Input TRS:
    1: +(|0|(),y) -> y
    2: +(s(x),y) -> s(+(x,y))
    3: sum1(nil()) -> |0|()
    4: sum1(cons(x,y)) -> +(x,sum1(y))
    5: sum2(nil(),z) -> z
    6: sum2(cons(x,y),z) -> sum2(y,+(x,z))
    7: tests(|0|()) -> true()
    8: tests(s(x)) -> and(test(rands(rand(|0|()),nil())),x)
    9: test(done(y)) -> eq(f(y),g(y))
    10: eq(x,x) -> true()
    11: rands(|0|(),y) -> done(y)
    12: rands(s(x),y) -> rands(x,|::|(rand(|0|()),y))
    13: rand(x) ->= x
    14: rand(x) ->= rand(s(x))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 10 7 11 9 6
   |0|()	weight: 0
 rands(x1,x2)	weight: (/ 1 4) + 2 * x2 + x1
 tests(x1)	weight: (/ 80071 4) + x1
  test(x1)	weight: (/ 160139 8) + x1
     s(x1)	weight: x1
  done(x1)	weight: (/ 1 8) + 2 * x1
   and(x1,x2)	weight: x2 + x1
    eq(x1,x2)	weight: (/ 1 8) + x2 + x1
  sum2(x1,x2)	weight: (/ 1 8) + x2 + x1
  true()	weight: 0
  rand(x1)	weight: x1
     f(x1)	weight: (/ 6721 8) + x1
   nil()	weight: 0
  |::|(x1,x2)	weight: x2 + x1
  cons(x1,x2)	weight: (/ 1 4) + x2 + x1
     +(x1,x2)	weight: (/ 1 8) + x2 + x1
     g(x1)	weight: (/ 153417 8) + x1
  sum1(x1)	weight: (/ 1 8) + x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(s(x),y) -> #+(x,y)
   #2: #rands(s(x),y) -> #rands(x,|::|(rand(|0|()),y))
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
   |0|()	weight: (/ 1 4)	status: []	precedence above:
 rands(x1,x2)	weight: (/ 1 2) + x2 + x1	status: [x2,x1]	precedence above: |0|
 tests(x1)	weight: (/ 1 4)	status: []	precedence above:
  test(x1)	weight: x1	status: []	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: + #+
  done(x1)	weight: x1	status: []	precedence above:
   and(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x2,x1]	precedence above:
    eq(x1,x2)	weight: (/ 1 4) + x1	status: [x1]	precedence above:
  sum2(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
  true()	weight: 0	status: []	precedence above:
  rand(x1)	weight: (/ 1 2) + x1	status: []	precedence above: |0| rands s + #+
     f(x1)	weight: x1	status: []	precedence above:
#rands(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
   nil()	weight: 0	status: []	precedence above:
  |::|(x1,x2)	weight: x2	status: x2
  cons(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
     +(x1,x2)	weight: x1	status: [x1]	precedence above: s #+
     g(x1)	weight: x1	status: []	precedence above:
   #+(x1,x2)	weight: x1	status: [x1]	precedence above:
  sum1(x1)	weight: x1	status: []	precedence above:
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
   |0|()	weight: 0	status: []	precedence above:
 rands(x1,x2)	weight: (/ 1 4)	status: []	precedence above: |0|
 tests(x1)	weight: (/ 1 4)	status: []	precedence above:
  test(x1)	weight: x1	status: []	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: |0| rand #rands |::| #+
  done(x1)	weight: x1	status: []	precedence above:
   and(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x2,x1]	precedence above:
    eq(x1,x2)	weight: (/ 1 4) + x1	status: [x1]	precedence above:
  sum2(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
  true()	weight: 0	status: []	precedence above:
  rand(x1)	weight: (/ 1 2) + x1	status: []	precedence above: |0| s #rands |::| #+
     f(x1)	weight: x1	status: []	precedence above:
#rands(x1,x2)	weight: x2 + x1	status: [x2,x1]	precedence above: |0| #+
   nil()	weight: 0	status: []	precedence above:
  |::|(x1,x2)	weight: 0	status: []	precedence above: |0| s rand #rands #+
  cons(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
     +(x1,x2)	weight: (/ 1 4) + x1	status: [x1]	precedence above: |0| s rand #rands |::| #+
     g(x1)	weight: x1	status: []	precedence above:
   #+(x1,x2)	weight: x1	status: [x1]	precedence above:
  sum1(x1)	weight: x1	status: []	precedence above:
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES