Input TRS:
    1: app(f(),a()) -> app(f(),b())
    2: app(g(),b()) -> app(g(),a())
    3: app(app(map(),fun),nil()) -> nil()
    4: app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
    5: app(app(filter(),fun),nil()) -> nil()
    6: app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
    7: app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
    8: app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆1_f(a()) -> app❆1_f(b())
2: app❆1_g(b()) -> app❆1_g(a())
3: app❆2_map(fun,nil()) -> nil()
4: app❆2_map(fun,app❆2_cons(x,xs)) -> app❆2_cons(app(fun,x),app❆2_map(fun,xs))
5: app❆2_filter(fun,nil()) -> nil()
6: app❆2_filter(fun,app❆2_cons(x,xs)) -> app❆4_filter2(app(fun,x),fun,x,xs)
7: app❆4_filter2(true(),fun,x,xs) -> app❆2_cons(x,app❆2_filter(fun,xs))
8: app❆4_filter2(false(),fun,x,xs) -> app❆2_filter(fun,xs)
9: app(cons(),_1) ->= app❆1_cons(_1)
10: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
11: app(filter(),_1) ->= app❆1_filter(_1)
12: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
13: app(map(),_1) ->= app❆1_map(_1)
14: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
15: app(g(),_1) ->= app❆1_g(_1)
16: app(f(),_1) ->= app❆1_f(_1)
17: app(filter2(),_1) ->= app❆1_filter2(_1)
18: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
19: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
20: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app❆1_g(b()) -> #app❆1_g(a())
   #2: #app❆2_filter(fun,app❆2_cons(x,xs)) -> #app❆4_filter2(app(fun,x),fun,x,xs)
   #3: #app❆2_filter(fun,app❆2_cons(x,xs)) -> #app(fun,x)
   #4: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #5: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #6: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #7: #app❆4_filter2(true(),fun,x,xs) -> #app❆2_filter(fun,xs)
   #8: #app(f(),_1) ->? #app❆1_f(_1)
   #9: #app❆1_f(a()) -> #app❆1_f(b())
   #10: #app❆4_filter2(false(),fun,x,xs) -> #app❆2_filter(fun,xs)
   #11: #app(g(),_1) ->? #app❆1_g(_1)
   #12: #app❆2_map(fun,app❆2_cons(x,xs)) -> #app(fun,x)
   #13: #app❆2_map(fun,app❆2_cons(x,xs)) -> #app❆2_map(fun,xs)
Number of SCCs: 1, DPs: 8, edges: 15
	SCC { #3..7 #10 #12 #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
#app❆2_map(x1,x2)	weight: (/ 1 4) + x2
app❆1_map(x1)	weight: (/ 1 4)
     b()	weight: 0
app❆4_filter2(x1,x2,x3,x4)	weight: 0
#app❆1_g(x1)	weight: 0
app❆2_map(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
     f()	weight: 0
filter2()	weight: 0
app❆2_filter(x1,x2)	weight: 0
app❆1_f(x1)	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
#app❆1_f(x1)	weight: 0
filter()	weight: 0
app❆1_g(x1)	weight: 0
app❆1_filter2(x1)	weight: 0
app❆1_cons(x1)	weight: 0
app❆3_filter2(x1,x2,x3)	weight: (/ 1 4)
     g()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3..7 #10 #12 #13
Number of SCCs: 0, DPs: 0, edges: 0
YES