Input TRS:
    1: cond1(true(),x) -> cond2(even(x),x)
    2: cond2(true(),x) -> cond1(neq(x,0()),div2(x))
    3: cond2(false(),x) -> cond1(neq(x,0()),p(x))
    4: neq(0(),0()) -> false()
    5: neq(0(),s(x)) -> true()
    6: neq(s(x),0()) -> true()
    7: neq(s(x),s(y())) -> neq(x,y())
    8: even(0()) -> true()
    9: even(s(0())) -> false()
    10: even(s(s(x))) -> even(x)
    11: div2(0()) -> 0()
    12: div2(s(0())) -> 0()
    13: div2(s(s(x))) -> s(div2(x))
    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) -> #cond1(neq(x,0()),div2(x))
   #2: #cond2(true(),x) -> #neq(x,0())
   #3: #cond2(true(),x) -> #div2(x)
   #4: #div2(s(s(x))) -> #div2(x)
   #5: #neq(s(x),s(y())) -> #neq(x,y())
   #6: #even(s(s(x))) -> #even(x)
   #7: #cond2(false(),x) -> #cond1(neq(x,0()),p(x))
   #8: #cond2(false(),x) -> #neq(x,0())
   #9: #cond2(false(),x) -> #p(x)
   #10: #cond1(true(),x) -> #cond2(even(x),x)
   #11: #cond1(true(),x) -> #even(x)
Number of SCCs: 3, DPs: 5, edges: 6
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   neq(x1,x2)	weight: 0
 cond2(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#cond1(x1,x2)	weight: 0
     y()	weight: 0
  even(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
 cond1(x1,x2)	weight: 0
#even(x1)	weight: x1
     p(x1)	weight: 0
     0()	weight: 0
 #neq(x1,x2)	weight: 0
  div2(x1)	weight: 0
#div2(x1)	weight: 0
#cond2(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 4, edges: 5
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   neq(x1,x2)	weight: 0
 cond2(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#cond1(x1,x2)	weight: 0
     y()	weight: 0
  even(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
 cond1(x1,x2)	weight: 0
#even(x1)	weight: 0
     p(x1)	weight: 0
     0()	weight: 0
 #neq(x1,x2)	weight: 0
  div2(x1)	weight: 0
#div2(x1)	weight: x1
#cond2(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #1 #7 #10 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
   neq(x1,x2)	weight: (max (/ 1 4) 0)
 cond2(x1,x2)	weight: 0
     s(x1)	weight: max{0, (/ 3 4) + x1}
#cond1(x1,x2)	weight: max{0, (- (/ 1 2)) + x1, (- (/ 5 8)) + x2}
     y()	weight: 0
  even(x1)	weight: max{0, (- (/ 1 2)) + x1}
 false()	weight: (/ 1 4)
   #p(x1)	weight: 0
  true()	weight: 0
 cond1(x1,x2)	weight: 0
#even(x1)	weight: 0
     p(x1)	weight: max{0, (- (/ 1 8)) + x1}
     0()	weight: 0
 #neq(x1,x2)	weight: 0
  div2(x1)	weight: max{0, (- (/ 1 8)) + x1}
#div2(x1)	weight: 0
#cond2(x1,x2)	weight: max{0, (- (/ 1 8)) + x1, (- (/ 5 8)) + x2}
    Usable rules: { 4 6 8..15 }
    Removed DPs: #7
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #10 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
   neq(x1,x2)	weight: max{0, x1}
 cond2(x1,x2)	weight: 0
     s(x1)	weight: max{0, (/ 1 4) + x1}
#cond1(x1,x2)	weight: max{0, (- (/ 3 16)) + x1, (- (/ 1 16)) + x2}
     y()	weight: 0
  even(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: (/ 1 4)
 cond1(x1,x2)	weight: 0
#even(x1)	weight: 0
     p(x1)	weight: max{0, (- (/ 1 4)) + x1}
     0()	weight: 0
 #neq(x1,x2)	weight: 0
  div2(x1)	weight: max{0, (- (/ 1 16)) + x1}
#div2(x1)	weight: 0
#cond2(x1,x2)	weight: max{0, (- (/ 1 8)) + x2}
    Usable rules: { 4 6 11..13 }
    Removed DPs: #10
Number of SCCs: 0, DPs: 0, edges: 0
YES