Input TRS:
    1: cond1(true(),x,y) -> cond2(gr(x,y),x,y)
    2: cond2(true(),x,y) -> cond3(gr(x,0()),x,y)
    3: cond2(false(),x,y) -> cond4(gr(y,0()),x,y)
    4: cond3(true(),x,y) -> cond3(gr(x,0()),p(x),y)
    5: cond3(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
    6: cond4(true(),x,y) -> cond4(gr(y,0()),x,p(y))
    7: cond4(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
    8: gr(0(),x) -> false()
    9: gr(s(x),0()) -> true()
    10: gr(s(x),s(y)) -> gr(x,y)
    11: and(true(),true()) -> true()
    12: and(false(),x) -> false()
    13: and(x,false()) -> false()
    14: p(0()) -> 0()
    15: p(s(x)) -> x
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #cond2(true(),x,y) -> #cond3(gr(x,0()),x,y)
   #2: #cond2(true(),x,y) -> #gr(x,0())
   #3: #cond4(true(),x,y) -> #cond4(gr(y,0()),x,p(y))
   #4: #cond4(true(),x,y) -> #gr(y,0())
   #5: #cond4(true(),x,y) -> #p(y)
   #6: #cond4(false(),x,y) -> #cond1(and(gr(x,0()),gr(y,0())),x,y)
   #7: #cond4(false(),x,y) -> #and(gr(x,0()),gr(y,0()))
   #8: #cond4(false(),x,y) -> #gr(x,0())
   #9: #cond4(false(),x,y) -> #gr(y,0())
   #10: #gr(s(x),s(y)) -> #gr(x,y)
   #11: #cond3(false(),x,y) -> #cond1(and(gr(x,0()),gr(y,0())),x,y)
   #12: #cond3(false(),x,y) -> #and(gr(x,0()),gr(y,0()))
   #13: #cond3(false(),x,y) -> #gr(x,0())
   #14: #cond3(false(),x,y) -> #gr(y,0())
   #15: #cond2(false(),x,y) -> #cond4(gr(y,0()),x,y)
   #16: #cond2(false(),x,y) -> #gr(y,0())
   #17: #cond1(true(),x,y) -> #cond2(gr(x,y),x,y)
   #18: #cond1(true(),x,y) -> #gr(x,y)
   #19: #cond3(true(),x,y) -> #cond3(gr(x,0()),p(x),y)
   #20: #cond3(true(),x,y) -> #gr(x,0())
   #21: #cond3(true(),x,y) -> #p(x)
Number of SCCs: 2, DPs: 8, edges: 13
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 cond2(x1,x2,x3)	weight: 0
#cond3(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#cond1(x1,x2,x3)	weight: 0
   and(x1,x2)	weight: 0
#cond4(x1,x2,x3)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
 cond4(x1,x2,x3)	weight: 0
  true()	weight: 0
 cond1(x1,x2,x3)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
  #gr(x1,x2)	weight: x2
 cond3(x1,x2,x3)	weight: 0
#cond2(x1,x2,x3)	weight: 0
    gr(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 7, edges: 12
	SCC { #1 #3 #6 #11 #15 #17 #19 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
 cond2(x1,x2,x3)	weight: 0
#cond3(x1,x2,x3)	weight: max{0, x3}
     s(x1)	weight: max{0, (/ 1 4) + x1}
#cond1(x1,x2,x3)	weight: max{0, x3}
   and(x1,x2)	weight: 0
#cond4(x1,x2,x3)	weight: max{0, (- (/ 1 4)) + x1, x3}
 false()	weight: (/ 1 8)
   #p(x1)	weight: 0
 cond4(x1,x2,x3)	weight: 0
  true()	weight: (/ 3 8)
 cond1(x1,x2,x3)	weight: 0
     p(x1)	weight: max{0, (- (/ 1 8)) + x1}
     0()	weight: 0
  #gr(x1,x2)	weight: 0
 cond3(x1,x2,x3)	weight: 0
#cond2(x1,x2,x3)	weight: max{0, x3}
    gr(x1,x2)	weight: max{0, (/ 1 8) + x1}
 #and(x1,x2)	weight: 0
    Usable rules: { 8 9 14 15 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 6, edges: 9
	SCC { #1 #6 #11 #15 #17 #19 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
 cond2(x1,x2,x3)	weight: 0
#cond3(x1,x2,x3)	weight: max{0, (/ 1 16) + x1, x2}
     s(x1)	weight: max{0, (/ 5 16) + x1}
#cond1(x1,x2,x3)	weight: max{0, x2}
   and(x1,x2)	weight: max{0, (/ 5 16) + x1}
#cond4(x1,x2,x3)	weight: max{0, x2}
 false()	weight: 0
   #p(x1)	weight: 0
 cond4(x1,x2,x3)	weight: 0
  true()	weight: (/ 3 16)
 cond1(x1,x2,x3)	weight: 0
     p(x1)	weight: max{0, (- (/ 1 16)) + x1}
     0()	weight: 0
  #gr(x1,x2)	weight: 0
 cond3(x1,x2,x3)	weight: 0
#cond2(x1,x2,x3)	weight: max{0, (- (/ 1 16)) + x1, x2}
    gr(x1,x2)	weight: max{0, (- (/ 1 8)) + x1}
 #and(x1,x2)	weight: 0
    Usable rules: { 8..10 14 15 }
    Removed DPs: #19
Number of SCCs: 1, DPs: 5, edges: 6
	SCC { #1 #6 #11 #15 #17 }
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