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