Input TRS:
    1: half(x) -> if(ge(x,s(s(0()))),x)
    2: if(false(),x) -> 0()
    3: if(true(),x) -> s(half(p(p(x))))
    4: p(0()) -> 0()
    5: p(s(x)) -> x
    6: ge(x,0()) -> true()
    7: ge(0(),s(x)) -> false()
    8: ge(s(x),s(y)) -> ge(x,y)
    9: log(0()) -> 0()
    10: log(s(x)) -> s(log(half(s(x))))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #log(s(x)) -> #log(half(s(x)))
   #2: #log(s(x)) -> #half(s(x))
   #3: #if(true(),x) -> #half(p(p(x)))
   #4: #if(true(),x) -> #p(p(x))
   #5: #if(true(),x) -> #p(x)
   #6: #half(x) -> #if(ge(x,s(s(0()))),x)
   #7: #half(x) -> #ge(x,s(s(0())))
   #8: #ge(s(x),s(y)) -> #ge(x,y)
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #1 }
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)... succeeded.
     s(x1)	weight: max{0, (/ 1 4) + x1_1}; (- (/ 1 4)) + x1_2
 false()	weight: 0; (- (/ 3 8))
  #ge(x1,x2)	weight: 0; 0
 #log(x1)	weight: max{0, (/ 1 8) + x1_1}; 0
#half(x1)	weight: 0; 0
   #p(x1)	weight: 0; 0
  true()	weight: (/ 3 8); (- (/ 3 8))
  half(x1)	weight: max{0, (- (/ 1 4)) + x1_1}; (- (/ 1 8))
     p(x1)	weight: max{0, (- (/ 1 8)) + x1_1}; 0
   log(x1)	weight: 0; 0
     0()	weight: 0; (- (/ 1 8))
    if(x1,x2)	weight: max{0, (- (/ 1 8)) + x1_1, (- (/ 1 4)) + x2_1}; (- (/ 1 8))
    ge(x1,x2)	weight: max{0, (/ 1 2) + x2_2 + x1_1}; (- (/ 1 8))
  #if(x1,x2)	weight: 0; 0
    Usable rules: { 1..8 }
    Removed DPs: #1
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
 false()	weight: 0
  #ge(x1,x2)	weight: x2
 #log(x1)	weight: 0
#half(x1)	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
  half(x1)	weight: (/ 1 8)
     p(x1)	weight: (/ 1 8)
   log(x1)	weight: 0
     0()	weight: 0
    if(x1,x2)	weight: (/ 1 4)
    ge(x1,x2)	weight: (/ 1 8)
  #if(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #3 #6 }
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)... succeeded.
     s(x1)	weight: max{0, (/ 1 4) + x1_1}; (- (/ 1 4)) + x1_2
 false()	weight: 0; (- (/ 3 8))
  #ge(x1,x2)	weight: 0; 0
 #log(x1)	weight: max{0, x1_1}; 0
#half(x1)	weight: max{0, (- (/ 1 8)) + x1_1}; 0
   #p(x1)	weight: 0; 0
  true()	weight: (/ 3 8); (- (/ 3 8))
  half(x1)	weight: max{0, (- (/ 1 4)) + x1_1}; (- (/ 1 8))
     p(x1)	weight: max{0, (- (/ 1 4)) + x1_1}; 0
   log(x1)	weight: 0; 0
     0()	weight: 0; (- (/ 1 8))
    if(x1,x2)	weight: max{0, (- (/ 1 8)) + x1_1, (- (/ 3 8)) + x2_1}; (- (/ 1 8))
    ge(x1,x2)	weight: max{0, (/ 1 2) + x2_2 + x1_1}; (- (/ 1 8))
  #if(x1,x2)	weight: max{0, (- (/ 1 4)) + x1_1, (- (/ 1 2)) + x2_1}; 0
    Usable rules: { 4..8 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES