Input TRS:
    1: *(X,+(Y,1())) -> +(*(X,+(Y,*(1(),0()))),X)
    2: *(X,1()) -> X
    3: *(X,0()) -> X
    4: *(X,0()) -> 0()
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #*(X,+(Y,1())) -> #*(X,+(Y,*(1(),0())))
   #2: #*(X,+(Y,1())) -> #*(1(),0())
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.
  #*(X_{1},+(Y_{1},1()))	-#1->
  #*(X_{1},+(Y_{1},*(1(),0())))	--->*
  #*(X_{1},+(Y_{1},1()))
  Looping with: [ Y_{1} := Y_{1}; X_{1} := X_{1}; ]
NO