/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: active(minus(0(),Y)) -> mark(0())
    2: active(minus(s(X),s(Y))) -> mark(minus(X,Y))
    3: active(geq(X,0())) -> mark(true())
    4: active(geq(0(),s(Y))) -> mark(false())
    5: active(geq(s(X),s(Y))) -> mark(geq(X,Y))
    6: active(div(0(),s(Y))) -> mark(0())
    7: active(div(s(X),s(Y))) -> mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0()))
    8: active(if(true(),X,Y)) -> mark(X)
    9: active(if(false(),X,Y)) -> mark(Y)
    10: mark(minus(X1,X2)) -> active(minus(X1,X2))
    11: mark(0()) -> active(0())
    12: mark(s(X)) -> active(s(mark(X)))
    13: mark(geq(X1,X2)) -> active(geq(X1,X2))
    14: mark(true()) -> active(true())
    15: mark(false()) -> active(false())
    16: mark(div(X1,X2)) -> active(div(mark(X1),X2))
    17: mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3))
    18: minus(mark(X1),X2) -> minus(X1,X2)
    19: minus(X1,mark(X2)) -> minus(X1,X2)
    20: minus(active(X1),X2) -> minus(X1,X2)
    21: minus(X1,active(X2)) -> minus(X1,X2)
    22: s(mark(X)) -> s(X)
    23: s(active(X)) -> s(X)
    24: geq(mark(X1),X2) -> geq(X1,X2)
    25: geq(X1,mark(X2)) -> geq(X1,X2)
    26: geq(active(X1),X2) -> geq(X1,X2)
    27: geq(X1,active(X2)) -> geq(X1,X2)
    28: div(mark(X1),X2) -> div(X1,X2)
    29: div(X1,mark(X2)) -> div(X1,X2)
    30: div(active(X1),X2) -> div(X1,X2)
    31: div(X1,active(X2)) -> div(X1,X2)
    32: if(mark(X1),X2,X3) -> if(X1,X2,X3)
    33: if(X1,mark(X2),X3) -> if(X1,X2,X3)
    34: if(X1,X2,mark(X3)) -> if(X1,X2,X3)
    35: if(active(X1),X2,X3) -> if(X1,X2,X3)
    36: if(X1,active(X2),X3) -> if(X1,X2,X3)
    37: if(X1,X2,active(X3)) -> if(X1,X2,X3)
Number of strict rules: 37
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(minus(s(X),s(Y))) -> #mark(minus(X,Y))
   #2: #active(minus(s(X),s(Y))) -> #minus(X,Y)
   #3: #div(X1,mark(X2)) -> #div(X1,X2)
   #4: #if(active(X1),X2,X3) -> #if(X1,X2,X3)
   #5: #if(X1,X2,active(X3)) -> #if(X1,X2,X3)
   #6: #active(div(0(),s(Y))) -> #mark(0())
   #7: #mark(geq(X1,X2)) -> #active(geq(X1,X2))
   #8: #active(if(false(),X,Y)) -> #mark(Y)
   #9: #mark(0()) -> #active(0())
   #10: #geq(mark(X1),X2) -> #geq(X1,X2)
   #11: #s(active(X)) -> #s(X)
   #12: #mark(s(X)) -> #active(s(mark(X)))
   #13: #mark(s(X)) -> #s(mark(X))
   #14: #mark(s(X)) -> #mark(X)
   #15: #div(X1,active(X2)) -> #div(X1,X2)
   #16: #mark(true()) -> #active(true())
   #17: #div(active(X1),X2) -> #div(X1,X2)
   #18: #geq(X1,mark(X2)) -> #geq(X1,X2)
   #19: #minus(active(X1),X2) -> #minus(X1,X2)
   #20: #active(div(s(X),s(Y))) -> #mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0()))
   #21: #active(div(s(X),s(Y))) -> #if(geq(X,Y),s(div(minus(X,Y),s(Y))),0())
   #22: #active(div(s(X),s(Y))) -> #geq(X,Y)
   #23: #active(div(s(X),s(Y))) -> #s(div(minus(X,Y),s(Y)))
   #24: #active(div(s(X),s(Y))) -> #div(minus(X,Y),s(Y))
   #25: #active(div(s(X),s(Y))) -> #minus(X,Y)
   #26: #mark(minus(X1,X2)) -> #active(minus(X1,X2))
   #27: #if(X1,mark(X2),X3) -> #if(X1,X2,X3)
   #28: #active(geq(s(X),s(Y))) -> #mark(geq(X,Y))
   #29: #active(geq(s(X),s(Y))) -> #geq(X,Y)
   #30: #div(mark(X1),X2) -> #div(X1,X2)
   #31: #s(mark(X)) -> #s(X)
   #32: #if(X1,X2,mark(X3)) -> #if(X1,X2,X3)
   #33: #geq(X1,active(X2)) -> #geq(X1,X2)
   #34: #mark(if(X1,X2,X3)) -> #active(if(mark(X1),X2,X3))
   #35: #mark(if(X1,X2,X3)) -> #if(mark(X1),X2,X3)
   #36: #mark(if(X1,X2,X3)) -> #mark(X1)
   #37: #if(mark(X1),X2,X3) -> #if(X1,X2,X3)
   #38: #minus(X1,mark(X2)) -> #minus(X1,X2)
   #39: #geq(active(X1),X2) -> #geq(X1,X2)
   #40: #if(X1,active(X2),X3) -> #if(X1,X2,X3)
   #41: #minus(X1,active(X2)) -> #minus(X1,X2)
   #42: #mark(div(X1,X2)) -> #active(div(mark(X1),X2))
   #43: #mark(div(X1,X2)) -> #div(mark(X1),X2)
   #44: #mark(div(X1,X2)) -> #mark(X1)
   #45: #active(geq(X,0())) -> #mark(true())
   #46: #active(minus(0(),Y)) -> #mark(0())
   #47: #active(if(true(),X,Y)) -> #mark(X)
   #48: #mark(false()) -> #active(false())
   #49: #active(geq(0(),s(Y))) -> #mark(false())
   #50: #minus(mark(X1),X2) -> #minus(X1,X2)
Number of SCCs: 8, DPs: 32
	SCC { #11 #31 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (0)
  minus(x1,x2)		w: (0)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  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)
  #s(x1)		w: (x1)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #11 #31
Number of SCCs: 7, DPs: 30
	SCC { #7 #28 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (2 + x1)
  minus(x1,x2)		w: (0)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (21239 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 24..27 }
    Removed DPs: #7 #28
Number of SCCs: 6, DPs: 28
	SCC { #1 #26 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (8856 + x2 + x1)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (23676 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #1 #26
Number of SCCs: 5, DPs: 26
	SCC { #10 #18 #33 #39 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (17221 + x2 + x1)
  #geq(x1,x2)		w: (x1)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (35473 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #10 #39
Number of SCCs: 5, DPs: 24
	SCC { #18 #33 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (27671 + x2 + x1)
  #geq(x1,x2)		w: (x2)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (67758 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #18 #33
Number of SCCs: 4, DPs: 22
	SCC { #19 #38 #41 #50 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (33524 + x2 + x1)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (98370 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (x2)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #38 #41
Number of SCCs: 4, DPs: 20
	SCC { #19 #50 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (34666 + x2 + x1)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (126470 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (x1)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #19 #50
Number of SCCs: 3, DPs: 18
	SCC { #3 #15 #17 #30 }
Sum... succeeded.
  #div(x1,x2)		w: (x2 + x1)
  s(x1)		w: (1)
  minus(x1,x2)		w: (55203 + x2 + x1)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (126751 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #3 #15 #17 #30
Number of SCCs: 2, DPs: 14
	SCC { #4 #5 #27 #32 #37 #40 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (64148 + x2 + x1)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (142672 + x1)
  true()		w: (0)
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (1 + x1)
  #if(x1,x2,x3)		w: (x3 + x2 + x1)
  #active(x1)		w: (x1)
    USABLE RULES: { 18..21 24..27 }
    Removed DPs: #4 #5 #27 #32 #37 #40
Number of SCCs: 1, DPs: 8
	SCC { #8 #14 #20 #34 #36 #42 #44 #47 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (18458 + x1)
  minus(x1,x2)		w: (0)
  #geq(x1,x2)		w: (0)
  false()		w: (0)
  div(x1,x2)		w: (1 + x1)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  #mark(x1)		w: (47561 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (x3 + x2 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (47561 + x1)
    USABLE RULES: { 1..37 }
    Removed DPs: #14 #44
Number of SCCs: 1, DPs: 6
	SCC { #8 #20 #34 #36 #42 #47 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (12618)
  minus(x1,x2)		w: (12457)
  #geq(x1,x2)		w: (0)
  false()		w: (1)
  div(x1,x2)		w: (5 + x2 + x1)
  geq(x1,x2)		w: (1)
  true()		w: (1)
  #mark(x1)		w: (48426 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (1 + x3 + x2 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (x1)
  #minus(x1,x2)		w: (0)
  active(x1)		w: (x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (48425 + x1)
    USABLE RULES: { 1..37 }
    Removed DPs: #8 #20 #34 #36 #42 #47
Number of SCCs: 0, DPs: 0