Input TRS:
    1: app(app(mapt(),f),app(leaf(),x)) -> app(leaf(),app(f,x))
    2: app(app(mapt(),f),app(node(),xs)) -> app(node(),app(app(maptlist(),f),xs))
    3: app(app(maptlist(),f),nil()) -> nil()
    4: app(app(maptlist(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆2_mapt(f,app❆1_leaf(x)) -> app❆1_leaf(app(f,x))
2: app❆2_mapt(f,app❆1_node(xs)) -> app❆1_node(app❆2_maptlist(f,xs))
3: app❆2_maptlist(f,nil()) -> nil()
4: app❆2_maptlist(f,app❆2_cons(x,xs)) -> app❆2_cons(app❆2_mapt(f,x),app❆2_maptlist(f,xs))
5: app(cons(),_1) ->= app❆1_cons(_1)
6: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
7: app(maptlist(),_1) ->= app❆1_maptlist(_1)
8: app(app❆1_maptlist(_1),_2) ->= app❆2_maptlist(_1,_2)
9: app(leaf(),_1) ->= app❆1_leaf(_1)
10: app(mapt(),_1) ->= app❆1_mapt(_1)
11: app(app❆1_mapt(_1),_2) ->= app❆2_mapt(_1,_2)
12: app(node(),_1) ->= app❆1_node(_1)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app❆2_mapt(f,app❆1_node(xs)) -> #app❆2_maptlist(f,xs)
   #2: #app(app❆1_mapt(_1),_2) ->? #app❆2_mapt(_1,_2)
   #3: #app❆2_mapt(f,app❆1_leaf(x)) -> #app(f,x)
   #4: #app(app❆1_maptlist(_1),_2) ->? #app❆2_maptlist(_1,_2)
   #5: #app❆2_maptlist(f,app❆2_cons(x,xs)) -> #app❆2_mapt(f,x)
   #6: #app❆2_maptlist(f,app❆2_cons(x,xs)) -> #app❆2_maptlist(f,xs)
Number of SCCs: 1, DPs: 6, edges: 12
	SCC { #1..6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
app❆1_node(x1)	weight: (/ 1 4) + x1
  mapt()	weight: 0
#app❆2_maptlist(x1,x2)	weight: x2
maptlist()	weight: 0
app❆2_maptlist(x1,x2)	weight: 0
app❆1_mapt(x1)	weight: (/ 1 4)
app❆1_maptlist(x1)	weight: (/ 1 4)
#app❆2_mapt(x1,x2)	weight: x2
   nil()	weight: 0
 #app(x1,x2)	weight: (/ 1 4) + x2
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 4) + x1 + x2
  leaf()	weight: 0
app❆2_mapt(x1,x2)	weight: 0
app❆1_cons(x1)	weight: 0
  node()	weight: 0
   app(x1,x2)	weight: 0
app❆1_leaf(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #1..6
Number of SCCs: 0, DPs: 0, edges: 0
YES