/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
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 POLO(bPol) ... failed.
Uncurrying ... 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
  SCC { #7 }
POLO(Sum)... succeeded.
      s 	w: x1
      #reverse	w: x1
      minus	w: x1 + 1
      #less_leaves	w: 0
      #concat	w: 0
      false	w: 0
      reverse	w: x1
      true	w: 0
      rand	w: x1
      shuffle	w: x1 + 1
      concat	w: x1 + x2 + 1
      0 	w: 1
      quot	w: 1
      less_leaves	w: x1 + x2
      nil	w: 0
      #app	w: 0
      #minus	w: 0
      #shuffle	w: 0
      cons	w: x1 + x2 + 1
      add	w: x2 + 1
      #quot	w: 0
      leaf	w: 1
      app	w: x1 + x2
    Removed DPs: #7
Number of SCCs: 6, DPs: 6
  SCC { #4 }
POLO(Sum)... succeeded.
      s 	w: x1
      #reverse	w: 0
      minus	w: x1 + 1
      #less_leaves	w: 0
      #concat	w: 0
      false	w: 0
      reverse	w: x1
      true	w: 0
      rand	w: x1
      shuffle	w: x1 + 1
      concat	w: x1 + x2 + 1
      0 	w: 1
      quot	w: 1
      less_leaves	w: x1 + x2
      nil	w: 0
      #app	w: 0
      #minus	w: 0
      #shuffle	w: x1
      cons	w: x1 + x2 + 1
      add	w: x2 + 1
      #quot	w: 0
      leaf	w: 1
      app	w: x1 + x2
    Removed DPs: #4
Number of SCCs: 5, DPs: 5
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      #reverse	s: []	p: 0	w: 1
      minus	s: 1
      #less_leaves	s: [2,1]	p: 0	w: x1 + x2
      #concat	s: []	p: 0	w: 0
      false	s: []	p: 2	w: 2
      reverse	s: []	p: 2	w: x1 + 3
      true	s: []	p: 1	w: 8
      rand	s: []	p: 0	w: x1 + 1
      shuffle	s: []	p: 0	w: 5
      concat	s: []	p: 0	w: x1 + x2 + 1
      0 	s: []	p: 1	w: 1
      quot	s: [1]	p: 1	w: max(x1 + 1)
      less_leaves	s: []	p: 1	w: x1 + x2 + 2
      nil	s: []	p: 1	w: 4
      #app	s: [2,1]	p: 0	w: x1 + x2 + 1
      #minus	s: [2,1]	p: 1	w: max(x1 + 4, x2 + 1)
      #shuffle	s: []	p: 0	w: 0
      cons	s: []	p: 0	w: x1 + x2 + 5
      add	s: []	p: 0	w: 1
      #quot	s: []	p: 0	w: max(x2)
      leaf	s: []	p: 0	w: 1
      app	s: [2]	p: 1	w: x2 + 2
    Removed DPs: #1
Number of SCCs: 4, DPs: 4
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: x1
      #reverse	w: 0
      minus	w: x1 + 1
      #less_leaves	w: 0
      #concat	w: x1
      false	w: 0
      reverse	w: x1
      true	w: 0
      rand	w: x1
      shuffle	w: x1 + 1
      concat	w: x1 + x2 + 1
      0 	w: 1
      quot	w: 1
      less_leaves	w: x1 + x2
      nil	w: 0
      #app	w: 0
      #minus	w: 0
      #shuffle	w: 0
      cons	w: x1 + x2 + 1
      add	w: x2 + 1
      #quot	w: 0
      leaf	w: 1
      app	w: x1 + x2
    Removed DPs: #3
Number of SCCs: 3, DPs: 3
  SCC { #2 }
POLO(Sum)... succeeded.
      s 	w: x1
      #reverse	w: 0
      minus	w: x1 + 1
      #less_leaves	w: 0
      #concat	w: 0
      false	w: 0
      reverse	w: x1
      true	w: 0
      rand	w: x1
      shuffle	w: x1 + 1
      concat	w: x1 + x2 + 1
      0 	w: 1
      quot	w: 1
      less_leaves	w: x1 + x2
      nil	w: 0
      #app	w: x1
      #minus	w: 0
      #shuffle	w: 0
      cons	w: x1 + x2 + 1
      add	w: x2 + 1
      #quot	w: 0
      leaf	w: 1
      app	w: x1 + x2
    Removed DPs: #2
Number of SCCs: 2, DPs: 2
  SCC { #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 1	w: x1
      #reverse	s: []	p: 0	w: 1
      minus	s: 1
      #less_leaves	s: [2,1]	p: 0	w: x1 + x2
      #concat	s: []	p: 0	w: 0
      false	s: []	p: 2	w: 2
      reverse	s: []	p: 2	w: x1 + 3
      true	s: []	p: 1	w: 8
      rand	s: []	p: 0	w: x1 + 1
      shuffle	s: []	p: 0	w: 5
      concat	s: []	p: 0	w: x1 + x2 + 1
      0 	s: []	p: 2	w: 1
      quot	s: [1]	p: 2	w: max(x1 + 1)
      less_leaves	s: []	p: 1	w: x1 + x2 + 2
      nil	s: []	p: 1	w: 4
      #app	s: [2,1]	p: 0	w: x1 + x2 + 1
      #minus	s: [2,1]	p: 1	w: max(x1 + 4, x2 + 1)
      #shuffle	s: []	p: 0	w: 0
      cons	s: []	p: 0	w: x1 + x2 + 5
      add	s: []	p: 0	w: 1
      #quot	s: [1]	p: 0	w: max(x1 + 1)
      leaf	s: []	p: 0	w: 1
      app	s: [2]	p: 1	w: x2 + 2
    Removed DPs: #11
Number of SCCs: 1, DPs: 1
  SCC { #8 }
POLO(Sum)... succeeded.
      s 	w: x1
      #reverse	w: 0
      minus	w: x1 + 1
      #less_leaves	w: x1
      #concat	w: 0
      false	w: 0
      reverse	w: x1
      true	w: 0
      rand	w: x1
      shuffle	w: x1 + 1
      concat	w: x1 + x2 + 1
      0 	w: 1
      quot	w: 1
      less_leaves	w: x1 + x2
      nil	w: 0
      #app	w: 0
      #minus	w: 0
      #shuffle	w: 0
      cons	w: x1 + x2 + 2
      add	w: x2 + 1
      #quot	w: 0
      leaf	w: 1
      app	w: x1 + x2
    Removed DPs: #8
Number of SCCs: 0, DPs: 0