/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: le(0(),y) -> true()
    2: le(s(x),0()) -> false()
    3: le(s(x),s(y)) -> le(x,y)
    4: minus(0(),y) -> 0()
    5: minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
    6: if_minus(true(),s(x),y) -> 0()
    7: if_minus(false(),s(x),y) -> s(minus(x,y))
    8: mod(0(),y) -> 0()
    9: mod(s(x),0()) -> 0()
    10: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
    11: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
    12: if_mod(false(),s(x),s(y)) -> s(x)
    13: rand(x) ->= x
    14: rand(x) ->= rand(s(x))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying le
1: le^1_0(y) -> true()
2: le^1_s(x,0()) -> false()
3: le^1_s(x,s(y)) -> le(x,y)
4: minus(0(),y) -> 0()
5: minus(s(x),y) -> if_minus(le^1_s(x,y),s(x),y)
6: if_minus(true(),s(x),y) -> 0()
7: if_minus(false(),s(x),y) -> s(minus(x,y))
8: mod(0(),y) -> 0()
9: mod(s(x),0()) -> 0()
10: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
11: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
12: if_mod(false(),s(x),s(y)) -> s(x)
13: rand(x) ->= x
14: rand(x) ->= rand(s(x))
15: le(0(),_1) ->= le^1_0(_1)
16: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #if_mod(true(),s(x),s(y)) -> #mod(minus(x,y),s(y))
   #2: #if_mod(true(),s(x),s(y)) -> #minus(x,y)
   #3: #if_minus(false(),s(x),y) -> #minus(x,y)
   #4: #mod(s(x),s(y)) -> #if_mod(le(y,x),s(x),s(y))
   #5: #mod(s(x),s(y)) -> #le(y,x)
   #6: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
   #7: #minus(s(x),y) -> #le^1_s(x,y)
   #8: #le(s(_1),_2) ->? #le^1_s(_1,_2)
   #9: #le^1_s(x,s(y)) -> #le(x,y)
   #10: #le(0(),_1) ->? #le^1_0(_1)
Number of SCCs: 3, DPs: 6
  SCC { #8 #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: 2
      le	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
      le^1_s	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
      s 	s: [1]	p: 2	w: x1
      #le	s: 2
      #le^1_0	s: []	p: 0	w: 0
      minus	s: [1]	p: 2	w: max(x1)
      mod	s: 1
      false	s: []	p: 1	w: 3
      true	s: []	p: 1	w: 1
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: 2
      0 	s: []	p: 2	w: 0
      #if_minus	s: [1,3,2]	p: 0	w: max(x1 + 1, x2, x3)
      #minus	s: []	p: 0	w: max(x2)
      #mod	s: []	p: 0	w: max(x2)
      #if_mod	s: []	p: 0	w: max(x1 + 1)
      le^1_0	s: []	p: 3	w: 1
      if_minus	s: [2]	p: 2	w: max(x2)
    Removed DPs: #9
Number of SCCs: 2, DPs: 4
  SCC { #3 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: 2
      le	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
      le^1_s	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
      s 	s: [1]	p: 2	w: x1
      #le	s: 2
      #le^1_0	s: []	p: 0	w: 0
      minus	s: [1]	p: 2	w: max(x1)
      mod	s: 1
      false	s: []	p: 0	w: 3
      true	s: []	p: 1	w: 1
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: 2
      0 	s: []	p: 2	w: 0
      #if_minus	s: [3,2]	p: 1	w: max(x1 + 3, x2 + 5, x3 + 7)
      #minus	s: [2,1]	p: 1	w: max(x1 + 5, x2 + 7)
      #mod	s: []	p: 0	w: max(x2)
      #if_mod	s: []	p: 0	w: max(x1 + 1)
      le^1_0	s: []	p: 3	w: 1
      if_minus	s: [2]	p: 2	w: max(x2)
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #1 #4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: 2
      le	s: [2]	p: 4	w: max(x1 + 1, x2)
      le^1_s	s: [2]	p: 4	w: max(x1 + 1, x2)
      s 	s: [1]	p: 5	w: x1
      #le	s: 2
      #le^1_0	s: []	p: 0	w: 0
      minus	s: 1
      mod	s: []	p: 6	w: max(x1 + 3, x2 + 2)
      false	s: []	p: 1	w: 0
      true	s: []	p: 3	w: 0
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 6	w: max(x1 + 1, x2 + 3, x3 + 2)
      0 	s: []	p: 2	w: 0
      #if_minus	s: [3,1]	p: 1	w: max(x1 + 3, x2 + 5, x3 + 7)
      #minus	s: [2]	p: 1	w: max(x2 + 7)
      #mod	s: [1]	p: 6	w: max(x1 + 2)
      #if_mod	s: [2]	p: 6	w: max(x2 + 2)
      le^1_0	s: []	p: 3	w: 0
      if_minus	s: 2
    Removed DPs: #1
Number of SCCs: 0, DPs: 0