Input TRS:
    1: plus(0(),x) -> x
    2: plus(s(x),y) -> s(plus(x,y))
    3: times(0(),y) -> 0()
    4: times(s(x),y) -> plus(y,times(x,y))
    5: p(s(x)) -> x
    6: p(0()) -> 0()
    7: minus(x,0()) -> x
    8: minus(0(),x) -> 0()
    9: minus(x,s(y)) -> p(minus(x,y))
    10: isZero(0()) -> true()
    11: isZero(s(x)) -> false()
    12: facIter(x,y) -> if(isZero(x),minus(x,s(0())),y,times(y,x))
    13: if(true(),x,y,z) -> y
    14: if(false(),x,y,z) -> facIter(x,z)
    15: factorial(x) -> facIter(x,s(0()))
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #plus(s(x),y) -> #plus(x,y)
   #2: #minus(x,s(y)) -> #p(minus(x,y))
   #3: #minus(x,s(y)) -> #minus(x,y)
   #4: #facIter(x,y) -> #if(isZero(x),minus(x,s(0())),y,times(y,x))
   #5: #facIter(x,y) -> #isZero(x)
   #6: #facIter(x,y) -> #minus(x,s(0()))
   #7: #facIter(x,y) -> #times(y,x)
   #8: #if(false(),x,y,z) -> #facIter(x,z)
   #9: #factorial(x) -> #facIter(x,s(0()))
   #10: #times(s(x),y) -> #plus(y,times(x,y))
   #11: #times(s(x),y) -> #times(x,y)
Number of SCCs: 4, DPs: 5, edges: 5
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
facIter(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#isZero(x1)	weight: 0
 minus(x1,x2)	weight: 0
#plus(x1,x2)	weight: x1
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
     p(x1)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
 times(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
factorial(x1)	weight: 0
isZero(x1)	weight: 0
#factorial(x1)	weight: 0
#facIter(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
facIter(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#isZero(x1)	weight: 0
 minus(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
     p(x1)	weight: 0
#times(x1,x2)	weight: x1
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
 times(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
factorial(x1)	weight: 0
isZero(x1)	weight: 0
#factorial(x1)	weight: 0
#facIter(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #11
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
facIter(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#isZero(x1)	weight: 0
 minus(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
  true()	weight: 0
     p(x1)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
 times(x1,x2)	weight: 0
#minus(x1,x2)	weight: x2
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
factorial(x1)	weight: 0
isZero(x1)	weight: 0
#factorial(x1)	weight: 0
#facIter(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #4 #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)... succeeded.
facIter(x1,x2)	weight: 0; 0
     s(x1)	weight: max{0, (/ 5 16) + x1_1}; (- (/ 3 16)) + x1_2
#isZero(x1)	weight: 0; 0
 minus(x1,x2)	weight: max{0, (/ 1 4) + x2_2 + x1_1}; 0
#plus(x1,x2)	weight: 0; 0
 false()	weight: (/ 1 4); (- (/ 1 16))
   #p(x1)	weight: 0; 0
  true()	weight: 0; (- (/ 1 16))
     p(x1)	weight: max{0, (- (/ 1 4)) + x1_1}; 0
#times(x1,x2)	weight: 0; 0
     0()	weight: 0; (- (/ 3 16))
    if(x1,x2,x3,x4)	weight: 0; 0
 times(x1,x2)	weight: max{0, (/ 1 8) + x1_2}; (- (/ 1 16)) + x1_2
#minus(x1,x2)	weight: 0; 0
  plus(x1,x2)	weight: max{0, (/ 3 8) + x1_2, (/ 5 16) + x1_1}; x1_2
  #if(x1,x2,x3,x4)	weight: max{0, (- (/ 3 16)) + x1_1, (- (/ 1 16)) + x2_1}; x1_2
factorial(x1)	weight: 0; 0
isZero(x1)	weight: max{0, (- (/ 1 16)) + x1_1}; (- (/ 1 16))
#factorial(x1)	weight: 0; 0
#facIter(x1,x2)	weight: max{0, (- (/ 1 8)) + x1_2, (- (/ 1 8)) + x1_1, (- (/ 1 8)) + x2_2}; (- (/ 1 16))
    Usable rules: { 5..11 }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0, edges: 0
YES