YES

Problem:
 a1() -> b1()
 a1() -> c1()
 b1() -> b2()
 c1() -> c2()
 a2() -> b2()
 a2() -> c2()
 b2() -> b3()
 c2() -> c3()
 a3() -> b3()
 a3() -> c3()
 b3() -> b4()
 c3() -> c4()
 a4() -> b4()
 a4() -> c4()
 b4() -> b5()
 c4() -> c5()
 a5() -> b5()
 a5() -> c5()
 b5() -> d()
 c5() -> d()

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [d] = 0,
   
   [a5] = 4,
   
   [c5] = 2,
   
   [b5] = 1,
   
   [a4] = 4,
   
   [c4] = 3,
   
   [b4] = 2,
   
   [a3] = 5,
   
   [c3] = 4,
   
   [b3] = 3,
   
   [a2] = 6,
   
   [c2] = 5,
   
   [b2] = 4,
   
   [c1] = 6,
   
   [b1] = 6,
   
   [a1] = 7
  orientation:
   a1() = 7 >= 6 = b1()
   
   a1() = 7 >= 6 = c1()
   
   b1() = 6 >= 4 = b2()
   
   c1() = 6 >= 5 = c2()
   
   a2() = 6 >= 4 = b2()
   
   a2() = 6 >= 5 = c2()
   
   b2() = 4 >= 3 = b3()
   
   c2() = 5 >= 4 = c3()
   
   a3() = 5 >= 3 = b3()
   
   a3() = 5 >= 4 = c3()
   
   b3() = 3 >= 2 = b4()
   
   c3() = 4 >= 3 = c4()
   
   a4() = 4 >= 2 = b4()
   
   a4() = 4 >= 3 = c4()
   
   b4() = 2 >= 1 = b5()
   
   c4() = 3 >= 2 = c5()
   
   a5() = 4 >= 1 = b5()
   
   a5() = 4 >= 2 = c5()
   
   b5() = 1 >= 0 = d()
   
   c5() = 2 >= 0 = d()
  problem:
   
  Qed