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