Input TRS:
    1: cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
    2: cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
    3: cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
    4: gr(0(),x) -> false()
    5: gr(s(x),0()) -> true()
    6: gr(s(x),s(y)) -> gr(x,y)
    7: p(0()) -> 0()
    8: p(s(x)) -> x
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #cond2(true(),x,y) -> #cond2(gr(y,0()),x,p(y))
   #2: #cond2(true(),x,y) -> #gr(y,0())
   #3: #cond2(true(),x,y) -> #p(y)
   #4: #gr(s(x),s(y)) -> #gr(x,y)
   #5: #cond2(false(),x,y) -> #cond1(gr(x,0()),p(x),y)
   #6: #cond2(false(),x,y) -> #gr(x,0())
   #7: #cond2(false(),x,y) -> #p(x)
   #8: #cond1(true(),x,y) -> #cond2(gr(y,0()),x,y)
   #9: #cond1(true(),x,y) -> #gr(y,0())
Number of SCCs: 2, DPs: 4, edges: 6
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 cond2(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#cond1(x1,x2,x3)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
 cond1(x1,x2,x3)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
  #gr(x1,x2)	weight: x2
#cond2(x1,x2,x3)	weight: 0
    gr(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #1 #5 #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
 cond2(x1,x2,x3)	weight: 0
     s(x1)	weight: max{0, (/ 3 8) + x1}
#cond1(x1,x2,x3)	weight: max{0, (/ 1 4) + x3}
 false()	weight: (/ 1 4)
   #p(x1)	weight: 0
  true()	weight: (/ 1 2)
 cond1(x1,x2,x3)	weight: 0
     p(x1)	weight: max{0, (- (/ 3 8)) + x1}
     0()	weight: 0
  #gr(x1,x2)	weight: 0
#cond2(x1,x2,x3)	weight: max{0, (- (/ 1 8)) + x1, (/ 1 4) + x3}
    gr(x1,x2)	weight: max{0, (/ 1 4) + x1}
    Usable rules: { 4 5 7 8 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #5 #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
 cond2(x1,x2,x3)	weight: 0
     s(x1)	weight: max{0, (/ 1 2) + x1}
#cond1(x1,x2,x3)	weight: max{0, (- (/ 1 2)) + x1, x2}
 false()	weight: (/ 1 4)
   #p(x1)	weight: 0
  true()	weight: (/ 3 4)
 cond1(x1,x2,x3)	weight: 0
     p(x1)	weight: max{0, (- (/ 1 2)) + x1}
     0()	weight: 0
  #gr(x1,x2)	weight: 0
#cond2(x1,x2,x3)	weight: max{0, (- (/ 1 4)) + x2}
    gr(x1,x2)	weight: max{0, (/ 1 4) + x1}
    Usable rules: { 4 5 7 8 }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0, edges: 0
YES