Input TRS:
    1: app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆2_F(app❆2_F(f,x),x) -> app❆2_F(app❆1_G(app❆2_F(f,x)),app(f,x))
2: app(G(),_1) ->= app❆1_G(_1)
3: app(F(),_1) ->= app❆1_F(_1)
4: app(app❆1_F(_1),_2) ->= app❆2_F(_1,_2)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app❆2_F(app❆2_F(f,x),x) -> #app❆2_F(app❆1_G(app❆2_F(f,x)),app(f,x))
   #2: #app❆2_F(app❆2_F(f,x),x) -> #app(f,x)
   #3: #app(app❆1_F(_1),_2) ->? #app❆2_F(_1,_2)
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     G()	weight: 0
     F()	weight: 0
app❆2_F(x1,x2)	weight: (/ 1 2) + x1 + x2
app❆1_F(x1)	weight: (/ 1 2) + x1
 #app(x1,x2)	weight: x1
app❆1_G(x1)	weight: 0
#app❆2_F(x1,x2)	weight: x1
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0, edges: 0
YES