Input TRS:
    1: app(D(),t()) -> 1()
    2: app(D(),constant()) -> 0()
    3: app(D(),app(app(+(),x),y)) -> app(app(+(),app(D(),x)),app(D(),y))
    4: app(D(),app(app(*(),x),y)) -> app(app(+(),app(app(*(),y),app(D(),x))),app(app(*(),x),app(D(),y)))
    5: app(D(),app(app(-(),x),y)) -> app(app(-(),app(D(),x)),app(D(),y))
    6: app(app(map(),f),nil()) -> nil()
    7: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    8: app(app(filter(),f),nil()) -> nil()
    9: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    10: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    11: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆1_D(t()) -> 1()
2: app❆1_D(constant()) -> 0()
3: app❆1_D(app❆2_+(x,y)) -> app❆2_+(app❆1_D(x),app❆1_D(y))
4: app❆1_D(app❆2_*(x,y)) -> app❆2_+(app❆2_*(y,app❆1_D(x)),app❆2_*(x,app❆1_D(y)))
5: app❆1_D(app❆2_-(x,y)) -> app❆2_-(app❆1_D(x),app❆1_D(y))
6: app❆2_map(f,nil()) -> nil()
7: app❆2_map(f,app❆2_cons(x,xs)) -> app❆2_cons(app(f,x),app❆2_map(f,xs))
8: app❆2_filter(f,nil()) -> nil()
9: app❆2_filter(f,app❆2_cons(x,xs)) -> app❆4_filter2(app(f,x),f,x,xs)
10: app❆4_filter2(true(),f,x,xs) -> app❆2_cons(x,app❆2_filter(f,xs))
11: app❆4_filter2(false(),f,x,xs) -> app❆2_filter(f,xs)
12: app(cons(),_1) ->= app❆1_cons(_1)
13: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
14: app(filter(),_1) ->= app❆1_filter(_1)
15: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
16: app(+(),_1) ->= app❆1_+(_1)
17: app(app❆1_+(_1),_2) ->= app❆2_+(_1,_2)
18: app(-(),_1) ->= app❆1_-(_1)
19: app(app❆1_-(_1),_2) ->= app❆2_-(_1,_2)
20: app(map(),_1) ->= app❆1_map(_1)
21: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
22: app(D(),_1) ->= app❆1_D(_1)
23: app(filter2(),_1) ->= app❆1_filter2(_1)
24: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
25: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
26: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
27: app(*(),_1) ->= app❆1_*(_1)
28: app(app❆1_*(_1),_2) ->= app❆2_*(_1,_2)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app❆4_filter2(app(f,x),f,x,xs)
   #2: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app(f,x)
   #3: #app❆4_filter2(false(),f,x,xs) -> #app❆2_filter(f,xs)
   #4: #app❆2_map(f,app❆2_cons(x,xs)) -> #app(f,x)
   #5: #app❆2_map(f,app❆2_cons(x,xs)) -> #app❆2_map(f,xs)
   #6: #app❆4_filter2(true(),f,x,xs) -> #app❆2_filter(f,xs)
   #7: #app❆1_D(app❆2_-(x,y)) -> #app❆1_D(x)
   #8: #app❆1_D(app❆2_-(x,y)) -> #app❆1_D(y)
   #9: #app(D(),_1) ->? #app❆1_D(_1)
   #10: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #11: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #12: #app❆1_D(app❆2_+(x,y)) -> #app❆1_D(x)
   #13: #app❆1_D(app❆2_+(x,y)) -> #app❆1_D(y)
   #14: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #15: #app❆1_D(app❆2_*(x,y)) -> #app❆1_D(x)
   #16: #app❆1_D(app❆2_*(x,y)) -> #app❆1_D(y)
Number of SCCs: 2, DPs: 14, edges: 51
	SCC { #7 #8 #12 #13 #15 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
#app❆2_map(x1,x2)	weight: 0
app❆1_map(x1)	weight: 0
constant()	weight: 0
app❆4_filter2(x1,x2,x3,x4)	weight: 0
app❆2_*(x1,x2)	weight: (/ 1 2) + x1 + x2
app❆2_map(x1,x2)	weight: 0
     t()	weight: 0
 false()	weight: 0
app❆1_D(x1)	weight: 0
app❆1_-(x1)	weight: 0
     D()	weight: 0
app❆2_-(x1,x2)	weight: (/ 1 2) + x1 + x2
  true()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: 0
     0()	weight: 0
app❆2_+(x1,x2)	weight: (/ 1 2) + x1 + x2
   nil()	weight: 0
app❆1_filter(x1)	weight: 0
     -()	weight: 0
 #app(x1,x2)	weight: 0
   map()	weight: 0
#app❆4_filter2(x1,x2,x3,x4)	weight: 0
#app❆1_D(x1)	weight: x1
app❆2_filter2(x1,x2)	weight: 0
#app❆2_filter(x1,x2)	weight: 0
app❆1_*(x1)	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: 0
filter()	weight: 0
     +()	weight: 0
app❆1_+(x1)	weight: 0
app❆1_filter2(x1)	weight: 0
app❆1_cons(x1)	weight: 0
app❆3_filter2(x1,x2,x3)	weight: 0
     *()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7 #8 #12 #13 #15 #16
Number of SCCs: 1, DPs: 8, edges: 15
	SCC { #2..6 #10 #11 #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
#app❆2_map(x1,x2)	weight: (/ 1 4) + x1
app❆1_map(x1)	weight: (/ 1 2) + x1
constant()	weight: 0
app❆4_filter2(x1,x2,x3,x4)	weight: 0
app❆2_*(x1,x2)	weight: (/ 1 4)
app❆2_map(x1,x2)	weight: 0
     t()	weight: 0
 false()	weight: 0
app❆1_D(x1)	weight: 0
app❆1_-(x1)	weight: 0
     D()	weight: 0
app❆2_-(x1,x2)	weight: (/ 1 4)
  true()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: 0
     0()	weight: 0
app❆2_+(x1,x2)	weight: (/ 1 4)
   nil()	weight: 0
app❆1_filter(x1)	weight: (/ 1 2) + x1
     -()	weight: 0
 #app(x1,x2)	weight: x1
   map()	weight: 0
#app❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 2) + x2
#app❆1_D(x1)	weight: 0
app❆2_filter2(x1,x2)	weight: 0
#app❆2_filter(x1,x2)	weight: (/ 1 4) + x1
app❆1_*(x1)	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 4)
filter()	weight: 0
     +()	weight: 0
app❆1_+(x1)	weight: 0
app❆1_filter2(x1)	weight: 0
app❆1_cons(x1)	weight: 0
app❆3_filter2(x1,x2,x3)	weight: (/ 3 4) + x2
     *()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2..4 #6 #10 #11 #14
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
#app❆2_map(x1,x2)	weight: (/ 1 4) + x2
app❆1_map(x1)	weight: (/ 1 2)
constant()	weight: 0
app❆4_filter2(x1,x2,x3,x4)	weight: 0
app❆2_*(x1,x2)	weight: (/ 1 4)
app❆2_map(x1,x2)	weight: 0
     t()	weight: 0
 false()	weight: 0
app❆1_D(x1)	weight: 0
app❆1_-(x1)	weight: 0
     D()	weight: 0
app❆2_-(x1,x2)	weight: (/ 1 4)
  true()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: 0
     0()	weight: 0
app❆2_+(x1,x2)	weight: (/ 1 4)
   nil()	weight: 0
app❆1_filter(x1)	weight: (/ 1 2)
     -()	weight: 0
 #app(x1,x2)	weight: 0
   map()	weight: 0
#app❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 2)
#app❆1_D(x1)	weight: 0
app❆2_filter2(x1,x2)	weight: 0
#app❆2_filter(x1,x2)	weight: (/ 1 4)
app❆1_*(x1)	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 4) + x2
filter()	weight: 0
     +()	weight: 0
app❆1_+(x1)	weight: 0
app❆1_filter2(x1)	weight: 0
app❆1_cons(x1)	weight: 0
app❆3_filter2(x1,x2,x3)	weight: (/ 3 4)
     *()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0, edges: 0
YES