Input TRS:
    1: a__p(0()) -> 0()
    2: a__p(s(X)) -> mark(X)
    3: a__leq(0(),Y) -> true()
    4: a__leq(s(X),0()) -> false()
    5: a__leq(s(X),s(Y)) -> a__leq(mark(X),mark(Y))
    6: a__if(true(),X,Y) -> mark(X)
    7: a__if(false(),X,Y) -> mark(Y)
    8: a__diff(X,Y) -> a__if(a__leq(mark(X),mark(Y)),0(),s(diff(p(X),Y)))
    9: mark(p(X)) -> a__p(mark(X))
    10: mark(leq(X1,X2)) -> a__leq(mark(X1),mark(X2))
    11: mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
    12: mark(diff(X1,X2)) -> a__diff(mark(X1),mark(X2))
    13: mark(0()) -> 0()
    14: mark(s(X)) -> s(mark(X))
    15: mark(true()) -> true()
    16: mark(false()) -> false()
    17: a__p(X) -> p(X)
    18: a__leq(X1,X2) -> leq(X1,X2)
    19: a__if(X1,X2,X3) -> if(X1,X2,X3)
    20: a__diff(X1,X2) -> diff(X1,X2)
Number of strict rules: 20
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__p(s(X)) -> #mark(X)
   #2: #a__if(true(),X,Y) -> #mark(X)
   #3: #mark(p(X)) -> #a__p(mark(X))
   #4: #mark(p(X)) -> #mark(X)
   #5: #mark(if(X1,X2,X3)) -> #a__if(mark(X1),X2,X3)
   #6: #mark(if(X1,X2,X3)) -> #mark(X1)
   #7: #mark(diff(X1,X2)) -> #a__diff(mark(X1),mark(X2))
   #8: #mark(diff(X1,X2)) -> #mark(X1)
   #9: #mark(diff(X1,X2)) -> #mark(X2)
   #10: #mark(s(X)) -> #mark(X)
   #11: #a__if(false(),X,Y) -> #mark(Y)
   #12: #mark(leq(X1,X2)) -> #a__leq(mark(X1),mark(X2))
   #13: #mark(leq(X1,X2)) -> #mark(X1)
   #14: #mark(leq(X1,X2)) -> #mark(X2)
   #15: #a__leq(s(X),s(Y)) -> #a__leq(mark(X),mark(Y))
   #16: #a__leq(s(X),s(Y)) -> #mark(X)
   #17: #a__leq(s(X),s(Y)) -> #mark(Y)
   #18: #a__diff(X,Y) -> #a__if(a__leq(mark(X),mark(Y)),0(),s(diff(p(X),Y)))
   #19: #a__diff(X,Y) -> #a__leq(mark(X),mark(Y))
   #20: #a__diff(X,Y) -> #mark(X)
   #21: #a__diff(X,Y) -> #mark(Y)
Number of SCCs: 1, DPs: 21, edges: 172
	SCC { #1..21 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#a__diff(x1,x2)	weight: max{(/ 9 16) + x2, (/ 1 2) + x1}
  diff(x1,x2)	weight: max{(/ 1 2) + x2, (/ 7 16) + x1}
     s(x1)	weight: x1
 false()	weight: (/ 1 4)
  a__p(x1)	weight: x1
   leq(x1,x2)	weight: max{(/ 5 16) + x2, (/ 3 16) + x1}
a__leq(x1,x2)	weight: max{(/ 5 16) + x2, (/ 3 16) + x1}
  true()	weight: (/ 5 16)
     p(x1)	weight: x1
#mark(x1)	weight: (/ 1 16) + x1
     0()	weight: (/ 1 16)
    if(x1,x2,x3)	weight: max{x3, (/ 1 16) + x2, (/ 1 8) + x1}
a__diff(x1,x2)	weight: max{(/ 1 2) + x2, (/ 7 16) + x1}
  mark(x1)	weight: x1
#a__p(x1)	weight: (/ 1 16) + x1
#a__leq(x1,x2)	weight: max{(/ 3 16) + x2, (/ 1 8) + x1}
#a__if(x1,x2,x3)	weight: max{0, (/ 1 16) + x3, (/ 1 8) + x2}
 a__if(x1,x2,x3)	weight: max{x3, (/ 1 16) + x2, (/ 1 8) + x1}
    Usable rules: { 1..20 }
    Removed DPs: #2 #6 #8 #9 #12..14 #16 #17 #19..21
Number of SCCs: 2, DPs: 9, edges: 25
	SCC { #15 }
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...  failed.
MAYBE