Input TRS:
    1: +(x,0()) -> x
    2: +(minus(x),x) -> 0()
    3: minus(0()) -> 0()
    4: minus(minus(x)) -> x
    5: minus(+(x,y)) -> +(minus(y),minus(x))
    6: *(x,1()) -> x
    7: *(x,0()) -> 0()
    8: *(x,+(y,z)) -> +(*(x,y),*(x,z))
    9: *(x,minus(y)) -> minus(*(x,y))
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #*(x,minus(y)) -> #minus(*(x,y))
   #2: #*(x,minus(y)) -> #*(x,y)
   #3: #minus(+(x,y)) -> #+(minus(y),minus(x))
   #4: #minus(+(x,y)) -> #minus(y)
   #5: #minus(+(x,y)) -> #minus(x)
   #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: 5, edges: 13
	SCC { #4 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
 minus(x1)	weight: 0
   #*(x1,x2)	weight: 0
     0()	weight: 0
#minus(x1)	weight: x1
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #5
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #2 #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
 minus(x1)	weight: (/ 1 2) + x1
   #*(x1,x2)	weight: x2
     0()	weight: 0
#minus(x1)	weight: 0
     +(x1,x2)	weight: (/ 1 2) + x1 + x2
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #7 #8
Number of SCCs: 0, DPs: 0, edges: 0
YES