/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: merge(nil(),y) -> y
    2: merge(x,nil()) -> x
    3: merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    4: ++(nil(),y) -> y
    5: ++(.(x,y),z) -> .(x,++(y,z))
    6: if(true(),x,y) -> x
    7: if(false(),x,y) -> x
Number of strict rules: 7
Direct poly ... failed.
Freezing if
1: merge(nil(),y) -> y
2: merge(x,nil()) -> x
3: merge(.(x,y),.(u,v)) -> if❆1_<(x,u,.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
4: ++(nil(),y) -> y
5: ++(.(x,y),z) -> .(x,++(y,z))
6: if❆1_true(x,y) -> x
7: if❆1_false(x,y) -> x
8: if(false(),_2,_3) ->= if❆1_false(_2,_3)
9: if(true(),_2,_3) ->= if❆1_true(_2,_3)
10: if(<(_1,_2),_4,_5) ->= if❆1_<(_1,_2,_4,_5)
Number of strict rules: 7
Direct poly ... failed.
Dependency Pairs:
   #1: #if(true(),_2,_3) ->? #if❆1_true(_2,_3)
   #2: #++(.(x,y),z) -> #++(y,z)
   #3: #merge(.(x,y),.(u,v)) -> #merge(y,.(u,v))
   #4: #merge(.(x,y),.(u,v)) -> #merge(.(x,y),v)
   #5: #if(false(),_2,_3) ->? #if❆1_false(_2,_3)
Number of SCCs: 2, DPs: 3
	SCC { #2 }
Sum... succeeded.
  merge(x1,x2)		w: (0)
  <(x1,x2)		w: (0)
  ++(x1,x2)		w: (0)
  false()		w: (0)
  if❆1_false(x1,x2)		w: (0)
  #if❆1_false(x1,x2)		w: (0)
  #merge(x1,x2)		w: (0)
  true()		w: (0)
  if(x1,x2,x3)		w: (0)
  #++(x1,x2)		w: (x1)
  nil()		w: (0)
  if❆1_true(x1,x2)		w: (0)
  .(x1,x2)		w: (1 + x2)
  #if(x1,x2,x3)		w: (0)
  #if❆1_true(x1,x2)		w: (0)
  if❆1_<(x1,x2,x3,x4)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
	SCC { #3 #4 }
Sum... succeeded.
  merge(x1,x2)		w: (0)
  <(x1,x2)		w: (0)
  ++(x1,x2)		w: (0)
  false()		w: (0)
  if❆1_false(x1,x2)		w: (0)
  #if❆1_false(x1,x2)		w: (0)
  #merge(x1,x2)		w: (x2 + x1)
  true()		w: (0)
  if(x1,x2,x3)		w: (0)
  #++(x1,x2)		w: (0)
  nil()		w: (0)
  if❆1_true(x1,x2)		w: (0)
  .(x1,x2)		w: (1 + x2 + x1)
  #if(x1,x2,x3)		w: (0)
  #if❆1_true(x1,x2)		w: (0)
  if❆1_<(x1,x2,x3,x4)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3 #4
Number of SCCs: 0, DPs: 0