Input TRS:
    1: +(x,0()) -> x
    2: +(x,i(x)) -> 0()
    3: +(+(x,y),z) -> +(x,+(y,z))
    4: *(x,+(y,z)) -> +(*(x,y),*(x,z))
    5: *(+(x,y),z) -> +(*(x,z),*(y,z))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #*(+(x,y),z) -> #+(*(x,z),*(y,z))
   #2: #*(+(x,y),z) -> #*(x,z)
   #3: #*(+(x,y),z) -> #*(y,z)
   #4: #+(+(x,y),z) -> #+(x,+(y,z))
   #5: #+(+(x,y),z) -> #+(y,z)
   #6: #*(x,+(y,z)) -> #+(*(x,y),*(x,z))
   #7: #*(x,+(y,z)) -> #*(x,y)
   #8: #*(x,+(y,z)) -> #*(x,z)
Number of SCCs: 2, DPs: 6, edges: 20
	SCC { #4 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #*(x1,x2)	weight: 0
     0()	weight: 0
     i(x1)	weight: (/ 1 4) + x1
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #5
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #2 #3 #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #*(x1,x2)	weight: x1
     0()	weight: 0
     i(x1)	weight: (/ 1 4) + x1
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #3
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   #*(x1,x2)	weight: x2
     0()	weight: 0
     i(x1)	weight: (/ 1 4) + x1
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7 #8
Number of SCCs: 0, DPs: 0, edges: 0
YES