Input TRS:
    1: cond(true(),x,y) -> cond(gr(x,y),x,add(x,y))
    2: gr(0(),x) -> false()
    3: gr(s(x),0()) -> true()
    4: gr(s(x),s(y)) -> gr(x,y)
    5: add(0(),x) -> x
    6: add(s(x),y) -> s(add(x,y))
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #add(s(x),y) -> #add(x,y)
   #2: #cond(true(),x,y) -> #cond(gr(x,y),x,add(x,y))
   #3: #cond(true(),x,y) -> #gr(x,y)
   #4: #cond(true(),x,y) -> #add(x,y)
   #5: #gr(s(x),s(y)) -> #gr(x,y)
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
  true()	weight: 0
#cond(x1,x2,x3)	weight: 0
     0()	weight: 0
  #gr(x1,x2)	weight: 0
 #add(x1,x2)	weight: x1
   add(x1,x2)	weight: 0
    gr(x1,x2)	weight: 0
  cond(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
  true()	weight: 0
#cond(x1,x2,x3)	weight: 0
     0()	weight: 0
  #gr(x1,x2)	weight: x2
 #add(x1,x2)	weight: 0
   add(x1,x2)	weight: 0
    gr(x1,x2)	weight: 0
  cond(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE