Input TRS:
    1: *(x,+(y,z)) -> +(*(x,y),*(x,z))
    2: *(+(x,y),z) -> +(*(x,z),*(y,z))
    3: *(x,1()) -> x
    4: *(1(),y) -> y
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #*(+(x,y),z) -> #*(x,z)
   #2: #*(+(x,y),z) -> #*(y,z)
   #3: #*(x,+(y,z)) -> #*(x,y)
   #4: #*(x,+(y,z)) -> #*(x,z)
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #1..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #*(x1,x2)	weight: x1
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #2
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #3 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   #*(x1,x2)	weight: x2
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3 #4
Number of SCCs: 0, DPs: 0, edges: 0
YES