Input TRS:
    1: p(|0|()) -> |0|()
    2: p(s(x)) -> x
    3: le(|0|(),y) -> true()
    4: le(s(x),|0|()) -> false()
    5: le(s(x),s(y)) -> le(x,y)
    6: minus(x,|0|()) -> x
    7: minus(x,s(y)) -> if(le(x,s(y)),|0|(),p(minus(x,p(s(y)))))
    8: if(true(),x,y) -> x
    9: if(false(),x,y) -> y
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing p
1: p❆1_|0|() -> |0|()
2: p❆1_s(x) -> x
3: le(|0|(),y) -> true()
4: le(s(x),|0|()) -> false()
5: le(s(x),s(y)) -> le(x,y)
6: minus(x,|0|()) -> x
7: minus(x,s(y)) -> if(le(x,s(y)),|0|(),p(minus(x,p❆1_s(y))))
8: if(true(),x,y) -> x
9: if(false(),x,y) -> y
10: p(|0|()) ->= p❆1_|0|()
11: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #p(s(_1)) ->? #p❆1_s(_1)
   #2: #minus(x,s(y)) -> #if(le(x,s(y)),|0|(),p(minus(x,p❆1_s(y))))
   #3: #minus(x,s(y)) -> #le(x,s(y))
   #4: #minus(x,s(y)) -> #p(minus(x,p❆1_s(y)))
   #5: #minus(x,s(y)) -> #minus(x,p❆1_s(y))
   #6: #minus(x,s(y)) -> #p❆1_s(y)
   #7: #p(|0|()) ->? #p❆1_|0|()
   #8: #le(s(x),s(y)) -> #le(x,y)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: x2
 minus(x1,x2)	weight: 0
p❆1_s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
p❆1_|0|()	weight: 0
#p❆1_s(x1)	weight: 0
  true()	weight: 0
     p(x1)	weight: 0
    if(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#p❆1_|0|()	weight: 0
  #if(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
    le(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: 0
 minus(x1,x2)	weight: 0
p❆1_s(x1)	weight: (/ 1 4) + x1
 false()	weight: 0
   #p(x1)	weight: 0
p❆1_|0|()	weight: 0
#p❆1_s(x1)	weight: 0
  true()	weight: 0
     p(x1)	weight: 0
    if(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: x2
#p❆1_|0|()	weight: 0
  #if(x1,x2,x3)	weight: 0
    Usable rules: { 2 }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0, edges: 0
YES