Input TRS:
    1: ap(ap(g(),x),y) -> y
    2: ap(f(),x) -> ap(f(),app(g(),x))
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 1
    ap(x1,x2)	weight: (/ 1 4) + 2 * x1 + x2
     f()	weight: 0
     g()	weight: 0
   app(x1,x2)	weight: x1 + x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ap
2: ap❆1_f(x) -> ap❆1_f(app(g(),x))
3: ap(f(),_1) ->= ap❆1_f(_1)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 3
    ap(x1,x2)	weight: (/ 1 2) + x1 + x2
     f()	weight: 0
ap❆1_f(x1)	weight: x1
     g()	weight: 0
   app(x1,x2)	weight: x1 + x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #ap❆1_f(x) -> #ap❆1_f(app(g(),x))
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  found.
  #ap❆1_f(x)	-#1->
  #ap❆1_f(app(g(),x))	--->*
  #ap❆1_f(app(g(),x))
  Looping with: [ x := app(g(),x); ]
NO