Input TRS:
    1: minus(0()) -> 0()
    2: +(x,0()) -> x
    3: +(0(),y) -> y
    4: +(minus(1()),1()) -> 0()
    5: minus(minus(x)) -> x
    6: +(x,minus(y)) -> minus(+(minus(x),y))
    7: +(x,+(y,z)) -> +(+(x,y),z)
    8: +(minus(+(x,1())),1()) -> minus(x)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 7 2
     1()	weight: 0
 minus(x1)	weight: 2438 + x1
     0()	weight: 0
     +(x1,x2)	weight: 21239 + x1 + 2 * x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(x,minus(y)) -> #+(minus(x),y)
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
 minus(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES