/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: pred(s(x)) -> x
    2: minus(x,0()) -> x
    3: minus(x,s(y)) -> pred(minus(x,y))
    4: quot(0(),s(y)) -> 0()
    5: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    6: log(s(0())) -> 0()
    7: log(s(s(x))) -> s(log(s(quot(x,s(s(0()))))))
    8: rand(x) ->= x
    9: rand(x) ->= rand(s(x))
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying log
1: pred(s(x)) -> x
2: minus(x,0()) -> x
3: minus(x,s(y)) -> pred(minus(x,y))
4: quot(0(),s(y)) -> 0()
5: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
6: log^1_s(0()) -> 0()
7: log^1_s(s(x)) -> s(log^1_s(quot(x,s(s(0())))))
8: rand(x) ->= x
9: rand(x) ->= rand(s(x))
10: log(s(_1)) ->= log^1_s(_1)
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #log^1_s(s(x)) -> #log^1_s(quot(x,s(s(0()))))
   #2: #log^1_s(s(x)) -> #quot(x,s(s(0())))
   #3: #log(s(_1)) ->? #log^1_s(_1)
   #4: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
   #5: #quot(s(x),s(y)) -> #minus(x,y)
   #6: #minus(x,s(y)) -> #pred(minus(x,y))
   #7: #minus(x,s(y)) -> #minus(x,y)
Number of SCCs: 3, DPs: 3
  SCC { #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 1	w: x1
      minus	s: 1
      #log^1_s	s: []	p: 0	w: 0
      #log	s: []	p: 0	w: 0
      pred	s: 1
      rand	s: []	p: 0	w: x1 + 1
      log	s: [1]	p: 1	w: x1 + 1
      0 	s: []	p: 1	w: 1
      quot	s: 1
      #minus	s: [2]	p: 0	w: max(x2)
      #pred	s: []	p: 0	w: 0
      #quot	s: []	p: 0	w: max(x2)
      log^1_s	s: 1
    Removed DPs: #7
Number of SCCs: 2, DPs: 2
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 1	w: x1
      minus	s: 1
      #log^1_s	s: [1]	p: 0	w: x1
      #log	s: []	p: 0	w: 0
      pred	s: 1
      rand	s: []	p: 0	w: x1 + 1
      log	s: [1]	p: 1	w: x1 + 1
      0 	s: []	p: 1	w: 1
      quot	s: 1
      #minus	s: [2]	p: 0	w: max(x2)
      #pred	s: []	p: 0	w: 0
      #quot	s: []	p: 0	w: max(x2)
      log^1_s	s: 1
    Removed DPs: #1
Number of SCCs: 1, DPs: 1
  SCC { #4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #log^1_s	s: [1]	p: 0	w: x1
      #log	s: []	p: 0	w: 0
      pred	s: 1
      rand	s: []	p: 0	w: x1 + 1
      log	s: [1]	p: 0	w: x1 + 1
      0 	s: []	p: 0	w: 1
      quot	s: 1
      #minus	s: [2]	p: 0	w: max(x2)
      #pred	s: []	p: 0	w: 0
      #quot	s: [1]	p: 0	w: max(x1 + 1)
      log^1_s	s: 1
    Removed DPs: #4
Number of SCCs: 0, DPs: 0