Input TRS:
    1: null(nil()) -> true()
    2: null(add(n,x)) -> false()
    3: tail(add(n,x)) -> x
    4: tail(nil()) -> nil()
    5: head(add(n,x)) -> n
    6: app(nil(),y) -> y
    7: app(add(n,x),y) -> add(n,app(x,y))
    8: reverse(nil()) -> nil()
    9: reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
    10: shuffle(x) -> shuff(x,nil())
    11: shuff(x,y) -> if(null(x),x,y,app(y,add(head(x),nil())))
    12: if(true(),x,y,z) -> y
    13: if(false(),x,y,z) -> shuff(reverse(tail(x)),z)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #if(false(),x,y,z) -> #shuff(reverse(tail(x)),z)
   #2: #if(false(),x,y,z) -> #reverse(tail(x))
   #3: #if(false(),x,y,z) -> #tail(x)
   #4: #reverse(add(n,x)) -> #app(reverse(x),add(n,nil()))
   #5: #reverse(add(n,x)) -> #reverse(x)
   #6: #shuff(x,y) -> #if(null(x),x,y,app(y,add(head(x),nil())))
   #7: #shuff(x,y) -> #null(x)
   #8: #shuff(x,y) -> #app(y,add(head(x),nil()))
   #9: #shuff(x,y) -> #head(x)
   #10: #app(add(n,x),y) -> #app(x,y)
   #11: #shuffle(x) -> #shuff(x,nil())
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#reverse(x1)	weight: x1
 false()	weight: 0
#head(x1)	weight: 0
reverse(x1)	weight: 0
  true()	weight: 0
shuffle(x1)	weight: 0
  tail(x1)	weight: 0
    if(x1,x2,x3,x4)	weight: 0
  null(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
 #app(x1,x2)	weight: 0
#shuffle(x1)	weight: 0
#shuff(x1,x2)	weight: 0
#null(x1)	weight: 0
  head(x1)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
 shuff(x1,x2)	weight: 0
   add(x1,x2)	weight: (/ 1 2) + x2
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#reverse(x1)	weight: 0
 false()	weight: 0
#head(x1)	weight: 0
reverse(x1)	weight: 0
  true()	weight: 0
shuffle(x1)	weight: 0
  tail(x1)	weight: 0
    if(x1,x2,x3,x4)	weight: 0
  null(x1)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
 #app(x1,x2)	weight: x1
#shuffle(x1)	weight: 0
#shuff(x1,x2)	weight: 0
#null(x1)	weight: 0
  head(x1)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
 shuff(x1,x2)	weight: 0
   add(x1,x2)	weight: (/ 1 2) + x2
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #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)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE