Input TRS:
    1: cond(true(),x,y) -> cond(and(gr(x,|0|()),gr(y,|0|())),p(x),p(y))
    2: and(true(),true()) -> true()
    3: and(x,false()) -> false()
    4: and(false(),x) -> false()
    5: gr(|0|(),|0|()) -> false()
    6: gr(|0|(),x) -> false()
    7: gr(s(x),|0|()) -> true()
    8: gr(s(x),s(y)) -> gr(x,y)
    9: p(|0|()) -> |0|()
    10: p(s(x)) -> x
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #cond(true(),x,y) -> #cond(and(gr(x,|0|()),gr(y,|0|())),p(x),p(y))
   #2: #cond(true(),x,y) -> #and(gr(x,|0|()),gr(y,|0|()))
   #3: #cond(true(),x,y) -> #gr(x,|0|())
   #4: #cond(true(),x,y) -> #gr(y,|0|())
   #5: #cond(true(),x,y) -> #p(x)
   #6: #cond(true(),x,y) -> #p(y)
   #7: #gr(s(x),s(y)) -> #gr(x,y)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
   and(x1,x2)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
     p(x1)	weight: 0
#cond(x1,x2,x3)	weight: 0
  #gr(x1,x2)	weight: x2
    gr(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
  cond(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: max{0, (/ 15 16) + x1}
   and(x1,x2)	weight: max{0, (/ 5 16) + x1, (/ 1 2) + x2}
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: (/ 9 16)
     p(x1)	weight: max{0, (- (/ 1 4)) + x1}
#cond(x1,x2,x3)	weight: max{0, (- (/ 3 16)) + x1, (- (/ 1 8)) + x2, (/ 1 16) + x3}
  #gr(x1,x2)	weight: 0
    gr(x1,x2)	weight: max{0, (- (/ 3 8)) + x1}
 #and(x1,x2)	weight: 0
  cond(x1,x2,x3)	weight: 0
    Usable rules: { 2..7 9 10 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES