Input TRS:
    1: a__f(a(),b(),X) -> a__f(mark(X),X,mark(X))
    2: a__c() -> a()
    3: a__c() -> b()
    4: mark(f(X1,X2,X3)) -> a__f(mark(X1),X2,mark(X3))
    5: mark(c()) -> a__c()
    6: mark(a()) -> a()
    7: mark(b()) -> b()
    8: a__f(X1,X2,X3) -> f(X1,X2,X3)
    9: a__c() -> c()
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(c()) -> #a__c()
   #2: #a__f(a(),b(),X) -> #a__f(mark(X),X,mark(X))
   #3: #a__f(a(),b(),X) -> #mark(X)
   #4: #a__f(a(),b(),X) -> #mark(X)
   #5: #mark(f(X1,X2,X3)) -> #a__f(mark(X1),X2,mark(X3))
   #6: #mark(f(X1,X2,X3)) -> #mark(X1)
   #7: #mark(f(X1,X2,X3)) -> #mark(X3)
Number of SCCs: 1, DPs: 6, edges: 18
	SCC { #2..7 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 1 16)
#a__c()	weight: 0
     b()	weight: (/ 1 8)
  a__f(x1,x2,x3)	weight: max{(/ 7 16) + x3, (/ 1 8) + x2, (/ 5 16) + x1}
     c()	weight: (/ 1 8)
     f(x1,x2,x3)	weight: max{(/ 7 16) + x3, (/ 1 8) + x2, (/ 5 16) + x1}
#mark(x1)	weight: (/ 1 16) + x1
  mark(x1)	weight: x1
#a__f(x1,x2,x3)	weight: max{0, (/ 1 8) + x3, (/ 1 16) + x2}
  a__c()	weight: (/ 1 8)
    Usable rules: { 1..9 }
    Removed DPs: #3..7
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
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