/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_in(0(),n) -> ack_out(s(n))
    2: ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
    3: u11(ack_out(n)) -> ack_out(n)
    4: ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
    5: u21(ack_out(n),m) -> u22(ack_in(m,n))
    6: u22(ack_out(n)) -> ack_out(n)
Number of strict rules: 6
Direct poly ... failed.
Freezing ack_in
1: ack_in❆1_0(n) -> ack_out(s(n))
2: ack_in❆1_s(m,0()) -> u11(ack_in(m,s(0())))
3: u11(ack_out(n)) -> ack_out(n)
4: ack_in❆1_s(m,s(n)) -> u21(ack_in❆1_s(m,n),m)
5: u21(ack_out(n),m) -> u22(ack_in(m,n))
6: u22(ack_out(n)) -> ack_out(n)
7: ack_in(0(),_1) ->= ack_in❆1_0(_1)
8: ack_in(s(_1),_2) ->= ack_in❆1_s(_1,_2)
Number of strict rules: 6
Direct poly ... failed.
Dependency Pairs:
   #1: #ack_in❆1_s(m,0()) -> #u11(ack_in(m,s(0())))
   #2: #ack_in❆1_s(m,0()) -> #ack_in(m,s(0()))
   #3: #ack_in(0(),_1) ->? #ack_in❆1_0(_1)
   #4: #u21(ack_out(n),m) -> #u22(ack_in(m,n))
   #5: #u21(ack_out(n),m) -> #ack_in(m,n)
   #6: #ack_in(s(_1),_2) ->? #ack_in❆1_s(_1,_2)
   #7: #ack_in❆1_s(m,s(n)) -> #u21(ack_in❆1_s(m,n),m)
   #8: #ack_in❆1_s(m,s(n)) -> #ack_in❆1_s(m,n)
Number of SCCs: 1, DPs: 5
	SCC { #2 #5..8 }
Sum... succeeded.
  ack_in❆1_s(x1,x2)		w: (26963 + x2 + x1)
  #u22(x1)		w: (0)
  #ack_in(x1,x2)		w: (x1)
  s(x1)		w: (3 + x1)
  #u21(x1,x2)		w: (1 + x2)
  #u11(x1)		w: (0)
  0()		w: (1)
  ack_out(x1)		w: (28101 + x1)
  u11(x1)		w: (6 + x1)
  u21(x1,x2)		w: (4 + x2 + x1)
  u22(x1)		w: (28106)
  #ack_in❆1_s(x1,x2)		w: (2 + x1)
  ack_in(x1,x2)		w: (26959 + x1)
  #ack_in❆1_0(x1)		w: (0)
  ack_in❆1_0(x1)		w: (26961 + x1)
    USABLE RULES: { }
    Removed DPs: #2 #5..7
Number of SCCs: 1, DPs: 1
	SCC { #8 }
Sum... succeeded.
  ack_in❆1_s(x1,x2)		w: (5 + x2 + x1)
  #u22(x1)		w: (0)
  #ack_in(x1,x2)		w: (0)
  s(x1)		w: (3 + x1)
  #u21(x1,x2)		w: (1)
  #u11(x1)		w: (0)
  0()		w: (1)
  ack_out(x1)		w: (1 + x1)
  u11(x1)		w: (28104 + x1)
  u21(x1,x2)		w: (4 + x2 + x1)
  u22(x1)		w: (28106)
  #ack_in❆1_s(x1,x2)		w: (2 + x2)
  ack_in(x1,x2)		w: (1 + x1)
  #ack_in❆1_0(x1)		w: (0)
  ack_in❆1_0(x1)		w: (3 + x1)
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0