/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) -> ifMinus(le(s(X),Y),s(X),Y)
    6: ifMinus(true(),s(X),Y) -> 0()
    7: ifMinus(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)))
Number of strict rules: 9
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) -> ifMinus(le^1_s(X,Y),s(X),Y)
6: ifMinus(true(),s(X),Y) -> 0()
7: ifMinus(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: le(0(),_1) ->= le^1_0(_1)
11: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #quot(s(X),s(Y)) -> #quot(minus(X,Y),s(Y))
   #2: #quot(s(X),s(Y)) -> #minus(X,Y)
   #3: #le(s(_1),_2) ->? #le^1_s(_1,_2)
   #4: #ifMinus(false(),s(X),Y) -> #minus(X,Y)
   #5: #le(0(),_1) ->? #le^1_0(_1)
   #6: #minus(s(X),Y) -> #ifMinus(le^1_s(X,Y),s(X),Y)
   #7: #minus(s(X),Y) -> #le^1_s(X,Y)
   #8: #le^1_s(X,s(Y)) -> #le(X,Y)
Number of SCCs: 3, DPs: 5
  SCC { #1 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: x1 + x2 + 4
      le^1_s	w: x2 + 1
      s 	w: x1 + 2
      #le	w: 0
      #le^1_0	w: 0
      minus	w: x1 + 1
      false	w: 3
      true	w: 1
      ifMinus	w: x2 + 1
      0 	w: 1
      quot	w: 0
      #minus	w: 0
      le^1_0	w: 0
      #quot	w: x1
      #ifMinus	w: 0
    USABLE RULES: { 4..7 }
    Removed DPs: #1
Number of SCCs: 2, DPs: 4
  SCC { #3 #8 }
POLO(Sum)... succeeded.
      #le^1_s	w: x1 + x2
      le	w: x1 + x2 + 4
      le^1_s	w: x2 + 1
      s 	w: x1 + 2
      #le	w: x1 + x2
      #le^1_0	w: 0
      minus	w: x1 + 1
      false	w: 3
      true	w: 1
      ifMinus	w: x2 + 1
      0 	w: 1
      quot	w: 0
      #minus	w: 0
      le^1_0	w: 0
      #quot	w: x1
      #ifMinus	w: 0
    USABLE RULES: { 4..7 }
    Removed DPs: #3 #8
Number of SCCs: 1, DPs: 2
  SCC { #4 #6 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: 1
      le^1_s	w: 1
      s 	w: x1 + 2
      #le	w: 0
      #le^1_0	w: 0
      minus	w: x1 + 1
      false	w: 1
      true	w: 1
      ifMinus	w: x2 + 1
      0 	w: 0
      quot	w: 0
      #minus	w: x1 + x2 + 2
      le^1_0	w: 1
      #quot	w: x1
      #ifMinus	w: x1 + x2 + x3
    USABLE RULES: { 1..7 10 11 }
    Removed DPs: #4 #6
Number of SCCs: 0, DPs: 0