Input TRS:
    1: active(and(tt(),X)) -> mark(X)
    2: active(plus(N,0())) -> mark(N)
    3: active(plus(N,s(M))) -> mark(s(plus(N,M)))
    4: active(x(N,0())) -> mark(0())
    5: active(x(N,s(M))) -> mark(plus(x(N,M),N))
    6: mark(and(X1,X2)) -> active(and(mark(X1),X2))
    7: mark(tt()) -> active(tt())
    8: mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
    9: mark(0()) -> active(0())
    10: mark(s(X)) -> active(s(mark(X)))
    11: mark(x(X1,X2)) -> active(x(mark(X1),mark(X2)))
    12: and(mark(X1),X2) -> and(X1,X2)
    13: and(X1,mark(X2)) -> and(X1,X2)
    14: and(active(X1),X2) -> and(X1,X2)
    15: and(X1,active(X2)) -> and(X1,X2)
    16: plus(mark(X1),X2) -> plus(X1,X2)
    17: plus(X1,mark(X2)) -> plus(X1,X2)
    18: plus(active(X1),X2) -> plus(X1,X2)
    19: plus(X1,active(X2)) -> plus(X1,X2)
    20: s(mark(X)) -> s(X)
    21: s(active(X)) -> s(X)
    22: x(mark(X1),X2) -> x(X1,X2)
    23: x(X1,mark(X2)) -> x(X1,X2)
    24: x(active(X1),X2) -> x(X1,X2)
    25: x(X1,active(X2)) -> x(X1,X2)
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(plus(N,0())) -> #mark(N)
   #2: #mark(and(X1,X2)) -> #active(and(mark(X1),X2))
   #3: #mark(and(X1,X2)) -> #and(mark(X1),X2)
   #4: #mark(and(X1,X2)) -> #mark(X1)
   #5: #and(X1,mark(X2)) -> #and(X1,X2)
   #6: #mark(0()) -> #active(0())
   #7: #mark(x(X1,X2)) -> #active(x(mark(X1),mark(X2)))
   #8: #mark(x(X1,X2)) -> #x(mark(X1),mark(X2))
   #9: #mark(x(X1,X2)) -> #mark(X1)
   #10: #mark(x(X1,X2)) -> #mark(X2)
   #11: #x(active(X1),X2) -> #x(X1,X2)
   #12: #x(X1,mark(X2)) -> #x(X1,X2)
   #13: #and(mark(X1),X2) -> #and(X1,X2)
   #14: #and(active(X1),X2) -> #and(X1,X2)
   #15: #x(X1,active(X2)) -> #x(X1,X2)
   #16: #s(mark(X)) -> #s(X)
   #17: #mark(tt()) -> #active(tt())
   #18: #mark(s(X)) -> #active(s(mark(X)))
   #19: #mark(s(X)) -> #s(mark(X))
   #20: #mark(s(X)) -> #mark(X)
   #21: #active(x(N,s(M))) -> #mark(plus(x(N,M),N))
   #22: #active(x(N,s(M))) -> #plus(x(N,M),N)
   #23: #active(x(N,s(M))) -> #x(N,M)
   #24: #x(mark(X1),X2) -> #x(X1,X2)
   #25: #plus(X1,mark(X2)) -> #plus(X1,X2)
   #26: #plus(X1,active(X2)) -> #plus(X1,X2)
   #27: #s(active(X)) -> #s(X)
   #28: #plus(mark(X1),X2) -> #plus(X1,X2)
   #29: #active(plus(N,s(M))) -> #mark(s(plus(N,M)))
   #30: #active(plus(N,s(M))) -> #s(plus(N,M))
   #31: #active(plus(N,s(M))) -> #plus(N,M)
   #32: #active(and(tt(),X)) -> #mark(X)
   #33: #mark(plus(X1,X2)) -> #active(plus(mark(X1),mark(X2)))
   #34: #mark(plus(X1,X2)) -> #plus(mark(X1),mark(X2))
   #35: #mark(plus(X1,X2)) -> #mark(X1)
   #36: #mark(plus(X1,X2)) -> #mark(X2)
   #37: #and(X1,active(X2)) -> #and(X1,X2)
   #38: #active(x(N,0())) -> #mark(0())
   #39: #plus(active(X1),X2) -> #plus(X1,X2)
Number of SCCs: 5, DPs: 27, edges: 132
	SCC { #16 #27 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #16 #27
Number of SCCs: 4, DPs: 25, edges: 128
	SCC { #25 #26 #28 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: x2
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #25 #26
Number of SCCs: 4, DPs: 23, edges: 116
	SCC { #28 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: x1
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #28 #39
Number of SCCs: 3, DPs: 21, edges: 112
	SCC { #11 #12 #15 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: x2
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #15
Number of SCCs: 4, DPs: 19, edges: 100
	SCC { #11 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: x1
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #11 #24
Number of SCCs: 3, DPs: 17, edges: 96
	SCC { #5 #13 #14 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #13 #14
Number of SCCs: 4, DPs: 15, edges: 84
	SCC { #5 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     x(x1,x2)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
  plus(x1,x2)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    tt()	weight: 0
 #and(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #5 #37
Number of SCCs: 3, DPs: 13, edges: 80
	SCC { #1 #2 #4 #7 #9 #10 #20 #21 #29 #32 #33 #35 #36 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: x1
   and(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 4) + x1}
#plus(x1,x2)	weight: 0
     x(x1,x2)	weight: max{(/ 23595 2) + x2, (/ 47189 4) + x1}
#mark(x1)	weight: x1
     0()	weight: (/ 23595 2)
   #x(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: x1
  plus(x1,x2)	weight: max{(/ 47189 4) + x2, x1}
active(x1)	weight: x1
#active(x1)	weight: x1
    tt()	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { 1..25 }
    Removed DPs: #4 #9 #10 #32 #36
Number of SCCs: 4, DPs: 7, edges: 18
	SCC { #1 #7 #20 #21 #29 #33 #35 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
     s(x1)	status: [x1]	precedence above:
   and(x1,x2)	status: x2
#plus(x1,x2)	status: [x2]	precedence above:
     x(x1,x2)	status: [x1,x2]	precedence above: s 0 mark plus
#mark(x1)	status: x1
     0()	status: []	precedence above:
   #x(x1,x2)	status: [x1,x2]	precedence above:
   #s(x1)	status: []	precedence above:
  mark(x1)	status: x1
  plus(x1,x2)	status: [x1,x2]	precedence above: s mark
active(x1)	status: x1
#active(x1)	status: x1
    tt()	status: []	precedence above:
 #and(x1,x2)	status: []	precedence above:
    Usable rules: { 1..25 }
    Removed DPs: #1 #20 #21 #29 #35
Number of SCCs: 3, DPs: 0, edges: 0
YES