(y))
        and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
        and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
        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(not0(),x5) -> not1(x5)
        app(or1(x7),x8) -> or2(x7,x8)
        app(or0(),x7) -> or1(x7)
        app(and1(x10),x11) -> and2(x10,x11)
        app(and0(),x10) -> and1(x10)
        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,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
       TRS:
        not1(not1(x)) -> x
        not1(or2(x,y)) -> and2(not1(x),not1(y))
        not1(and2(x,y)) -> or2(not1(x),not1(y))
        and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
        and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
        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(not0(),x5) -> not1(x5)
        app(or1(x7),x8) -> or2(x7,x8)
        app(or0(),x7) -> or1(x7)
        app(and1(x10),x11) -> and2(x10,x11)
        app(and0(),x10) -> and1(x10)
        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:
          not1(not1(x)) -> x
          not1(or2(x,y)) -> and2(not1(x),not1(y))
          not1(and2(x,y)) -> or2(not1(x),not1(y))
          and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
          and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
          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(not0(),x5) -> not1(x5)
          app(or1(x7),x8) -> or2(x7,x8)
          app(or0(),x7) -> or1(x7)
          app(and1(x10),x11) -> and2(x10,x11)
          app(and0(),x10) -> and1(x10)
          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(),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:
        not1(not1(x)) -> x
        not1(or2(x,y)) -> and2(not1(x),not1(y))
        not1(and2(x,y)) -> or2(not1(x),not1(y))
        and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
        and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
        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(not0(),x5) -> not1(x5)
        app(or1(x7),x8) -> or2(x7,x8)
        app(or0(),x7) -> or1(x7)
        app(and1(x10),x11) -> and2(x10,x11)
        app(and0(),x10) -> and1(x10)
        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(),f,x,xs) -> filter{2,#}(f,xs)
          filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
         TRS:
          not1(not1(x)) -> x
          not1(or2(x,y)) -> and2(not1(x),not1(y))
          not1(and2(x,y)) -> or2(not1(x),not1(y))
          and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
          and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
          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(not0(),x5) -> not1(x5)
          app(or1(x7),x8) -> or2(x7,x8)
          app(or0(),x7) -> or1(x7)
          app(and1(x10),x11) -> and2(x10,x11)
          app(and0(),x10) -> and1(x10)
          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:
      not{1,#}(or2(x,y)) -> not{1,#}(y)
      not{1,#}(or2(x,y)) -> not{1,#}(x)
      not{1,#}(and2(x,y)) -> not{1,#}(y)
      not{1,#}(and2(x,y)) -> not{1,#}(x)
     TRS:
      not1(not1(x)) -> x
      not1(or2(x,y)) -> and2(not1(x),not1(y))
      not1(and2(x,y)) -> or2(not1(x),not1(y))
      and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
      and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
      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(not0(),x5) -> not1(x5)
      app(or1(x7),x8) -> or2(x7,x8)
      app(or0(),x7) -> or1(x7)
      app(and1(x10),x11) -> and2(x10,x11)
      app(and0(),x10) -> and1(x10)
      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(not{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        not1(not1(x)) -> x
        not1(or2(x,y)) -> and2(not1(x),not1(y))
        not1(and2(x,y)) -> or2(not1(x),not1(y))
        and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
        and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
        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(not0(),x5) -> not1(x5)
        app(or1(x7),x8) -> or2(x7,x8)
        app(or0(),x7) -> or1(x7)
        app(and1(x10),x11) -> and2(x10,x11)
        app(and0(),x10) -> and1(x10)
        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:
      and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
      and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
      and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
      and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     TRS:
      not1(not1(x)) -> x
      not1(or2(x,y)) -> and2(not1(x),not1(y))
      not1(and2(x,y)) -> or2(not1(x),not1(y))
      and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
      and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
      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(not0(),x5) -> not1(x5)
      app(or1(x7),x8) -> or2(x7,x8)
      app(or0(),x7) -> or1(x7)
      app(and1(x10),x11) -> and2(x10,x11)
      app(and0(),x10) -> and1(x10)
      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)
     Size-Change Termination Processor:
      DPs:
       
      TRS:
       not1(not1(x)) -> x
       not1(or2(x,y)) -> and2(not1(x),not1(y))
       not1(and2(x,y)) -> or2(not1(x),not1(y))
       and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
       and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
       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(not0(),x5) -> not1(x5)
       app(or1(x7),x8) -> or2(x7,x8)
       app(or0(),x7) -> or1(x7)
       app(and1(x10),x11) -> and2(x10,x11)
       app(and0(),x10) -> and1(x10)
       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)
      The DP: and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) has the edges:
        0 >=  0
        1 >   1
      The DP: and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) has the edges:
        0 >=  0
        1 >   1
      The DP: and{2,#}(or2(y,z),x) -> and{2,#}(x,z) has the edges:
        0 >   1
        1 >=  0
      The DP: and{2,#}(or2(y,z),x) -> and{2,#}(x,y) has the edges:
        0 >   1
        1 >=  0
      Qed