Input TRS:
    1: a__and(tt(),X) -> mark(X)
    2: a__plus(N,0()) -> mark(N)
    3: a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
    4: a__x(N,0()) -> 0()
    5: a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    6: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    7: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    8: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    9: mark(tt()) -> tt()
    10: mark(0()) -> 0()
    11: mark(s(X)) -> s(mark(X))
    12: a__and(X1,X2) -> and(X1,X2)
    13: a__plus(X1,X2) -> plus(X1,X2)
    14: a__x(X1,X2) -> x(X1,X2)
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__plus(N,0()) -> #mark(N)
   #2: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #3: #mark(and(X1,X2)) -> #mark(X1)
   #4: #mark(s(X)) -> #mark(X)
   #5: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #6: #mark(plus(X1,X2)) -> #mark(X1)
   #7: #mark(plus(X1,X2)) -> #mark(X2)
   #8: #a__x(N,s(M)) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
   #9: #a__x(N,s(M)) -> #a__x(mark(N),mark(M))
   #10: #a__x(N,s(M)) -> #mark(N)
   #11: #a__x(N,s(M)) -> #mark(M)
   #12: #a__x(N,s(M)) -> #mark(N)
   #13: #a__plus(N,s(M)) -> #a__plus(mark(N),mark(M))
   #14: #a__plus(N,s(M)) -> #mark(N)
   #15: #a__plus(N,s(M)) -> #mark(M)
   #16: #a__and(tt(),X) -> #mark(X)
   #17: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
   #18: #mark(x(X1,X2)) -> #mark(X1)
   #19: #mark(x(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 19, edges: 140
	SCC { #1..19 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
a__plus(x1,x2)	weight: max{(/ 1 4) + x2, x1}
     s(x1)	weight: x1
   and(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 8) + x1}
#a__x(x1,x2)	weight: max{(/ 3 4) + x2, (/ 5 8) + x1}
  a__x(x1,x2)	weight: max{(/ 3 8) + x2, (/ 1 4) + x1}
     x(x1,x2)	weight: max{(/ 3 8) + x2, (/ 1 4) + x1}
#a__plus(x1,x2)	weight: max{(/ 1 2) + x2, (/ 3 8) + x1}
#mark(x1)	weight: (/ 3 8) + x1
     0()	weight: (/ 3 8)
#a__and(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 8) + x1}
  mark(x1)	weight: x1
  plus(x1,x2)	weight: max{(/ 1 4) + x2, x1}
    tt()	weight: (/ 1 8)
a__and(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 8) + x1}
    Usable rules: { 1..14 }
    Removed DPs: #2 #3 #7 #10..12 #15 #16 #18 #19
Number of SCCs: 1, DPs: 9, edges: 29
	SCC { #1 #4..6 #8 #9 #13 #14 #17 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
a__plus(x1,x2)	status: [x1,x2]	precedence above: s #a__plus plus
     s(x1)	status: [x1]	precedence above:
   and(x1,x2)	status: x2
#a__x(x1,x2)	status: [x2,x1]	precedence above: a__plus s a__x x #a__plus 0 mark plus
  a__x(x1,x2)	status: [x2,x1]	precedence above: a__plus s #a__x x #a__plus 0 mark plus
     x(x1,x2)	status: [x2,x1]	precedence above: a__plus s #a__x a__x #a__plus 0 mark plus
#a__plus(x1,x2)	status: [x2,x1]	precedence above:
#mark(x1)	status: x1
     0()	status: []	precedence above:
#a__and(x1,x2)	status: [x1]	precedence above:
  mark(x1)	status: x1
  plus(x1,x2)	status: [x1,x2]	precedence above: a__plus s #a__plus
    tt()	status: []	precedence above:
a__and(x1,x2)	status: x2
    Usable rules: { 1..14 }
    Removed DPs: #1 #4..6 #8 #9 #14
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
a__plus(x1,x2)	status: [x1,x2]	precedence above: s #a__plus plus
     s(x1)	status: [x1]	precedence above:
   and(x1,x2)	status: x2
#a__x(x1,x2)	status: [x2,x1]	precedence above: a__plus s a__x x #a__plus 0 mark plus
  a__x(x1,x2)	status: [x2,x1]	precedence above: a__plus s #a__x x #a__plus 0 mark plus
     x(x1,x2)	status: [x2,x1]	precedence above: a__plus s #a__x a__x #a__plus 0 mark plus
#a__plus(x1,x2)	status: [x2,x1]	precedence above:
#mark(x1)	status: x1
     0()	status: []	precedence above:
#a__and(x1,x2)	status: [x1]	precedence above:
  mark(x1)	status: x1
  plus(x1,x2)	status: [x1,x2]	precedence above: a__plus s #a__plus
    tt()	status: []	precedence above:
a__and(x1,x2)	status: x2
    Usable rules: { 1..14 }
    Removed DPs: #13
Number of SCCs: 0, DPs: 0, edges: 0
YES