Input TRS:
    1: minus(x,0()) -> x
    2: minus(s(x),s(y)) -> minus(x,y)
    3: quot(0(),s(y)) -> 0()
    4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    5: app(nil(),y) -> y
    6: app(add(n,x),y) -> add(n,app(x,y))
    7: reverse(nil()) -> nil()
    8: reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
    9: shuffle(nil()) -> nil()
    10: shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
    11: concat(leaf(),y) -> y
    12: concat(cons(u,v),y) -> cons(u,concat(v,y))
    13: less_leaves(x,leaf()) -> false()
    14: less_leaves(leaf(),cons(w,z)) -> true()
    15: less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    16: rand(x) ->= x
    17: rand(x) ->= rand(s(x))
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #minus(s(x),s(y)) -> #minus(x,y)
   #2: #app(add(n,x),y) -> #app(x,y)
   #3: #concat(cons(u,v),y) -> #concat(v,y)
   #4: #shuffle(add(n,x)) -> #shuffle(reverse(x))
   #5: #shuffle(add(n,x)) -> #reverse(x)
   #6: #reverse(add(n,x)) -> #app(reverse(x),add(n,nil()))
   #7: #reverse(add(n,x)) -> #reverse(x)
   #8: #less_leaves(cons(u,v),cons(w,z)) -> #less_leaves(concat(u,v),concat(w,z))
   #9: #less_leaves(cons(u,v),cons(w,z)) -> #concat(u,v)
   #10: #less_leaves(cons(u,v),cons(w,z)) -> #concat(w,z)
   #11: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
   #12: #quot(s(x),s(y)) -> #minus(x,y)
Number of SCCs: 7, DPs: 7, edges: 7
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: x1
#reverse(x1)	weight: x1
 minus(x1,x2)	weight: (/ 1 2) + x1
#less_leaves(x1,x2)	weight: 0
#concat(x1,x2)	weight: 0
 false()	weight: 0
reverse(x1)	weight: x1
  true()	weight: 0
  rand(x1)	weight: x1
shuffle(x1)	weight: (/ 1 2) + x1
concat(x1,x2)	weight: (/ 1 2) + x2
     0()	weight: 0
  quot(x1,x2)	weight: (/ 1 2)
less_leaves(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
#shuffle(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
   add(x1,x2)	weight: (/ 1 2) + x2
#quot(x1,x2)	weight: 0
  leaf()	weight: 0
   app(x1,x2)	weight: x1 + x2
    Removed DPs: #7
Number of SCCs: 6, DPs: 6, edges: 6
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: x1
#reverse(x1)	weight: 0
 minus(x1,x2)	weight: (/ 1 2) + x1
#less_leaves(x1,x2)	weight: 0
#concat(x1,x2)	weight: 0
 false()	weight: 0
reverse(x1)	weight: x1
  true()	weight: 0
  rand(x1)	weight: x1
shuffle(x1)	weight: (/ 1 2) + x1
concat(x1,x2)	weight: (/ 1 2) + x2
     0()	weight: 0
  quot(x1,x2)	weight: (/ 1 2)
less_leaves(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
#shuffle(x1)	weight: x1
  cons(x1,x2)	weight: (/ 1 2)
   add(x1,x2)	weight: (/ 1 2) + x2
#quot(x1,x2)	weight: 0
  leaf()	weight: 0
   app(x1,x2)	weight: x1 + x2
    Removed DPs: #4
Number of SCCs: 5, DPs: 5, edges: 5
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: x1
#reverse(x1)	weight: 0
 minus(x1,x2)	weight: (/ 1 2) + x1
#less_leaves(x1,x2)	weight: 0
#concat(x1,x2)	weight: 0
 false()	weight: 0
reverse(x1)	weight: x1
  true()	weight: 0
  rand(x1)	weight: x1
shuffle(x1)	weight: (/ 1 2) + x1
concat(x1,x2)	weight: (/ 1 2) + x2
     0()	weight: 0
  quot(x1,x2)	weight: (/ 1 2)
less_leaves(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: x1
#minus(x1,x2)	weight: 0
#shuffle(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
   add(x1,x2)	weight: (/ 1 2) + x2
#quot(x1,x2)	weight: 0
  leaf()	weight: 0
   app(x1,x2)	weight: x1 + x2
    Removed DPs: #2
Number of SCCs: 4, DPs: 4, edges: 4
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: x1
#reverse(x1)	weight: 0
 minus(x1,x2)	weight: (/ 1 2) + x1
#less_leaves(x1,x2)	weight: 0
#concat(x1,x2)	weight: x1
 false()	weight: 0
reverse(x1)	weight: x1
  true()	weight: 0
  rand(x1)	weight: x1
shuffle(x1)	weight: (/ 1 2) + x1
concat(x1,x2)	weight: (/ 1 2) + x1 + x2
     0()	weight: 0
  quot(x1,x2)	weight: (/ 1 2)
less_leaves(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
#shuffle(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
   add(x1,x2)	weight: (/ 1 2) + x2
#quot(x1,x2)	weight: 0
  leaf()	weight: 0
   app(x1,x2)	weight: x1 + x2
    Removed DPs: #3
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
     s(x1)	weight: x1	status: [x1]	precedence above: minus 0 #minus
#reverse(x1)	weight: x1	status: []	precedence above:
 minus(x1,x2)	weight: max{0, x1}	status: [x1]	precedence above:
#less_leaves(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
#concat(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
 false()	weight: (/ 1 4)	status: []	precedence above:
reverse(x1)	weight: (/ 1 2)	status: []	precedence above: shuffle add
  true()	weight: (/ 1 4)	status: []	precedence above:
  rand(x1)	weight: (/ 1 8) + x1	status: []	precedence above:
shuffle(x1)	weight: (/ 1 8) + x1	status: []	precedence above: add
concat(x1,x2)	weight: (/ 1 2) + x2 + x1	status: [x1,x2]	precedence above: less_leaves cons
     0()	weight: 0	status: []	precedence above:
  quot(x1,x2)	weight: max{0, (/ 1 8) + x1}	status: [x1]	precedence above: s minus 0 #minus
less_leaves(x1,x2)	weight: (/ 3 8)	status: []	precedence above: concat cons
   nil()	weight: (/ 1 4)	status: []	precedence above:
 #app(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
#minus(x1,x2)	weight: x1	status: [x1]	precedence above: s minus 0
#shuffle(x1)	weight: (/ 1 8)	status: []	precedence above:
  cons(x1,x2)	weight: (/ 1 8) + x1	status: [x1]	precedence above: concat less_leaves
   add(x1,x2)	weight: (/ 1 8)	status: []	precedence above: shuffle
#quot(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 8) + x1}	status: [x2,x1]	precedence above:
  leaf()	weight: (/ 1 8)	status: []	precedence above:
   app(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: reverse shuffle add
    Removed DPs: #1
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
     s(x1)	weight: x1	status: [x1]	precedence above: minus 0 #minus
#reverse(x1)	weight: x1	status: []	precedence above:
 minus(x1,x2)	weight: max{0, x1}	status: [x1]	precedence above:
#less_leaves(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
#concat(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
 false()	weight: (/ 1 4)	status: []	precedence above:
reverse(x1)	weight: (/ 1 2)	status: []	precedence above: shuffle add
  true()	weight: (/ 1 4)	status: []	precedence above:
  rand(x1)	weight: (/ 1 8) + x1	status: []	precedence above:
shuffle(x1)	weight: (/ 1 8) + x1	status: []	precedence above: add
concat(x1,x2)	weight: (/ 1 2) + x2 + x1	status: [x1,x2]	precedence above: less_leaves cons
     0()	weight: 0	status: []	precedence above:
  quot(x1,x2)	weight: max{0, (/ 1 8) + x1}	status: [x1]	precedence above: s minus 0 #minus
less_leaves(x1,x2)	weight: (/ 3 8)	status: []	precedence above: concat cons
   nil()	weight: (/ 1 4)	status: []	precedence above:
 #app(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
#minus(x1,x2)	weight: x1	status: [x1]	precedence above: s minus 0
#shuffle(x1)	weight: (/ 1 8)	status: []	precedence above:
  cons(x1,x2)	weight: (/ 1 8) + x1	status: [x1]	precedence above: concat less_leaves
   add(x1,x2)	weight: (/ 1 8)	status: []	precedence above: shuffle
#quot(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 4) + x1}	status: [x1]	precedence above: s minus 0 #minus
  leaf()	weight: (/ 1 8)	status: []	precedence above:
   app(x1,x2)	weight: (/ 1 4) + x2	status: []	precedence above: reverse shuffle add
    Removed DPs: #11
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: x1
#reverse(x1)	weight: 0
 minus(x1,x2)	weight: (/ 1 2) + x1
#less_leaves(x1,x2)	weight: x1 + x2
#concat(x1,x2)	weight: 0
 false()	weight: 0
reverse(x1)	weight: x1
  true()	weight: 0
  rand(x1)	weight: x1
shuffle(x1)	weight: (/ 1 2) + x1
concat(x1,x2)	weight: (/ 1 2) + x1 + x2
     0()	weight: 0
  quot(x1,x2)	weight: (/ 1 2)
less_leaves(x1,x2)	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
#shuffle(x1)	weight: 0
  cons(x1,x2)	weight: (/ 3 4) + x1 + x2
   add(x1,x2)	weight: (/ 1 2) + x2
#quot(x1,x2)	weight: 0
  leaf()	weight: 0
   app(x1,x2)	weight: x1 + x2
    Removed DPs: #8
Number of SCCs: 0, DPs: 0, edges: 0
YES