Input TRS:
    1: prod(xs) -> prodIter(xs,s(0()))
    2: prodIter(xs,x) -> ifProd(isempty(xs),xs,x)
    3: ifProd(true(),xs,x) -> x
    4: ifProd(false(),xs,x) -> prodIter(tail(xs),times(x,head(xs)))
    5: plus(0(),y) -> y
    6: plus(s(x),y) -> s(plus(x,y))
    7: times(x,y) -> timesIter(x,y,0(),0())
    8: timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
    9: ifTimes(true(),x,y,z,u) -> z
    10: ifTimes(false(),x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
    11: isempty(nil()) -> true()
    12: isempty(cons(x,xs)) -> false()
    13: head(nil()) -> error()
    14: head(cons(x,xs)) -> x
    15: tail(nil()) -> nil()
    16: tail(cons(x,xs)) -> xs
    17: ge(x,0()) -> true()
    18: ge(0(),s(y)) -> false()
    19: ge(s(x),s(y)) -> ge(x,y)
    20: a() -> b()
    21: a() -> c()
Number of strict rules: 21
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #prodIter(xs,x) -> #ifProd(isempty(xs),xs,x)
   #2: #prodIter(xs,x) -> #isempty(xs)
   #3: #plus(s(x),y) -> #plus(x,y)
   #4: #times(x,y) -> #timesIter(x,y,0(),0())
   #5: #ifTimes(false(),x,y,z,u) -> #timesIter(x,y,plus(y,z),s(u))
   #6: #ifTimes(false(),x,y,z,u) -> #plus(y,z)
   #7: #ge(s(x),s(y)) -> #ge(x,y)
   #8: #prod(xs) -> #prodIter(xs,s(0()))
   #9: #timesIter(x,y,z,u) -> #ifTimes(ge(u,x),x,y,z,u)
   #10: #timesIter(x,y,z,u) -> #ge(u,x)
   #11: #ifProd(false(),xs,x) -> #prodIter(tail(xs),times(x,head(xs)))
   #12: #ifProd(false(),xs,x) -> #tail(xs)
   #13: #ifProd(false(),xs,x) -> #times(x,head(xs))
   #14: #ifProd(false(),xs,x) -> #head(xs)
Number of SCCs: 4, DPs: 6, edges: 6
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
ifTimes(x1,x2,x3,x4,x5)	weight: 0
isempty(x1)	weight: 0
  prod(x1)	weight: 0
#prodIter(x1,x2)	weight: 0
timesIter(x1,x2,x3,x4)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     b()	weight: 0
#ifProd(x1,x2,x3)	weight: 0
#prod(x1)	weight: 0
#timesIter(x1,x2,x3,x4)	weight: 0
#plus(x1,x2)	weight: x1
#isempty(x1)	weight: 0
 false()	weight: 0
#head(x1)	weight: 0
  #ge(x1,x2)	weight: 0
     c()	weight: 0
ifProd(x1,x2,x3)	weight: 0
prodIter(x1,x2)	weight: 0
  true()	weight: 0
  tail(x1)	weight: 0
 error()	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
 times(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  plus(x1,x2)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
   #a()	weight: 0
#ifTimes(x1,x2,x3,x4,x5)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 3, DPs: 5, edges: 5
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
ifTimes(x1,x2,x3,x4,x5)	weight: 0
isempty(x1)	weight: 0
  prod(x1)	weight: 0
#prodIter(x1,x2)	weight: 0
timesIter(x1,x2,x3,x4)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     b()	weight: 0
#ifProd(x1,x2,x3)	weight: 0
#prod(x1)	weight: 0
#timesIter(x1,x2,x3,x4)	weight: 0
#plus(x1,x2)	weight: 0
#isempty(x1)	weight: 0
 false()	weight: 0
#head(x1)	weight: 0
  #ge(x1,x2)	weight: x2
     c()	weight: 0
ifProd(x1,x2,x3)	weight: 0
prodIter(x1,x2)	weight: 0
  true()	weight: 0
  tail(x1)	weight: 0
 error()	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
 times(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
  plus(x1,x2)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: 0
   #a()	weight: 0
#ifTimes(x1,x2,x3,x4,x5)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 4, edges: 4
	SCC { #1 #11 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     a()	weight: 0
ifTimes(x1,x2,x3,x4,x5)	weight: max{0, (/ 1 4) + x3, (/ 1 8) + x4}
isempty(x1)	weight: max{0, (- (/ 1 4)) + x1}
  prod(x1)	weight: 0
#prodIter(x1,x2)	weight: max{0, (/ 1 8) + x1, (- (/ 3 8)) + x2}
timesIter(x1,x2,x3,x4)	weight: max{0, (/ 1 4) + x2, (/ 1 8) + x3}
     s(x1)	weight: (max (/ 1 8) 0)
     b()	weight: 0
#ifProd(x1,x2,x3)	weight: max{0, (- (/ 1 4)) + x1, (- (/ 1 4)) + x2, (- (/ 3 8)) + x3}
#prod(x1)	weight: 0
#timesIter(x1,x2,x3,x4)	weight: 0
#plus(x1,x2)	weight: 0
#isempty(x1)	weight: 0
 false()	weight: (/ 5 8)
#head(x1)	weight: 0
  #ge(x1,x2)	weight: 0
     c()	weight: 0
ifProd(x1,x2,x3)	weight: 0
prodIter(x1,x2)	weight: 0
  true()	weight: 0
  tail(x1)	weight: max{0, (- (/ 5 8)) + x1}
 error()	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: max{0, (/ 1 8) + x1, (/ 3 8) + x2}
 times(x1,x2)	weight: max{0, (/ 1 4) + x2}
   nil()	weight: 0
#tail(x1)	weight: 0
  plus(x1,x2)	weight: max{0, (/ 1 8) + x1, x2}
  head(x1)	weight: max{0, (- (/ 3 8)) + x1}
  cons(x1,x2)	weight: max{0, (/ 7 8) + x2 + x1}
   #a()	weight: 0
#ifTimes(x1,x2,x3,x4,x5)	weight: 0
    Usable rules: { 5..16 }
    Removed DPs: #11
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #5 #9 }
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