Input TRS:
    1: cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
    2: cond2(true(),x,y) -> cond1(y,y)
    3: cond2(false(),x,y) -> cond1(p(x),y)
    4: gr(0(),x) -> false()
    5: gr(s(x),0()) -> true()
    6: gr(s(x),s(y)) -> gr(x,y)
    7: neq(0(),0()) -> false()
    8: neq(0(),s(x)) -> true()
    9: neq(s(x),0()) -> true()
    10: neq(s(x),s(y)) -> neq(x,y)
    11: p(0()) -> 0()
    12: p(s(x)) -> x
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing gr
1: cond1(s(x),y) -> cond2(gr❆1_s(x,y),s(x),y)
2: cond2(true(),x,y) -> cond1(y,y)
3: cond2(false(),x,y) -> cond1(p(x),y)
4: gr❆1_0(x) -> false()
5: gr❆1_s(x,0()) -> true()
6: gr❆1_s(x,s(y)) -> gr(x,y)
7: neq(0(),0()) -> false()
8: neq(0(),s(x)) -> true()
9: neq(s(x),0()) -> true()
10: neq(s(x),s(y)) -> neq(x,y)
11: p(0()) -> 0()
12: p(s(x)) -> x
13: gr(0(),_1) ->= gr❆1_0(_1)
14: gr(s(_1),_2) ->= gr❆1_s(_1,_2)
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #cond2(true(),x,y) -> #cond1(y,y)
   #2: #gr❆1_s(x,s(y)) -> #gr(x,y)
   #3: #gr(0(),_1) ->? #gr❆1_0(_1)
   #4: #gr(s(_1),_2) ->? #gr❆1_s(_1,_2)
   #5: #neq(s(x),s(y)) -> #neq(x,y)
   #6: #cond2(false(),x,y) -> #cond1(p(x),y)
   #7: #cond2(false(),x,y) -> #p(x)
   #8: #cond1(s(x),y) -> #cond2(gr❆1_s(x,y),s(x),y)
   #9: #cond1(s(x),y) -> #gr❆1_s(x,y)
Number of SCCs: 3, DPs: 6, edges: 7
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   neq(x1,x2)	weight: 0
 cond2(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#cond1(x1,x2)	weight: 0
#gr❆1_0(x1)	weight: 0
gr❆1_0(x1)	weight: 0
 false()	weight: 0
gr❆1_s(x1,x2)	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
 cond1(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
  #gr(x1,x2)	weight: 0
 #neq(x1,x2)	weight: x2
#cond2(x1,x2,x3)	weight: 0
#gr❆1_s(x1,x2)	weight: 0
    gr(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 5, edges: 6
	SCC { #2 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   neq(x1,x2)	weight: 0
 cond2(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#cond1(x1,x2)	weight: 0
#gr❆1_0(x1)	weight: 0
gr❆1_0(x1)	weight: 0
 false()	weight: 0
gr❆1_s(x1,x2)	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
 cond1(x1,x2)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
  #gr(x1,x2)	weight: (/ 1 4) + x2
 #neq(x1,x2)	weight: 0
#cond2(x1,x2,x3)	weight: 0
#gr❆1_s(x1,x2)	weight: x2
    gr(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #4
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #1 #6 #8 }
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