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