Input TRS:
    1: app(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) -> app(app(:(),app(app(:(),x),z)),app(app(:(),app(app(:(),app(app(:(),x),y)),z)),u))
    2: app(app(map(),f),nil()) -> nil()
    3: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    4: app(app(filter(),f),nil()) -> nil()
    5: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    6: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    7: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> app❆2_:(app❆2_:(x,z),app❆2_:(app❆2_:(app❆2_:(x,y),z),u))
2: app❆2_map(f,nil()) -> nil()
3: app❆2_map(f,app❆2_cons(x,xs)) -> app❆2_cons(app(f,x),app❆2_map(f,xs))
4: app❆2_filter(f,nil()) -> nil()
5: app❆2_filter(f,app❆2_cons(x,xs)) -> app❆4_filter2(app(f,x),f,x,xs)
6: app❆4_filter2(true(),f,x,xs) -> app❆2_cons(x,app❆2_filter(f,xs))
7: app❆4_filter2(false(),f,x,xs) -> app❆2_filter(f,xs)
8: app(cons(),_1) ->= app❆1_cons(_1)
9: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
10: app(:(),_1) ->= app❆1_:(_1)
11: app(app❆1_:(_1),_2) ->= app❆2_:(_1,_2)
12: app(filter(),_1) ->= app❆1_filter(_1)
13: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
14: app(map(),_1) ->= app❆1_map(_1)
15: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
16: app(filter2(),_1) ->= app❆1_filter2(_1)
17: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
18: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
19: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app❆4_filter2(true(),f,x,xs) -> #app❆2_filter(f,xs)
   #2: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #3: #app(app❆1_:(_1),_2) ->? #app❆2_:(_1,_2)
   #4: #app❆4_filter2(false(),f,x,xs) -> #app❆2_filter(f,xs)
   #5: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app❆4_filter2(app(f,x),f,x,xs)
   #6: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app(f,x)
   #7: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #8: #app❆2_map(f,app❆2_cons(x,xs)) -> #app(f,x)
   #9: #app❆2_map(f,app❆2_cons(x,xs)) -> #app❆2_map(f,xs)
   #10: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(app❆2_:(x,z),app❆2_:(app❆2_:(app❆2_:(x,y),z),u))
   #11: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(x,z)
   #12: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(app❆2_:(app❆2_:(x,y),z),u)
   #13: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(app❆2_:(x,y),z)
   #14: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(x,y)
   #15: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
Number of SCCs: 2, DPs: 13, edges: 40
	SCC { #1 #2 #4 #6..9 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_map(x1,x2)	weight: (/ 1 4) + x2
app❆1_map(x1)	weight: (/ 1 4)
app❆4_filter2(x1,x2,x3,x4)	weight: 0
app❆2_map(x1,x2)	weight: 0
 false()	weight: 0
app❆2_:(x1,x2)	weight: 0
     C()	weight: 0
app❆1_:(x1)	weight: 0
  true()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: 0
     :()	weight: 0
   nil()	weight: 0
app❆1_filter(x1)	weight: (/ 1 4)
 #app(x1,x2)	weight: (/ 1 2) + x2
   map()	weight: 0
#app❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 4) + x4
app❆2_filter2(x1,x2)	weight: 0
#app❆2_filter(x1,x2)	weight: x2
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 3 4) + x1 + x2
filter()	weight: 0
app❆1_filter2(x1)	weight: 0
#app❆2_:(x1,x2)	weight: 0
app❆1_cons(x1)	weight: 0
app❆3_filter2(x1,x2,x3)	weight: (/ 1 4)
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #2 #4 #6..9 #15
Number of SCCs: 1, DPs: 5, edges: 25
	SCC { #10..14 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#app❆2_map(x1,x2)	weight: 0
app❆1_map(x1)	weight: 0
app❆4_filter2(x1,x2,x3,x4)	weight: 0
app❆2_map(x1,x2)	weight: 0
 false()	weight: 0
app❆2_:(x1,x2)	weight: max{x2, (/ 1 8) + x1}
     C()	weight: 0
app❆1_:(x1)	weight: 0
  true()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: 0
     :()	weight: 0
   nil()	weight: 0
app❆1_filter(x1)	weight: 0
 #app(x1,x2)	weight: 0
   map()	weight: 0
#app❆4_filter2(x1,x2,x3,x4)	weight: 0
app❆2_filter2(x1,x2)	weight: 0
#app❆2_filter(x1,x2)	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: 0
filter()	weight: 0
app❆1_filter2(x1)	weight: 0
#app❆2_:(x1,x2)	weight: max{0, (/ 1 8) + x1}
app❆1_cons(x1)	weight: 0
app❆3_filter2(x1,x2,x3)	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { 1 }
    Removed DPs: #11 #13 #14
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #10 #12 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
#app❆2_map(x1,x2)	status: []	precedence above:
app❆1_map(x1)	status: []	precedence above:
app❆4_filter2(x1,x2,x3,x4)	status: [x2]	precedence above:
app❆2_map(x1,x2)	status: [x1,x2]	precedence above:
 false()	status: []	precedence above:
app❆2_:(x1,x2)	status: [x1,x2]	precedence above: #app❆2_:
     C()	status: []	precedence above:
app❆1_:(x1)	status: []	precedence above:
  true()	status: []	precedence above:
filter2()	status: []	precedence above:
app❆2_filter(x1,x2)	status: [x2]	precedence above:
     :()	status: []	precedence above:
   nil()	status: []	precedence above:
app❆1_filter(x1)	status: []	precedence above:
 #app(x1,x2)	status: [x1,x2]	precedence above:
   map()	status: []	precedence above:
#app❆4_filter2(x1,x2,x3,x4)	status: [x1,x3,x4,x2]	precedence above:
app❆2_filter2(x1,x2)	status: [x2,x1]	precedence above:
#app❆2_filter(x1,x2)	status: []	precedence above:
  cons()	status: []	precedence above:
app❆2_cons(x1,x2)	status: [x2,x1]	precedence above:
filter()	status: []	precedence above:
app❆1_filter2(x1)	status: []	precedence above:
#app❆2_:(x1,x2)	status: [x1]	precedence above: app❆2_:
app❆1_cons(x1)	status: []	precedence above:
app❆3_filter2(x1,x2,x3)	status: []	precedence above:
   app(x1,x2)	status: [x2]	precedence above:
    Usable rules: { 1 }
    Removed DPs: #10
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #12 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
#app❆2_map(x1,x2)	status: []	precedence above:
app❆1_map(x1)	status: []	precedence above:
app❆4_filter2(x1,x2,x3,x4)	status: [x2]	precedence above:
app❆2_map(x1,x2)	status: [x1,x2]	precedence above:
 false()	status: []	precedence above:
app❆2_:(x1,x2)	status: [x1,x2]	precedence above:
     C()	status: []	precedence above:
app❆1_:(x1)	status: []	precedence above:
  true()	status: []	precedence above:
filter2()	status: []	precedence above:
app❆2_filter(x1,x2)	status: [x2]	precedence above:
     :()	status: []	precedence above:
   nil()	status: []	precedence above:
app❆1_filter(x1)	status: []	precedence above:
 #app(x1,x2)	status: [x1,x2]	precedence above:
   map()	status: []	precedence above:
#app❆4_filter2(x1,x2,x3,x4)	status: [x1,x3,x4,x2]	precedence above:
app❆2_filter2(x1,x2)	status: [x2,x1]	precedence above:
#app❆2_filter(x1,x2)	status: []	precedence above:
  cons()	status: []	precedence above:
app❆2_cons(x1,x2)	status: [x2,x1]	precedence above:
filter()	status: []	precedence above:
app❆1_filter2(x1)	status: []	precedence above:
#app❆2_:(x1,x2)	status: [x1]	precedence above: app❆2_:
app❆1_cons(x1)	status: []	precedence above:
app❆3_filter2(x1,x2,x3)	status: []	precedence above:
   app(x1,x2)	status: [x2]	precedence above:
    Usable rules: { 1 }
    Removed DPs: #12
Number of SCCs: 0, DPs: 0, edges: 0
YES