Input TRS:
    1: app(app(plus(),0()),y) -> y
    2: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    3: app(app(app(curry(),f),x),y) -> app(app(f,x),y)
    4: add() -> app(curry(),plus())
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆2_plus(0(),y) -> y
2: app❆2_plus(app❆1_s(x),y) -> app❆1_s(app❆2_plus(x,y))
3: app❆3_curry(f,x,y) -> app(app(f,x),y)
4: add() -> app❆1_curry(plus())
5: app(plus(),_1) ->= app❆1_plus(_1)
6: app(app❆1_plus(_1),_2) ->= app❆2_plus(_1,_2)
7: app(curry(),_1) ->= app❆1_curry(_1)
8: app(app❆1_curry(_1),_2) ->= app❆2_curry(_1,_2)
9: app(app❆2_curry(_1,_2),_3) ->= app❆3_curry(_1,_2,_3)
10: app(s(),_1) ->= app❆1_s(_1)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 1 5 10 7 6 2
     s()	weight: 0
app❆1_plus(x1)	weight: (/ 1 4) + 2 * x1
app❆2_plus(x1,x2)	weight: (/ 61225 2) + 2 * x1 + x2
 curry()	weight: 0
app❆3_curry(x1,x2,x3)	weight: 61225 + x1 + 2 * x2 + 2 * x3
     0()	weight: 0
app❆1_curry(x1)	weight: x1
  plus()	weight: 0
app❆2_curry(x1,x2)	weight: (/ 61225 2) + x1 + 2 * x2
   add()	weight: 0
app❆1_s(x1)	weight: (/ 1 4) + x1
   app(x1,x2)	weight: (/ 61225 2) + x1 + 2 * x2
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app(app❆2_curry(_1,_2),_3) ->? #app❆3_curry(_1,_2,_3)
   #2: #app❆3_curry(f,x,y) -> #app(app(f,x),y)
   #3: #app❆3_curry(f,x,y) -> #app(f,x)
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #1..3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆3_curry(x1,x2,x3)	weight: (/ 1 2) + x1
     s()	weight: 0
app❆1_plus(x1)	weight: 0
app❆2_plus(x1,x2)	weight: 0
 curry()	weight: 0
app❆3_curry(x1,x2,x3)	weight: (/ 1 2) + x1
     0()	weight: 0
 #app(x1,x2)	weight: x1
app❆1_curry(x1)	weight: (/ 1 2) + x1
  plus()	weight: 0
app❆2_curry(x1,x2)	weight: (/ 3 4) + x1
 #add()	weight: 0
   add()	weight: 0
app❆1_s(x1)	weight: 0
   app(x1,x2)	weight: (/ 1 4) + x1
    Usable rules: { 3 8 9 }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0, edges: 0
YES