/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: minus(n__0(),Y) -> 0()
    2: minus(n__s(X),n__s(Y)) -> minus(activate(X),activate(Y))
    3: geq(X,n__0()) -> true()
    4: geq(n__0(),n__s(Y)) -> false()
    5: geq(n__s(X),n__s(Y)) -> geq(activate(X),activate(Y))
    6: div(0(),n__s(Y)) -> 0()
    7: div(s(X),n__s(Y)) -> if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0())
    8: if(true(),X,Y) -> activate(X)
    9: if(false(),X,Y) -> activate(Y)
    10: 0() -> n__0()
    11: s(X) -> n__s(X)
    12: div(X1,X2) -> n__div(X1,X2)
    13: minus(X1,X2) -> n__minus(X1,X2)
    14: activate(n__0()) -> 0()
    15: activate(n__s(X)) -> s(activate(X))
    16: activate(n__div(X1,X2)) -> div(activate(X1),X2)
    17: activate(n__minus(X1,X2)) -> minus(X1,X2)
    18: activate(X) -> X
Number of strict rules: 18
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #minus(n__s(X),n__s(Y)) -> #minus(activate(X),activate(Y))
   #2: #minus(n__s(X),n__s(Y)) -> #activate(X)
   #3: #minus(n__s(X),n__s(Y)) -> #activate(Y)
   #4: #if(false(),X,Y) -> #activate(Y)
   #5: #activate(n__0()) -> #0()
   #6: #div(s(X),n__s(Y)) -> #if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0())
   #7: #div(s(X),n__s(Y)) -> #geq(X,activate(Y))
   #8: #div(s(X),n__s(Y)) -> #activate(Y)
   #9: #div(s(X),n__s(Y)) -> #activate(Y)
   #10: #div(s(X),n__s(Y)) -> #activate(Y)
   #11: #geq(n__s(X),n__s(Y)) -> #geq(activate(X),activate(Y))
   #12: #geq(n__s(X),n__s(Y)) -> #activate(X)
   #13: #geq(n__s(X),n__s(Y)) -> #activate(Y)
   #14: #activate(n__minus(X1,X2)) -> #minus(X1,X2)
   #15: #activate(n__div(X1,X2)) -> #div(activate(X1),X2)
   #16: #activate(n__div(X1,X2)) -> #activate(X1)
   #17: #minus(n__0(),Y) -> #0()
   #18: #if(true(),X,Y) -> #activate(X)
   #19: #activate(n__s(X)) -> #s(activate(X))
   #20: #activate(n__s(X)) -> #activate(X)
Number of SCCs: 1, DPs: 17
	SCC { #1..4 #6..16 #18 #20 }
Sum... Max... succeeded.
  #0()		w: (0)
  #div(x1,x2)		w: (max{23603 + x2, 11803 + x1})
  s(x1)		w: (x1)
  minus(x1,x2)		w: (max{11799 + x2, x1})
  n__minus(x1,x2)		w: (max{11799 + x2, x1})
  activate(x1)		w: (x1)
  #geq(x1,x2)		w: (max{11801 + x2, 11802 + x1})
  #activate(x1)		w: (1 + x1)
  false()		w: (1)
  div(x1,x2)		w: (max{23602 + x2, 11802 + x1})
  geq(x1,x2)		w: (max{1 + x2, 0})
  true()		w: (1)
  n__s(x1)		w: (x1)
  n__div(x1,x2)		w: (max{23602 + x2, 11802 + x1})
  0()		w: (11800)
  if(x1,x2,x3)		w: (max{3 + x3, x2, 0})
  #s(x1)		w: (0)
  n__0()		w: (11800)
  #minus(x1,x2)		w: (max{11799 + x2, 1 + x1})
  #if(x1,x2,x3)		w: (max{2 + x3, 1 + x2, 1 + x1})
    USABLE RULES: { 1..18 }
    Removed DPs: #3 #4 #7..10 #12 #13 #16
Number of SCCs: 2, DPs: 8
	SCC { #11 }
Sum... succeeded.
  #0()		w: (0)
  #div(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  n__minus(x1,x2)		w: (0)
  activate(x1)		w: (x1)
  #geq(x1,x2)		w: (12329 + x2)
  #activate(x1)		w: (0)
  false()		w: (2)
  div(x1,x2)		w: (7177 + x2 + x1)
  geq(x1,x2)		w: (1)
  true()		w: (2)
  n__s(x1)		w: (1 + x1)
  n__div(x1,x2)		w: (7177 + x2 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (x3 + x2)
  #s(x1)		w: (0)
  n__0()		w: (0)
  #minus(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
    USABLE RULES: { 1 2 6..18 }
    Removed DPs: #11
Number of SCCs: 1, DPs: 7
	SCC { #1 #2 #6 #14 #15 #18 #20 }
Sum... succeeded.
  #0()		w: (0)
  #div(x1,x2)		w: (49235 + x2 + x1)
  s(x1)		w: (12832 + x1)
  minus(x1,x2)		w: (x1)
  n__minus(x1,x2)		w: (x1)
  activate(x1)		w: (x1)
  #geq(x1,x2)		w: (12329)
  #activate(x1)		w: (25067 + x1)
  false()		w: (2)
  div(x1,x2)		w: (24168 + x2 + x1)
  geq(x1,x2)		w: (1)
  true()		w: (2)
  n__s(x1)		w: (12832 + x1)
  n__div(x1,x2)		w: (24168 + x2 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (x3 + x2)
  #s(x1)		w: (0)
  n__0()		w: (0)
  #minus(x1,x2)		w: (12236 + x1)
  #if(x1,x2,x3)		w: (25067 + x2)
    USABLE RULES: { 1 2 6..18 }
    Removed DPs: #1 #2 #14 #20
Number of SCCs: 1, DPs: 3
	SCC { #6 #15 #18 }
Sum... succeeded.
  #0()		w: (0)
  #div(x1,x2)		w: (36029 + x1)
  s(x1)		w: (25532)
  minus(x1,x2)		w: (2)
  n__minus(x1,x2)		w: (1)
  activate(x1)		w: (18930 + x1)
  #geq(x1,x2)		w: (12329)
  #activate(x1)		w: (16334 + x1)
  false()		w: (15049)
  div(x1,x2)		w: (38626 + x1)
  geq(x1,x2)		w: (15047 + x1)
  true()		w: (15048)
  n__s(x1)		w: (25532)
  n__div(x1,x2)		w: (38626 + x1)
  0()		w: (1)
  if(x1,x2,x3)		w: (29273 + x3 + x2)
  #s(x1)		w: (0)
  n__0()		w: (1)
  #minus(x1,x2)		w: (12236 + x1)
  #if(x1,x2,x3)		w: (16335 + x3 + x2)
    USABLE RULES: { 1 2 6..18 }
    Removed DPs: #6 #15 #18
Number of SCCs: 0, DPs: 0