Input TRS:
    1: app(app(\\(),x),x) -> e()
    2: app(app(\\(),e()),x) -> x
    3: app(app(\\(),x),app(app(.(),x),y)) -> y
    4: app(app(\\(),app(app(/(),x),y)),x) -> y
    5: app(app(/(),x),x) -> e()
    6: app(app(/(),x),e()) -> x
    7: app(app(/(),app(app(.(),y),x)),x) -> y
    8: app(app(/(),x),app(app(\\(),y),x)) -> y
    9: app(app(.(),e()),x) -> x
    10: app(app(.(),x),e()) -> x
    11: app(app(.(),x),app(app(\\(),x),y)) -> y
    12: app(app(.(),app(app(/(),y),x)),x) -> y
    13: app(app(map(),f),nil()) -> nil()
    14: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    15: app(app(filter(),f),nil()) -> nil()
    16: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    17: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    18: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆2_\\(x,x) -> e()
2: app❆2_\\(e(),x) -> x
3: app❆2_\\(x,app❆2_.(x,y)) -> y
4: app❆2_\\(app❆2_/(x,y),x) -> y
5: app❆2_/(x,x) -> e()
6: app❆2_/(x,e()) -> x
7: app❆2_/(app❆2_.(y,x),x) -> y
8: app❆2_/(x,app❆2_\\(y,x)) -> y
9: app❆2_.(e(),x) -> x
10: app❆2_.(x,e()) -> x
11: app❆2_.(x,app❆2_\\(x,y)) -> y
12: app❆2_.(app❆2_/(y,x),x) -> y
13: app❆2_map(f,nil()) -> nil()
14: app❆2_map(f,app❆2_cons(x,xs)) -> app❆2_cons(app(f,x),app❆2_map(f,xs))
15: app❆2_filter(f,nil()) -> nil()
16: app❆2_filter(f,app❆2_cons(x,xs)) -> app❆4_filter2(app(f,x),f,x,xs)
17: app❆4_filter2(true(),f,x,xs) -> app❆2_cons(x,app❆2_filter(f,xs))
18: app❆4_filter2(false(),f,x,xs) -> app❆2_filter(f,xs)
19: app(cons(),_1) ->= app❆1_cons(_1)
20: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
21: app(/(),_1) ->= app❆1_/(_1)
22: app(app❆1_/(_1),_2) ->= app❆2_/(_1,_2)
23: app(filter(),_1) ->= app❆1_filter(_1)
24: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
25: app(\\(),_1) ->= app❆1_\\(_1)
26: app(app❆1_\\(_1),_2) ->= app❆2_\\(_1,_2)
27: app(map(),_1) ->= app❆1_map(_1)
28: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
29: app(filter2(),_1) ->= app❆1_filter2(_1)
30: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
31: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
32: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
33: app(.(),_1) ->= app❆1_.(_1)
34: app(app❆1_.(_1),_2) ->= app❆2_.(_1,_2)
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #2: #app❆2_map(f,app❆2_cons(x,xs)) -> #app(f,x)
   #3: #app❆2_map(f,app❆2_cons(x,xs)) -> #app❆2_map(f,xs)
   #4: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #5: #app(app❆1_/(_1),_2) ->? #app❆2_/(_1,_2)
   #6: #app(app❆1_.(_1),_2) ->? #app❆2_.(_1,_2)
   #7: #app❆4_filter2(true(),f,x,xs) -> #app❆2_filter(f,xs)
   #8: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #9: #app(app❆1_\\(_1),_2) ->? #app❆2_\\(_1,_2)
   #10: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app❆4_filter2(app(f,x),f,x,xs)
   #11: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app(f,x)
   #12: #app❆4_filter2(false(),f,x,xs) -> #app❆2_filter(f,xs)
Number of SCCs: 1, DPs: 9, edges: 20
	SCC { #1..4 #7 #8 #10..12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_map(x1,x2)	weight: x2
     /()	weight: 0
app❆1_map(x1)	weight: (/ 3 8) + x1
     \\()	weight: 0
app❆4_filter2(x1,x2,x3,x4)	weight: (/ 3 8) + x1 + x4
app❆1_.(x1)	weight: (/ 3 8) + x1
#app❆2_/(x1,x2)	weight: 0
app❆2_map(x1,x2)	weight: (/ 3 8) + x1
app❆2_\\(x1,x2)	weight: (/ 3 8)
 false()	weight: 0
  true()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: (/ 1 2) + x1
#app❆2_.(x1,x2)	weight: 0
app❆1_/(x1)	weight: (/ 3 8) + x1
app❆2_.(x1,x2)	weight: (/ 3 8)
   nil()	weight: 0
app❆1_filter(x1)	weight: (/ 3 8)
 #app(x1,x2)	weight: (/ 1 4) + x2
   map()	weight: 0
#app❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 8) + x4
     .()	weight: 0
app❆2_filter2(x1,x2)	weight: (/ 3 8) + x1 + x2
     e()	weight: 0
#app❆2_filter(x1,x2)	weight: x2
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 3 8) + x1 + x2
app❆2_/(x1,x2)	weight: (/ 3 8)
filter()	weight: 0
app❆1_\\(x1)	weight: (/ 3 8)
app❆1_filter2(x1)	weight: (/ 3 8) + x1
app❆1_cons(x1)	weight: (/ 3 8) + x1
app❆3_filter2(x1,x2,x3)	weight: (/ 3 8) + x1 + x2 + x3
#app❆2_\\(x1,x2)	weight: 0
   app(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #1..4 #7 #8 #10..12
Number of SCCs: 0, DPs: 0, edges: 0
YES