Input TRS:
    1: active(f(X)) -> mark(if(X,c(),f(true())))
    2: active(if(true(),X,Y)) -> mark(X)
    3: active(if(false(),X,Y)) -> mark(Y)
    4: active(f(X)) -> f(active(X))
    5: active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
    6: active(if(X1,X2,X3)) -> if(X1,active(X2),X3)
    7: f(mark(X)) -> mark(f(X))
    8: if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
    9: if(X1,mark(X2),X3) -> mark(if(X1,X2,X3))
    10: proper(f(X)) -> f(proper(X))
    11: proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
    12: proper(c()) -> ok(c())
    13: proper(true()) -> ok(true())
    14: proper(false()) -> ok(false())
    15: f(ok(X)) -> ok(f(X))
    16: if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
    17: top(mark(X)) -> top(proper(X))
    18: top(ok(X)) -> top(active(X))
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(if(X1,X2,X3)) -> #if(X1,active(X2),X3)
   #2: #active(if(X1,X2,X3)) -> #active(X2)
   #3: #if(X1,mark(X2),X3) -> #if(X1,X2,X3)
   #4: #proper(if(X1,X2,X3)) -> #if(proper(X1),proper(X2),proper(X3))
   #5: #proper(if(X1,X2,X3)) -> #proper(X1)
   #6: #proper(if(X1,X2,X3)) -> #proper(X2)
   #7: #proper(if(X1,X2,X3)) -> #proper(X3)
   #8: #f(mark(X)) -> #f(X)
   #9: #proper(f(X)) -> #f(proper(X))
   #10: #proper(f(X)) -> #proper(X)
   #11: #active(if(X1,X2,X3)) -> #if(active(X1),X2,X3)
   #12: #active(if(X1,X2,X3)) -> #active(X1)
   #13: #top(mark(X)) -> #top(proper(X))
   #14: #top(mark(X)) -> #proper(X)
   #15: #if(ok(X1),ok(X2),ok(X3)) -> #if(X1,X2,X3)
   #16: #active(f(X)) -> #if(X,c(),f(true()))
   #17: #active(f(X)) -> #f(true())
   #18: #if(mark(X1),X2,X3) -> #if(X1,X2,X3)
   #19: #f(ok(X)) -> #f(X)
   #20: #active(f(X)) -> #f(active(X))
   #21: #active(f(X)) -> #active(X)
   #22: #top(ok(X)) -> #top(active(X))
   #23: #top(ok(X)) -> #active(X)
Number of SCCs: 5, DPs: 14, edges: 42
	SCC { #8 #19 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: x1
#proper(x1)	weight: 0
active(x1)	weight: 0
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #8 #19
Number of SCCs: 4, DPs: 12, edges: 38
	SCC { #13 #22 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
   top(x1)	weight: x1	status: []	precedence above:
 false()	weight: (/ 1 2)	status: []	precedence above:
 #top(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above:
     c()	weight: 0	status: []	precedence above:
  true()	weight: 0	status: []	precedence above:
     f(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: c true proper if mark active
proper(x1)	weight: x1	status: x1
    ok(x1)	weight: x1	status: x1
    if(x1,x2,x3)	weight: x3 + x2 + x1	status: [x1,x2]	precedence above: c proper mark active
  mark(x1)	weight: x1	status: [x1]	precedence above: c proper active
   #f(x1)	weight: (/ 1 2)	status: []	precedence above:
#proper(x1)	weight: (/ 1 2)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  #if(x1,x2,x3)	weight: (/ 1 2) + x2 + x1	status: [x1,x2]	precedence above:
#active(x1)	weight: (/ 1 2)	status: []	precedence above:
    Usable rules: { 1..16 }
    Removed DPs: #13
Number of SCCs: 4, DPs: 11, edges: 35
	SCC { #22 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: x1
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: (/ 1 4) + x1
  mark(x1)	weight: 0
   #f(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { 1..9 15 16 }
    Removed DPs: #22
Number of SCCs: 3, DPs: 10, edges: 34
	SCC { #2 #12 #21 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: (/ 1 4) + x1 + x2
  mark(x1)	weight: 0
   #f(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #2 #12 #21
Number of SCCs: 3, DPs: 7, edges: 25
	SCC { #5..7 #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
  mark(x1)	weight: 0
   #f(x1)	weight: 0
#proper(x1)	weight: x1
active(x1)	weight: (/ 1 4) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5..7 #10
Number of SCCs: 2, DPs: 3, edges: 9
	SCC { #3 #15 #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
  mark(x1)	weight: 0
   #f(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  #if(x1,x2,x3)	weight: x3
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #15
Number of SCCs: 2, DPs: 2, edges: 4
	SCC { #3 #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: (/ 1 4) + x1 + x2
  mark(x1)	weight: (/ 1 4) + x1
   #f(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  #if(x1,x2,x3)	weight: x2
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 2, DPs: 1, edges: 1
	SCC { #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   top(x1)	weight: 0
 false()	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
  true()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: (/ 1 4) + x1
    ok(x1)	weight: (/ 1 2) + x1
    if(x1,x2,x3)	weight: (/ 1 4) + x1 + x2
  mark(x1)	weight: (/ 1 4) + x1
   #f(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  #if(x1,x2,x3)	weight: x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #18
Number of SCCs: 1, DPs: 0, edges: 0
YES