Input TRS:
    1: a__f(f(X)) -> a__c(f(g(f(X))))
    2: a__c(X) -> d(X)
    3: a__h(X) -> a__c(d(X))
    4: mark(f(X)) -> a__f(mark(X))
    5: mark(c(X)) -> a__c(X)
    6: mark(h(X)) -> a__h(mark(X))
    7: mark(g(X)) -> g(X)
    8: mark(d(X)) -> d(X)
    9: a__f(X) -> f(X)
    10: a__c(X) -> c(X)
    11: a__h(X) -> h(X)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... removes: 8 3 5 7
     h(x1)	weight: (/ 1 8) + x1
     d(x1)	weight: x1
  a__h(x1)	weight: (/ 1 8) + x1
  a__f(x1)	weight: (/ 1 8) + x1
     c(x1)	weight: x1
     f(x1)	weight: (/ 1 8) + x1
  mark(x1)	weight: (/ 1 8) + x1
     g(x1)	weight: x1
  a__c(x1)	weight: x1
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 11 6
     h(x1)	weight: (/ 1 4) + x1
     d(x1)	weight: x1
  a__h(x1)	weight: (/ 3 8) + x1
  a__f(x1)	weight: x1
     c(x1)	weight: x1
     f(x1)	weight: x1
  mark(x1)	weight: (/ 1 8) + 2 * x1
     g(x1)	weight: x1
  a__c(x1)	weight: x1
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 4 1 10 9 2
     h(x1)	weight: (/ 5 64) + x1
     d(x1)	weight: (/ 1 32) + x1
  a__h(x1)	weight: (/ 5 32) + x1
  a__f(x1)	weight: (/ 13 32) + x1
     c(x1)	weight: (/ 1 32) + x1
     f(x1)	weight: (/ 7 32) + x1
  mark(x1)	weight: (/ 1 32) + 2 * x1
     g(x1)	weight: (/ 1 32) + x1
  a__c(x1)	weight: (/ 1 8) + x1
Number of strict rules: 0
YES