/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: active(s(X)) -> s(active(X))
    11: active(div(X1,X2)) -> div(active(X1),X2)
    12: active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
    13: s(mark(X)) -> mark(s(X))
    14: div(mark(X1),X2) -> mark(div(X1,X2))
    15: if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
    16: proper(minus(X1,X2)) -> minus(proper(X1),proper(X2))
    17: proper(0()) -> ok(0())
    18: proper(s(X)) -> s(proper(X))
    19: proper(geq(X1,X2)) -> geq(proper(X1),proper(X2))
    20: proper(true()) -> ok(true())
    21: proper(false()) -> ok(false())
    22: proper(div(X1,X2)) -> div(proper(X1),proper(X2))
    23: proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
    24: minus(ok(X1),ok(X2)) -> ok(minus(X1,X2))
    25: s(ok(X)) -> ok(s(X))
    26: geq(ok(X1),ok(X2)) -> ok(geq(X1,X2))
    27: div(ok(X1),ok(X2)) -> ok(div(X1,X2))
    28: if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
    29: top(mark(X)) -> top(proper(X))
    30: top(ok(X)) -> top(active(X))
Number of strict rules: 30
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(minus(s(X),s(Y))) -> #minus(X,Y)
   #2: #top(mark(X)) -> #top(proper(X))
   #3: #top(mark(X)) -> #proper(X)
   #4: #s(mark(X)) -> #s(X)
   #5: #active(div(X1,X2)) -> #div(active(X1),X2)
   #6: #active(div(X1,X2)) -> #active(X1)
   #7: #minus(ok(X1),ok(X2)) -> #minus(X1,X2)
   #8: #proper(if(X1,X2,X3)) -> #if(proper(X1),proper(X2),proper(X3))
   #9: #proper(if(X1,X2,X3)) -> #proper(X1)
   #10: #proper(if(X1,X2,X3)) -> #proper(X2)
   #11: #proper(if(X1,X2,X3)) -> #proper(X3)
   #12: #active(if(X1,X2,X3)) -> #if(active(X1),X2,X3)
   #13: #active(if(X1,X2,X3)) -> #active(X1)
   #14: #div(mark(X1),X2) -> #div(X1,X2)
   #15: #top(ok(X)) -> #top(active(X))
   #16: #top(ok(X)) -> #active(X)
   #17: #s(ok(X)) -> #s(X)
   #18: #active(div(s(X),s(Y))) -> #if(geq(X,Y),s(div(minus(X,Y),s(Y))),0())
   #19: #active(div(s(X),s(Y))) -> #geq(X,Y)
   #20: #active(div(s(X),s(Y))) -> #s(div(minus(X,Y),s(Y)))
   #21: #active(div(s(X),s(Y))) -> #div(minus(X,Y),s(Y))
   #22: #active(div(s(X),s(Y))) -> #minus(X,Y)
   #23: #active(s(X)) -> #s(active(X))
   #24: #active(s(X)) -> #active(X)
   #25: #active(geq(s(X),s(Y))) -> #geq(X,Y)
   #26: #if(ok(X1),ok(X2),ok(X3)) -> #if(X1,X2,X3)
   #27: #proper(div(X1,X2)) -> #div(proper(X1),proper(X2))
   #28: #proper(div(X1,X2)) -> #proper(X1)
   #29: #proper(div(X1,X2)) -> #proper(X2)
   #30: #div(ok(X1),ok(X2)) -> #div(X1,X2)
   #31: #proper(geq(X1,X2)) -> #geq(proper(X1),proper(X2))
   #32: #proper(geq(X1,X2)) -> #proper(X1)
   #33: #proper(geq(X1,X2)) -> #proper(X2)
   #34: #geq(ok(X1),ok(X2)) -> #geq(X1,X2)
   #35: #proper(minus(X1,X2)) -> #minus(proper(X1),proper(X2))
   #36: #proper(minus(X1,X2)) -> #proper(X1)
   #37: #proper(minus(X1,X2)) -> #proper(X2)
   #38: #if(mark(X1),X2,X3) -> #if(X1,X2,X3)
   #39: #proper(s(X)) -> #s(proper(X))
   #40: #proper(s(X)) -> #proper(X)
Number of SCCs: 8, DPs: 23
	SCC { #7 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (0)
  minus(x1,x2)		w: (0)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (0)
  #top(x1)		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  proper(x1)		w: (0)
  ok(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (0)
  #minus(x1,x2)		w: (x2 + x1)
  #proper(x1)		w: (0)
  active(x1)		w: (0)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 7, DPs: 22
	SCC { #34 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (0)
  minus(x1,x2)		w: (0)
  #geq(x1,x2)		w: (x2)
  top(x1)		w: (0)
  false()		w: (0)
  #top(x1)		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  proper(x1)		w: (0)
  ok(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (0)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (0)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #34
Number of SCCs: 6, DPs: 21
	SCC { #4 #17 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (0)
  minus(x1,x2)		w: (0)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (0)
  #top(x1)		w: (0)
  div(x1,x2)		w: (0)
  geq(x1,x2)		w: (0)
  true()		w: (0)
  proper(x1)		w: (0)
  ok(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #s(x1)		w: (x1)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (0)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #4 #17
Number of SCCs: 5, DPs: 19
	SCC { #2 #15 }
Sum... Max... QLPOpS... succeeded.
  #div(x1,x2)	0[]
  s(x1)	5[x1]
  minus(x1,x2)	2[x1]
  #geq(x1,x2)	0[x2]
  top(x1)	0[]
  false()	0
  #top(x1)	0[x1]
  div(x1,x2)	6[x1]
  geq(x1,x2)	5[x1]
  true()	2
  proper(x1)	x1
  ok(x1)	x1
  0()	6
  if(x1,x2,x3)	4[x2,x3,x1]
  #s(x1)	0[]
  mark(x1)	1[x1]
  #minus(x1,x2)	0[x1]
  #proper(x1)	0[]
  active(x1)	x1
  #if(x1,x2,x3)	0[x2,x1,x3]
  #active(x1)	0[]
    USABLE RULES: { 1..28 }
    Removed DPs: #2
Number of SCCs: 5, DPs: 18
	SCC { #15 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (x1)
  minus(x1,x2)		w: (2)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (22115)
  #top(x1)		w: (x1)
  div(x1,x2)		w: (x1)
  geq(x1,x2)		w: (2)
  true()		w: (1)
  proper(x1)		w: (2)
  ok(x1)		w: (2)
  0()		w: (14137)
  if(x1,x2,x3)		w: (x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { 1..28 }
    Removed DPs: #15
Number of SCCs: 4, DPs: 17
	SCC { #14 #30 }
Sum... succeeded.
  #div(x1,x2)		w: (x2 + x1)
  s(x1)		w: (x1)
  minus(x1,x2)		w: (3)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (0)
  #top(x1)		w: (0)
  div(x1,x2)		w: (x1)
  geq(x1,x2)		w: (1)
  true()		w: (1)
  proper(x1)		w: (2)
  ok(x1)		w: (1 + x1)
  0()		w: (1)
  if(x1,x2,x3)		w: (x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (4)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { 1 3 4 6 13 15 17 20 21 25 28 }
    Removed DPs: #14 #30
Number of SCCs: 3, DPs: 15
	SCC { #6 #13 #24 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (2)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (0)
  #top(x1)		w: (0)
  div(x1,x2)		w: (1 + x1)
  geq(x1,x2)		w: (1 + x2)
  true()		w: (1)
  proper(x1)		w: (1)
  ok(x1)		w: (1)
  0()		w: (1)
  if(x1,x2,x3)		w: (x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (5 + x1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 1 3 4 6 13 15 17 20 21 25 28 }
    Removed DPs: #6 #24
Number of SCCs: 3, DPs: 13
	SCC { #13 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (1 + x2 + x1)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (18748)
  #top(x1)		w: (0)
  div(x1,x2)		w: (x1)
  geq(x1,x2)		w: (1 + x2 + x1)
  true()		w: (1)
  proper(x1)		w: (1 + x1)
  ok(x1)		w: (1 + x1)
  0()		w: (1)
  if(x1,x2,x3)		w: (1 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (1)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (x1)
    USABLE RULES: { 1 3 4 6 13 15 17 20 21 28 }
    Removed DPs: #13
Number of SCCs: 2, DPs: 12
	SCC { #26 #38 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (5969 + x2 + x1)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (17525)
  #top(x1)		w: (0)
  div(x1,x2)		w: (x1)
  geq(x1,x2)		w: (1 + x2 + x1)
  true()		w: (16335)
  proper(x1)		w: (1 + x1)
  ok(x1)		w: (1 + x1)
  0()		w: (1)
  if(x1,x2,x3)		w: (1 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (1)
  #if(x1,x2,x3)		w: (x3)
  #active(x1)		w: (0)
    USABLE RULES: { 1 3 4 6 13 15 17 20 21 28 }
    Removed DPs: #26
Number of SCCs: 2, DPs: 11
	SCC { #38 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1)
  minus(x1,x2)		w: (1 + x2 + x1)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (2)
  #top(x1)		w: (0)
  div(x1,x2)		w: (x1)
  geq(x1,x2)		w: (2 + x2 + x1)
  true()		w: (1)
  proper(x1)		w: (2 + x1)
  ok(x1)		w: (2 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (1 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (0)
  active(x1)		w: (2)
  #if(x1,x2,x3)		w: (x1)
  #active(x1)		w: (0)
    USABLE RULES: { 1 3 6 15 17 20 21 28 }
    Removed DPs: #38
Number of SCCs: 1, DPs: 10
	SCC { #9..11 #28 #29 #32 #33 #36 #37 #40 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (1 + x2 + x1)
  #geq(x1,x2)		w: (0)
  top(x1)		w: (0)
  false()		w: (3825)
  #top(x1)		w: (0)
  div(x1,x2)		w: (1 + x2 + x1)
  geq(x1,x2)		w: (2 + x2 + x1)
  true()		w: (1)
  proper(x1)		w: (x1)
  ok(x1)		w: (1 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (1 + x3 + x2 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (1 + x1)
  #minus(x1,x2)		w: (0)
  #proper(x1)		w: (x1)
  active(x1)		w: (2)
  #if(x1,x2,x3)		w: (0)
  #active(x1)		w: (0)
    USABLE RULES: { 3 6 15 28 }
    Removed DPs: #9..11 #28 #29 #32 #33 #36 #37 #40
Number of SCCs: 0, DPs: 0