/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: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
    2: sum(cons(0(),x),y) -> sum(x,y)
    3: sum(nil(),y) -> y
    4: empty(nil()) -> true()
    5: empty(cons(n,x)) -> false()
    6: tail(nil()) -> nil()
    7: tail(cons(n,x)) -> x
    8: head(cons(n,x)) -> n
    9: weight(x) -> if(empty(x),empty(tail(x)),x)
    10: if(true(),b,x) -> weight_undefined_error()
    11: if(false(),b,x) -> if2(b,x)
    12: if2(true(),x) -> head(x)
    13: if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x)))))
Number of strict rules: 13
Direct poly ... failed.
Freezing sum
1: sum❆1_cons(s(n),x,cons(m,y)) -> sum❆1_cons(n,x,cons(s(m),y))
2: sum❆1_cons(0(),x,y) -> sum(x,y)
3: sum❆1_nil(y) -> y
4: empty(nil()) -> true()
5: empty(cons(n,x)) -> false()
6: tail(nil()) -> nil()
7: tail(cons(n,x)) -> x
8: head(cons(n,x)) -> n
9: weight(x) -> if(empty(x),empty(tail(x)),x)
10: if(true(),b,x) -> weight_undefined_error()
11: if(false(),b,x) -> if2(b,x)
12: if2(true(),x) -> head(x)
13: if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x)))))
14: sum(cons(_1,_2),_3) ->= sum❆1_cons(_1,_2,_3)
15: sum(nil(),_1) ->= sum❆1_nil(_1)
Number of strict rules: 13
Direct poly ... failed.
Dependency Pairs:
   #1: #sum❆1_cons(0(),x,y) -> #sum(x,y)
   #2: #if2(false(),x) -> #weight(sum(x,cons(0(),tail(tail(x)))))
   #3: #if2(false(),x) -> #sum(x,cons(0(),tail(tail(x))))
   #4: #if2(false(),x) -> #tail(tail(x))
   #5: #if2(false(),x) -> #tail(x)
   #6: #weight(x) -> #if(empty(x),empty(tail(x)),x)
   #7: #weight(x) -> #empty(x)
   #8: #weight(x) -> #empty(tail(x))
   #9: #weight(x) -> #tail(x)
   #10: #if(false(),b,x) -> #if2(b,x)
   #11: #if2(true(),x) -> #head(x)
   #12: #sum(cons(_1,_2),_3) ->? #sum❆1_cons(_1,_2,_3)
   #13: #sum❆1_cons(s(n),x,cons(m,y)) -> #sum❆1_cons(n,x,cons(s(m),y))
   #14: #sum(nil(),_1) ->? #sum❆1_nil(_1)
Number of SCCs: 2, DPs: 6
	SCC { #2 #6 #10 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  #empty(x1)		w: (0)
  s(x1)		w: (max{0, x1})
  #weight(x1)		w: (max{0, -1109 + x1})
  sum❆1_cons(x1,x2,x3)		w: (max{0, 1 + x3, 519 + x2, 2 + x1})
  false()		w: (68810)
  #head(x1)		w: (0)
  #sum❆1_cons(x1,x2,x3)		w: (0)
  true()		w: (1)
  sum(x1,x2)		w: (max{0, 1 + x2, -3 + x1})
  if2(x1,x2)		w: (0)
  tail(x1)		w: (max{0, -33854 + x1})
  0()		w: (1)
  if(x1,x2,x3)		w: (0)
  nil()		w: (0)
  #tail(x1)		w: (0)
  weight_undefined_error()		w: (0)
  weight(x1)		w: (0)
  head(x1)		w: (0)
  cons(x1,x2)		w: (max{0, 67703 + x2 + x1})
  #if(x1,x2,x3)		w: (max{0, -1110 + x3, -1108 + x2, -2217 + x1})
  empty(x1)		w: (max{0, 1107 + x1})
  #sum(x1,x2)		w: (0)
  sum❆1_nil(x1)		w: (max{0, x1})
  #if2(x1,x2)		w: (max{0, -1111 + x2, -2213 + x1})
  #sum❆1_nil(x1)		w: (0)
    USABLE RULES: { 1..7 14 15 }
    Removed DPs: #2 #10
Number of SCCs: 1, DPs: 3
	SCC { #1 #12 #13 }
Sum... succeeded.
  #empty(x1)		w: (0)
  s(x1)		w: (1 + x1)
  #weight(x1)		w: (2)
  sum❆1_cons(x1,x2,x3)		w: (x2)
  false()		w: (2)
  #head(x1)		w: (0)
  #sum❆1_cons(x1,x2,x3)		w: (28881 + x2 + x1)
  true()		w: (2)
  sum(x1,x2)		w: (1)
  if2(x1,x2)		w: (0)
  tail(x1)		w: (1 + x1)
  0()		w: (1)
  if(x1,x2,x3)		w: (0)
  nil()		w: (1324)
  #tail(x1)		w: (0)
  weight_undefined_error()		w: (0)
  weight(x1)		w: (0)
  head(x1)		w: (0)
  cons(x1,x2)		w: (1 + x2 + x1)
  #if(x1,x2,x3)		w: (0)
  empty(x1)		w: (1)
  #sum(x1,x2)		w: (28881 + x1)
  sum❆1_nil(x1)		w: (2)
  #if2(x1,x2)		w: (1)
  #sum❆1_nil(x1)		w: (0)
    USABLE RULES: { 6 7 }
    Removed DPs: #1 #12 #13
Number of SCCs: 0, DPs: 0