/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: 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: quot(0(),s(y)) -> 0()
    9: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    10: log(s(0())) -> 0()
    11: log(s(s(x))) -> s(log(s(quot(x,s(s(0()))))))
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying log 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: quot(0(),s(y)) -> 0()
9: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
10: log^1_s(0()) -> 0()
11: log^1_s(s(x)) -> s(log^1_s(quot(x,s(s(0())))))
12: le(0(),_1) ->= le^1_0(_1)
13: le(s(_1),_2) ->= le^1_s(_1,_2)
14: log(s(_1)) ->= log^1_s(_1)
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #le(s(_1),_2) ->? #le^1_s(_1,_2)
   #2: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
   #3: #quot(s(x),s(y)) -> #minus(x,y)
   #4: #log^1_s(s(x)) -> #log^1_s(quot(x,s(s(0()))))
   #5: #log^1_s(s(x)) -> #quot(x,s(s(0())))
   #6: #le(0(),_1) ->? #le^1_0(_1)
   #7: #log(s(_1)) ->? #log^1_s(_1)
   #8: #if_minus(false(),s(x),y) -> #minus(x,y)
   #9: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
   #10: #minus(s(x),y) -> #le^1_s(x,y)
   #11: #le^1_s(x,s(y)) -> #le(x,y)
Number of SCCs: 4, DPs: 6
  SCC { #4 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: x1
      le^1_s	w: x2 + 3
      s 	w: x1 + 2
      #le	w: 0
      #le^1_0	w: 0
      minus	w: x1
      false	w: 5
      #log^1_s	w: x1
      #log	w: 0
      true	w: 1
      log	w: 0
      0 	w: 1
      quot	w: x1 + 1
      #if_minus	w: 0
      #minus	w: 0
      le^1_0	w: 0
      if_minus	w: x2
      #quot	w: 0
      log^1_s	w: 0
    USABLE RULES: { 4..9 }
    Removed DPs: #4
Number of SCCs: 3, DPs: 5
  SCC { #2 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: x1
      le^1_s	w: x2 + 3
      s 	w: x1 + 2
      #le	w: 0
      #le^1_0	w: 0
      minus	w: x1
      false	w: 5
      #log^1_s	w: x1
      #log	w: 0
      true	w: 1
      log	w: 0
      0 	w: 1
      quot	w: x1 + 1
      #if_minus	w: 0
      #minus	w: 0
      le^1_0	w: 0
      if_minus	w: x2
      #quot	w: x1
      log^1_s	w: 0
    USABLE RULES: { 4..9 }
    Removed DPs: #2
Number of SCCs: 2, DPs: 4
  SCC { #1 #11 }
POLO(Sum)... succeeded.
      #le^1_s	w: x1 + 1
      le	w: x1
      le^1_s	w: x2 + 3
      s 	w: x1 + 2
      #le	w: x1
      #le^1_0	w: 0
      minus	w: x1
      false	w: 5
      #log^1_s	w: x1
      #log	w: 0
      true	w: 1
      log	w: 0
      0 	w: 1
      quot	w: x1 + 1
      #if_minus	w: 0
      #minus	w: 0
      le^1_0	w: 0
      if_minus	w: x2
      #quot	w: x1
      log^1_s	w: 0
    USABLE RULES: { 4..9 }
    Removed DPs: #1 #11
Number of SCCs: 1, DPs: 2
  SCC { #8 #9 }
POLO(Sum)... succeeded.
      #le^1_s	w: 1
      le	w: x1
      le^1_s	w: x2 + 3
      s 	w: x1 + 2
      #le	w: 0
      #le^1_0	w: 0
      minus	w: x1
      false	w: 5
      #log^1_s	w: x1
      #log	w: 0
      true	w: 1
      log	w: 0
      0 	w: 1
      quot	w: x1 + 1
      #if_minus	w: x2
      #minus	w: x1 + 1
      le^1_0	w: 0
      if_minus	w: x2
      #quot	w: x1
      log^1_s	w: 0
    USABLE RULES: { 4..9 }
    Removed DPs: #8 #9
Number of SCCs: 0, DPs: 0