/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: ack(0(),y) -> s(y)
    2: ack(s(x),0()) -> ack(x,s(0()))
    3: ack(s(x),s(y)) -> ack(x,ack(s(x),y))
    4: f(s(x),y) -> f(x,s(x))
    5: f(x,s(y)) -> f(y,x)
    6: f(x,y) -> ack(x,y)
    7: ack(s(x),y) -> f(x,x)
Number of strict rules: 7
Direct poly ... failed.
Freezing ack
1: ack❆1_0(y) -> s(y)
2: ack❆1_s(x,0()) -> ack(x,s(0()))
3: ack❆1_s(x,s(y)) -> ack(x,ack❆1_s(x,y))
4: f(s(x),y) -> f(x,s(x))
5: f(x,s(y)) -> f(y,x)
6: f(x,y) -> ack(x,y)
7: ack❆1_s(x,y) -> f(x,x)
8: ack(0(),_1) ->= ack❆1_0(_1)
9: ack(s(_1),_2) ->= ack❆1_s(_1,_2)
Number of strict rules: 7
Direct poly ... failed.
Dependency Pairs:
   #1: #ack❆1_s(x,0()) -> #ack(x,s(0()))
   #2: #f(x,y) -> #ack(x,y)
   #3: #ack(s(_1),_2) ->? #ack❆1_s(_1,_2)
   #4: #ack❆1_s(x,y) -> #f(x,x)
   #5: #f(x,s(y)) -> #f(y,x)
   #6: #ack❆1_s(x,s(y)) -> #ack(x,ack❆1_s(x,y))
   #7: #ack❆1_s(x,s(y)) -> #ack❆1_s(x,y)
   #8: #ack(0(),_1) ->? #ack❆1_0(_1)
   #9: #f(s(x),y) -> #f(x,s(x))
Number of SCCs: 1, DPs: 8
	SCC { #1..7 #9 }
Sum... Max... succeeded.
  s(x1)		w: (1 + x1)
  ack(x1,x2)		w: (max{4 + x2, 3 + x1})
  #ack❆1_0(x1)		w: (0)
  f(x1,x2)		w: (max{0, 3 + x1})
  0()		w: (1)
  #f(x1,x2)		w: (max{2439 + x2, 2439 + x1})
  ack❆1_0(x1)		w: (0)
  #ack(x1,x2)		w: (max{0, 2438 + x1})
  ack❆1_s(x1,x2)		w: (max{1 + x2, 2 + x1})
  #ack❆1_s(x1,x2)		w: (max{0, 2439 + x1})
    USABLE RULES: { }
    Removed DPs: #1 #2 #6
Number of SCCs: 2, DPs: 3
	SCC { #7 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  ack(x1,x2)		w: (4 + x2 + x1)
  #ack❆1_0(x1)		w: (0)
  f(x1,x2)		w: (2)
  0()		w: (0)
  #f(x1,x2)		w: (0)
  ack❆1_0(x1)		w: (x1)
  #ack(x1,x2)		w: (0)
  ack❆1_s(x1,x2)		w: (1)
  #ack❆1_s(x1,x2)		w: (x2)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 2
	SCC { #5 #9 }
Sum... Max... succeeded.
  s(x1)		w: (5855 + x1)
  ack(x1,x2)		w: (max{7000 + x2, 6999 + x1})
  #ack❆1_0(x1)		w: (0)
  f(x1,x2)		w: (max{0, 6999 + x1})
  0()		w: (1)
  #f(x1,x2)		w: (max{28382 + x2, 34236 + x1})
  ack❆1_0(x1)		w: (0)
  #ack(x1,x2)		w: (0)
  ack❆1_s(x1,x2)		w: (max{1143 + x2, 2 + x1})
  #ack❆1_s(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #5 #9
Number of SCCs: 0, DPs: 0