Input TRS:
    1: f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> f(id(s(s(s(s(s(s(s(s(x))))))))),y,y)
    2: id(s(x)) -> s(id(x))
    3: id(0()) -> 0()
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing id
1: f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> f(id❆1_s(s(s(s(s(s(s(s(x)))))))),y,y)
2: id❆1_s(x) -> s(id(x))
3: id❆1_0() -> 0()
4: id(0()) ->= id❆1_0()
5: id(s(_1)) ->= id❆1_s(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #id❆1_s(x) -> #id(x)
   #2: #id(s(_1)) ->? #id❆1_s(_1)
   #3: #f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> #f(id❆1_s(s(s(s(s(s(s(s(x)))))))),y,y)
   #4: #f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> #id❆1_s(s(s(s(s(s(s(s(x))))))))
   #5: #id(0()) ->? #id❆1_0()
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#id❆1_s(x1)	weight: (/ 1 4) + x1
     s(x1)	weight: (/ 1 2) + x1
id❆1_s(x1)	weight: 0
  #id(x1)	weight: x1
id❆1_0()	weight: 0
     f(x1,x2,x3)	weight: 0
#id❆1_0()	weight: 0
     0()	weight: 0
   #f(x1,x2,x3)	weight: 0
    id(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #2
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
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...  failed.
MAYBE