/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: 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))
Number of strict rules: 3
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: ack(0(),_1) ->= ack❆1_0(_1)
5: ack(s(_1),_2) ->= ack❆1_s(_1,_2)
Number of strict rules: 3
Direct poly ... failed.
Dependency Pairs:
   #1: #ack❆1_s(x,0()) -> #ack(x,s(0()))
   #2: #ack(s(_1),_2) ->? #ack❆1_s(_1,_2)
   #3: #ack❆1_s(x,s(y)) -> #ack(x,ack❆1_s(x,y))
   #4: #ack❆1_s(x,s(y)) -> #ack❆1_s(x,y)
   #5: #ack(0(),_1) ->? #ack❆1_0(_1)
Number of SCCs: 1, DPs: 4
	SCC { #1..4 }
Sum... succeeded.
  s(x1)		w: (11802 + x1)
  ack(x1,x2)		w: (1 + x2 + x1)
  #ack❆1_0(x1)		w: (0)
  0()		w: (11799)
  ack❆1_0(x1)		w: (11801)
  #ack(x1,x2)		w: (x1)
  ack❆1_s(x1,x2)		w: (11804)
  #ack❆1_s(x1,x2)		w: (1 + x1)
    USABLE RULES: { }
    Removed DPs: #1..3
Number of SCCs: 1, DPs: 1
	SCC { #4 }
Sum... succeeded.
  s(x1)		w: (10455 + x1)
  ack(x1,x2)		w: (1 + x2 + x1)
  #ack❆1_0(x1)		w: (0)
  0()		w: (2)
  ack❆1_0(x1)		w: (4)
  #ack(x1,x2)		w: (0)
  ack❆1_s(x1,x2)		w: (10457)
  #ack❆1_s(x1,x2)		w: (1 + x2)
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0