/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: a__minus(0(),Y) -> 0()
    2: a__minus(s(X),s(Y)) -> a__minus(X,Y)
    3: a__geq(X,0()) -> true()
    4: a__geq(0(),s(Y)) -> false()
    5: a__geq(s(X),s(Y)) -> a__geq(X,Y)
    6: a__div(0(),s(Y)) -> 0()
    7: a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
    8: a__if(true(),X,Y) -> mark(X)
    9: a__if(false(),X,Y) -> mark(Y)
    10: mark(minus(X1,X2)) -> a__minus(X1,X2)
    11: mark(geq(X1,X2)) -> a__geq(X1,X2)
    12: mark(div(X1,X2)) -> a__div(mark(X1),X2)
    13: mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
    14: mark(0()) -> 0()
    15: mark(s(X)) -> s(mark(X))
    16: mark(true()) -> true()
    17: mark(false()) -> false()
    18: a__minus(X1,X2) -> minus(X1,X2)
    19: a__geq(X1,X2) -> geq(X1,X2)
    20: a__div(X1,X2) -> div(X1,X2)
    21: a__if(X1,X2,X3) -> if(X1,X2,X3)
Number of strict rules: 21
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__minus(s(X),s(Y)) -> #a__minus(X,Y)
   #2: #mark(if(X1,X2,X3)) -> #a__if(mark(X1),X2,X3)
   #3: #mark(if(X1,X2,X3)) -> #mark(X1)
   #4: #a__if(false(),X,Y) -> #mark(Y)
   #5: #mark(geq(X1,X2)) -> #a__geq(X1,X2)
   #6: #mark(div(X1,X2)) -> #a__div(mark(X1),X2)
   #7: #mark(div(X1,X2)) -> #mark(X1)
   #8: #a__div(s(X),s(Y)) -> #a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
   #9: #a__div(s(X),s(Y)) -> #a__geq(X,Y)
   #10: #mark(minus(X1,X2)) -> #a__minus(X1,X2)
   #11: #a__geq(s(X),s(Y)) -> #a__geq(X,Y)
   #12: #a__if(true(),X,Y) -> #mark(X)
   #13: #mark(s(X)) -> #mark(X)
Number of SCCs: 3, DPs: 10
	SCC { #11 }
Sum... succeeded.
  a__minus(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  a__div(x1,x2)		w: (0)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  #mark(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #a__minus(x1,x2)		w: (0)
  a__geq(x1,x2)		w: (0)
  mark(x1)		w: (0)
  #a__geq(x1,x2)		w: (x2)
  #a__if(x1,x2,x3)		w: (0)
  #a__div(x1,x2)		w: (0)
  a__if(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 2, DPs: 9
	SCC { #1 }
Sum... succeeded.
  a__minus(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  a__div(x1,x2)		w: (0)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  #mark(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #a__minus(x1,x2)		w: (x2)
  a__geq(x1,x2)		w: (0)
  mark(x1)		w: (0)
  #a__geq(x1,x2)		w: (0)
  #a__if(x1,x2,x3)		w: (0)
  #a__div(x1,x2)		w: (0)
  a__if(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 8
	SCC { #2..4 #6..8 #12 #13 }
Sum... succeeded.
  a__minus(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (1 + x2 + x1)
  a__div(x1,x2)		w: (1 + x2 + x1)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  #mark(x1)		w: (9725 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (x3 + x2 + x1)
  #a__minus(x1,x2)		w: (0)
  a__geq(x1,x2)		w: (0)
  mark(x1)		w: (x1)
  #a__geq(x1,x2)		w: (0)
  #a__if(x1,x2,x3)		w: (9725 + x3 + x2)
  #a__div(x1,x2)		w: (9726 + x2 + x1)
  a__if(x1,x2,x3)		w: (x3 + x2 + x1)
    USABLE RULES: { 1..21 }
    Removed DPs: #7 #13
Number of SCCs: 1, DPs: 6
	SCC { #2..4 #6 #8 #12 }
Sum... succeeded.
  a__minus(x1,x2)		w: (0)
  s(x1)		w: (2447)
  minus(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (4 + x1)
  a__div(x1,x2)		w: (4 + x1)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  #mark(x1)		w: (9725 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (2 + x3 + x2 + x1)
  #a__minus(x1,x2)		w: (0)
  a__geq(x1,x2)		w: (0)
  mark(x1)		w: (1 + x1)
  #a__geq(x1,x2)		w: (0)
  #a__if(x1,x2,x3)		w: (9726 + x3 + x2)
  #a__div(x1,x2)		w: (9727 + x1)
  a__if(x1,x2,x3)		w: (2 + x3 + x2 + x1)
    USABLE RULES: { 1..21 }
    Removed DPs: #2..4 #6 #8 #12
Number of SCCs: 0, DPs: 0