Input TRS:
    1: +(1(),x) -> +(+(0(),1()),x)
    2: +(0(),x) -> x
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing +
1: +❆1_1(x) -> +(+❆1_0(1()),x)
2: +❆1_0(x) -> x
3: +(1(),_1) ->= +❆1_1(_1)
4: +(0(),_1) ->= +❆1_0(_1)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 4
     1()	weight: 0
+❆1_0(x1)	weight: x1
+❆1_1(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #+(1(),_1) ->? #+❆1_1(_1)
   #2: #+❆1_1(x) -> #+(+❆1_0(1()),x)
   #3: #+❆1_1(x) -> #+❆1_0(1())
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #2 }
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.
  #+(1(),_1_{2})	-#1->
  #+❆1_1(_1_{2})	--->*
  #+❆1_1(_1_{2})	-#2->
  #+(+❆1_0(1()),_1_{2})	--->*
  #+(1(),_1_{2})
  Looping with: [ _1_{2} := _1_{2}; ]
NO