Input TRS:
    1: active(p(0())) -> mark(0())
    2: active(p(s(X))) -> mark(X)
    3: active(leq(0(),Y)) -> mark(true())
    4: active(leq(s(X),0())) -> mark(false())
    5: active(leq(s(X),s(Y))) -> mark(leq(X,Y))
    6: active(if(true(),X,Y)) -> mark(X)
    7: active(if(false(),X,Y)) -> mark(Y)
    8: active(diff(X,Y)) -> mark(if(leq(X,Y),0(),s(diff(p(X),Y))))
    9: mark(p(X)) -> active(p(mark(X)))
    10: mark(0()) -> active(0())
    11: mark(s(X)) -> active(s(mark(X)))
    12: mark(leq(X1,X2)) -> active(leq(mark(X1),mark(X2)))
    13: mark(true()) -> active(true())
    14: mark(false()) -> active(false())
    15: mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3))
    16: mark(diff(X1,X2)) -> active(diff(mark(X1),mark(X2)))
    17: p(mark(X)) -> p(X)
    18: p(active(X)) -> p(X)
    19: s(mark(X)) -> s(X)
    20: s(active(X)) -> s(X)
    21: leq(mark(X1),X2) -> leq(X1,X2)
    22: leq(X1,mark(X2)) -> leq(X1,X2)
    23: leq(active(X1),X2) -> leq(X1,X2)
    24: leq(X1,active(X2)) -> leq(X1,X2)
    25: if(mark(X1),X2,X3) -> if(X1,X2,X3)
    26: if(X1,mark(X2),X3) -> if(X1,X2,X3)
    27: if(X1,X2,mark(X3)) -> if(X1,X2,X3)
    28: if(active(X1),X2,X3) -> if(X1,X2,X3)
    29: if(X1,active(X2),X3) -> if(X1,X2,X3)
    30: if(X1,X2,active(X3)) -> if(X1,X2,X3)
    31: diff(mark(X1),X2) -> diff(X1,X2)
    32: diff(X1,mark(X2)) -> diff(X1,X2)
    33: diff(active(X1),X2) -> diff(X1,X2)
    34: diff(X1,active(X2)) -> diff(X1,X2)
Number of strict rules: 34
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(p(s(X))) -> #mark(X)
   #2: #if(X1,active(X2),X3) -> #if(X1,X2,X3)
   #3: #active(if(true(),X,Y)) -> #mark(X)
   #4: #mark(true()) -> #active(true())
   #5: #mark(p(X)) -> #active(p(mark(X)))
   #6: #mark(p(X)) -> #p(mark(X))
   #7: #mark(p(X)) -> #mark(X)
   #8: #mark(s(X)) -> #active(s(mark(X)))
   #9: #mark(s(X)) -> #s(mark(X))
   #10: #mark(s(X)) -> #mark(X)
   #11: #leq(X1,active(X2)) -> #leq(X1,X2)
   #12: #leq(active(X1),X2) -> #leq(X1,X2)
   #13: #mark(leq(X1,X2)) -> #active(leq(mark(X1),mark(X2)))
   #14: #mark(leq(X1,X2)) -> #leq(mark(X1),mark(X2))
   #15: #mark(leq(X1,X2)) -> #mark(X1)
   #16: #mark(leq(X1,X2)) -> #mark(X2)
   #17: #diff(mark(X1),X2) -> #diff(X1,X2)
   #18: #mark(false()) -> #active(false())
   #19: #if(X1,X2,active(X3)) -> #if(X1,X2,X3)
   #20: #if(mark(X1),X2,X3) -> #if(X1,X2,X3)
   #21: #s(active(X)) -> #s(X)
   #22: #active(if(false(),X,Y)) -> #mark(Y)
   #23: #mark(0()) -> #active(0())
   #24: #diff(active(X1),X2) -> #diff(X1,X2)
   #25: #active(leq(s(X),s(Y))) -> #mark(leq(X,Y))
   #26: #active(leq(s(X),s(Y))) -> #leq(X,Y)
   #27: #if(active(X1),X2,X3) -> #if(X1,X2,X3)
   #28: #leq(X1,mark(X2)) -> #leq(X1,X2)
   #29: #diff(X1,active(X2)) -> #diff(X1,X2)
   #30: #if(X1,X2,mark(X3)) -> #if(X1,X2,X3)
   #31: #p(mark(X)) -> #p(X)
   #32: #diff(X1,mark(X2)) -> #diff(X1,X2)
   #33: #s(mark(X)) -> #s(X)
   #34: #if(X1,mark(X2),X3) -> #if(X1,X2,X3)
   #35: #leq(mark(X1),X2) -> #leq(X1,X2)
   #36: #mark(diff(X1,X2)) -> #active(diff(mark(X1),mark(X2)))
   #37: #mark(diff(X1,X2)) -> #diff(mark(X1),mark(X2))
   #38: #mark(diff(X1,X2)) -> #mark(X1)
   #39: #mark(diff(X1,X2)) -> #mark(X2)
   #40: #active(leq(0(),Y)) -> #mark(true())
   #41: #active(p(0())) -> #mark(0())
   #42: #active(diff(X,Y)) -> #mark(if(leq(X,Y),0(),s(diff(p(X),Y))))
   #43: #active(diff(X,Y)) -> #if(leq(X,Y),0(),s(diff(p(X),Y)))
   #44: #active(diff(X,Y)) -> #leq(X,Y)
   #45: #active(diff(X,Y)) -> #s(diff(p(X),Y))
   #46: #active(diff(X,Y)) -> #diff(p(X),Y)
   #47: #active(diff(X,Y)) -> #p(X)
   #48: #mark(if(X1,X2,X3)) -> #active(if(mark(X1),X2,X3))
   #49: #mark(if(X1,X2,X3)) -> #if(mark(X1),X2,X3)
   #50: #mark(if(X1,X2,X3)) -> #mark(X1)
   #51: #active(leq(s(X),0())) -> #mark(false())
   #52: #p(active(X)) -> #p(X)
Number of SCCs: 6, DPs: 34, edges: 196
	SCC { #31 #52 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: x1
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: 0
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #31 #52
Number of SCCs: 5, DPs: 32, edges: 192
	SCC { #21 #33 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: 0
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #21 #33
Number of SCCs: 4, DPs: 30, edges: 188
	SCC { #17 #24 #29 #32 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: 0
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #17 #24
Number of SCCs: 4, DPs: 28, edges: 176
	SCC { #29 #32 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: 0
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: x2
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #29 #32
Number of SCCs: 3, DPs: 26, edges: 172
	SCC { #11 #12 #28 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: x2
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #11 #28
Number of SCCs: 4, DPs: 24, edges: 160
	SCC { #12 #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: x1
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #35
Number of SCCs: 3, DPs: 22, edges: 156
	SCC { #2 #19 #20 #27 #30 #34 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: 0
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: x2 + x3
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #19 #30 #34
Number of SCCs: 4, DPs: 18, edges: 124
	SCC { #20 #27 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
  diff(x1,x2)	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
   #p(x1)	weight: 0
   leq(x1,x2)	weight: 0
  true()	weight: 0
 #leq(x1,x2)	weight: 0
     p(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#diff(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  #if(x1,x2,x3)	weight: x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #20 #27
Number of SCCs: 3, DPs: 16, edges: 120
	SCC { #1 #3 #5 #7 #10 #13 #15 #16 #22 #25 #36 #38 #39 #42 #48 #50 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
  diff(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 4) + x1}
     s(x1)	weight: x1
 false()	weight: (/ 1 2)
   #p(x1)	weight: 0
   leq(x1,x2)	weight: max{(/ 3 8) + x2, (/ 1 8) + x1}
  true()	weight: (/ 3 8)
 #leq(x1,x2)	weight: 0
     p(x1)	weight: x1
#mark(x1)	weight: x1
     0()	weight: (/ 1 8)
    if(x1,x2,x3)	weight: max{x3, (/ 3 8) + x2, (/ 1 8) + x1}
   #s(x1)	weight: 0
  mark(x1)	weight: x1
#diff(x1,x2)	weight: 0
active(x1)	weight: x1
  #if(x1,x2,x3)	weight: 0
#active(x1)	weight: x1
    Usable rules: { 1..34 }
    Removed DPs: #3 #15 #16 #38 #39 #50
Number of SCCs: 5, DPs: 10, edges: 26
	SCC { #13 #25 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...