/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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 poly ... failed.
Freezing 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 poly ... 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 }
Sum... succeeded.
  le(x1,x2)		w: (6)
  s(x1)		w: (2 + x1)
  #le(x1,x2)		w: (0)
  minus(x1,x2)		w: (1 + x1)
  false()		w: (5)
  true()		w: (8)
  #le❆1_0(x1)		w: (0)
  le❆1_s(x1,x2)		w: (3 + x2)
  ifMinus(x1,x2,x3)		w: (1 + x2)
  0()		w: (1)
  quot(x1,x2)		w: (0)
  #le❆1_s(x1,x2)		w: (0)
  #minus(x1,x2)		w: (0)
  #quot(x1,x2)		w: (26285 + x2 + x1)
  #ifMinus(x1,x2,x3)		w: (0)
  le❆1_0(x1)		w: (7 + x1)
    USABLE RULES: { 4..7 }
    Removed DPs: #1
Number of SCCs: 2, DPs: 4
	SCC { #3 #8 }
Sum... succeeded.
  le(x1,x2)		w: (6)
  s(x1)		w: (2 + x1)
  #le(x1,x2)		w: (28881 + x1)
  minus(x1,x2)		w: (1 + x1)
  false()		w: (5)
  true()		w: (8)
  #le❆1_0(x1)		w: (0)
  le❆1_s(x1,x2)		w: (3 + x2)
  ifMinus(x1,x2,x3)		w: (1 + x2)
  0()		w: (1)
  quot(x1,x2)		w: (0)
  #le❆1_s(x1,x2)		w: (28882 + x1)
  #minus(x1,x2)		w: (0)
  #quot(x1,x2)		w: (26285 + x1)
  #ifMinus(x1,x2,x3)		w: (0)
  le❆1_0(x1)		w: (7 + x1)
    USABLE RULES: { 4..7 }
    Removed DPs: #3 #8
Number of SCCs: 1, DPs: 2
	SCC { #4 #6 }
Sum... succeeded.
  le(x1,x2)		w: (6)
  s(x1)		w: (2 + x1)
  #le(x1,x2)		w: (28881)
  minus(x1,x2)		w: (2447 + x1)
  false()		w: (5)
  true()		w: (8)
  #le❆1_0(x1)		w: (0)
  le❆1_s(x1,x2)		w: (3 + x2)
  ifMinus(x1,x2,x3)		w: (2447 + x2)
  0()		w: (1)
  quot(x1,x2)		w: (0)
  #le❆1_s(x1,x2)		w: (28882)
  #minus(x1,x2)		w: (1 + x1)
  #quot(x1,x2)		w: (26285 + x1)
  #ifMinus(x1,x2,x3)		w: (x2)
  le❆1_0(x1)		w: (7 + x1)
    USABLE RULES: { 4..7 }
    Removed DPs: #4 #6
Number of SCCs: 0, DPs: 0