Input TRS:
    1: +(0(),y) -> y
    2: +(s(x),y) -> s(+(x,y))
    3: +(p(x),y) -> p(+(x,y))
    4: minus(0()) -> 0()
    5: minus(s(x)) -> p(minus(x))
    6: minus(p(x)) -> s(minus(x))
    7: *(0(),y) -> 0()
    8: *(s(x),y) -> +(*(x,y),y)
    9: *(p(x),y) -> +(*(x,y),minus(y))
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(s(x),y) -> #+(x,y)
   #2: #minus(p(x)) -> #minus(x)
   #3: #*(p(x),y) -> #+(*(x,y),minus(y))
   #4: #*(p(x),y) -> #*(x,y)
   #5: #*(p(x),y) -> #minus(y)
   #6: #minus(s(x)) -> #minus(x)
   #7: #+(p(x),y) -> #+(x,y)
   #8: #*(s(x),y) -> #+(*(x,y),y)
   #9: #*(s(x),y) -> #*(x,y)
Number of SCCs: 3, DPs: 6, edges: 12
	SCC { #2 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 minus(x1)	weight: 0
   #*(x1,x2)	weight: 0
     p(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#minus(x1)	weight: x1
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #6
Number of SCCs: 2, DPs: 4, edges: 8
	SCC { #1 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 minus(x1)	weight: 0
   #*(x1,x2)	weight: 0
     p(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#minus(x1)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #7
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #4 #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 minus(x1)	weight: 0
   #*(x1,x2)	weight: x1
     p(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#minus(x1)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #9
Number of SCCs: 0, DPs: 0, edges: 0
YES