Input TRS:
    1: app(app(twice(),f),x) -> app(f,app(f,x))
    2: app(app(map(),f),nil()) -> nil()
    3: app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
    4: app(app(fmap(),nil()),x) -> nil()
    5: app(app(fmap(),app(app(cons(),f),t_f())),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆2_twice(f,x) -> app(f,app(f,x))
2: app❆2_map(f,nil()) -> nil()
3: app❆2_map(f,app❆2_cons(h,t)) -> app❆2_cons(app(f,h),app❆2_map(f,t))
4: app❆2_fmap(nil(),x) -> nil()
5: app❆2_fmap(app❆2_cons(f,t_f()),x) -> app❆2_cons(app(f,x),app❆2_fmap(t_f(),x))
6: app(fmap(),_1) ->= app❆1_fmap(_1)
7: app(app❆1_fmap(_1),_2) ->= app❆2_fmap(_1,_2)
8: app(cons(),_1) ->= app❆1_cons(_1)
9: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
10: app(twice(),_1) ->= app❆1_twice(_1)
11: app(app❆1_twice(_1),_2) ->= app❆2_twice(_1,_2)
12: app(map(),_1) ->= app❆1_map(_1)
13: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #2: #app(app❆1_twice(_1),_2) ->? #app❆2_twice(_1,_2)
   #3: #app(app❆1_fmap(_1),_2) ->? #app❆2_fmap(_1,_2)
   #4: #app❆2_fmap(app❆2_cons(f,t_f()),x) -> #app(f,x)
   #5: #app❆2_fmap(app❆2_cons(f,t_f()),x) -> #app❆2_fmap(t_f(),x)
   #6: #app❆2_map(f,app❆2_cons(h,t)) -> #app(f,h)
   #7: #app❆2_map(f,app❆2_cons(h,t)) -> #app❆2_map(f,t)
   #8: #app❆2_twice(f,x) -> #app(f,app(f,x))
   #9: #app❆2_twice(f,x) -> #app(f,x)
Number of SCCs: 1, DPs: 8, edges: 19
	SCC { #1..4 #6..9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_map(x1,x2)	weight: (/ 1 4) + x1
   t_f()	weight: 0
app❆2_fmap(x1,x2)	weight: (/ 1 2) + x2
#app❆2_twice(x1,x2)	weight: x1
app❆1_map(x1)	weight: (/ 1 2) + x1
 twice()	weight: 0
app❆1_fmap(x1)	weight: (/ 1 2) + x1
app❆2_map(x1,x2)	weight: (/ 1 2) + x1 + x2
app❆2_twice(x1,x2)	weight: (/ 1 2) + x2
  fmap()	weight: 0
#app❆2_fmap(x1,x2)	weight: x1
   nil()	weight: 0
 #app(x1,x2)	weight: x1
   map()	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 2) + x1 + x2
app❆1_cons(x1)	weight: (/ 1 2) + x1
app❆1_twice(x1)	weight: x1
   app(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #1 #3 #4 #6
Number of SCCs: 2, DPs: 4, edges: 5
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_map(x1,x2)	weight: (/ 1 4) + x2
   t_f()	weight: 0
app❆2_fmap(x1,x2)	weight: (/ 1 2) + x2
#app❆2_twice(x1,x2)	weight: 0
app❆1_map(x1)	weight: (/ 1 2) + x1
 twice()	weight: 0
app❆1_fmap(x1)	weight: (/ 1 2) + x1
app❆2_map(x1,x2)	weight: (/ 1 2) + x1 + x2
app❆2_twice(x1,x2)	weight: (/ 1 2) + x2
  fmap()	weight: 0
#app❆2_fmap(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: 0
   map()	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 2) + x1 + x2
app❆1_cons(x1)	weight: (/ 1 2) + x1
app❆1_twice(x1)	weight: x1
   app(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #2 #8 #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_map(x1,x2)	weight: (/ 1 4)
   t_f()	weight: 0
app❆2_fmap(x1,x2)	weight: (/ 3 4) + x2
#app❆2_twice(x1,x2)	weight: (/ 1 4) + x1
app❆1_map(x1)	weight: (/ 3 4) + x1
 twice()	weight: 0
app❆1_fmap(x1)	weight: (/ 3 4) + x1
app❆2_map(x1,x2)	weight: (/ 3 4) + x1 + x2
app❆2_twice(x1,x2)	weight: (/ 3 4) + x2
  fmap()	weight: 0
#app❆2_fmap(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: x1
   map()	weight: 0
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 3 4) + x1 + x2
app❆1_cons(x1)	weight: (/ 3 4) + x1
app❆1_twice(x1)	weight: (/ 1 2) + x1
   app(x1,x2)	weight: (/ 1 2)
    Usable rules: { }
    Removed DPs: #2 #8 #9
Number of SCCs: 0, DPs: 0, edges: 0
YES