MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
		(?, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ b >= 1 ]
		(?, 1)    f1(a, b, c) -> f4(a, b, d) [ 0 >= b ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d)
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = 1
	Pol(f1) = 1
	Pol(f4) = 0
orients all transitions weakly and the transition
	f1(a, b, c) -> f4(a, b, d) [ 0 >= b ]
strictly and produces the following problem:
2:	T:
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
		(?, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ b >= 1 ]
		(1, 1)    f1(a, b, c) -> f4(a, b, d) [ 0 >= b ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d)
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_2
	Pol(f1) = V_2
	Pol(f4) = V_2
orients all transitions weakly and the transition
	f1(a, b, c) -> f1(a, b - 1, d) [ b >= 1 ]
strictly and produces the following problem:
3:	T:
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ b >= 1 ]
		(1, 1)    f1(a, b, c) -> f4(a, b, d) [ 0 >= b ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d)
	start location:	f0
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f1: -X_1 >= 0 /\ X_1 >= 0
  For symbol f4: -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 >= 0


This yielded the following problem:
4:	T:
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(1, 1)    f1(a, b, c) -> f4(a, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(a, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b ] with all transitions in problem 4, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 2)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 3)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 4)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 5)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 6)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 7)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 8)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 9)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)    f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)    f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)    f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 10)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 11)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 12)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 13)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 14)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 17, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
18:	T:
		(1, 15)    f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

By chaining the transition f1(a, b, c) -> f4(1, b, d) [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 18, the following new transition is obtained:
	f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
19:	T:
		(1, 16)    f1(a, b, c) -> f4(1, b, d') [ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ a - b >= 0 /\ -b + 1 >= 0 /\ 1 >= 0 ]
		(?, 1)     f4(a, b, c) -> f4(1, b, d) [ -b >= 0 /\ a - b >= 0 /\ a >= 0 ]
		(b, 1)     f1(a, b, c) -> f1(a, b - 1, d) [ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(1, 1)     f0(a, b, c) -> f1(0, b, c)
	start location:	f0
	leaf cost:	0

Complexity upper bound ?

Time: 1.210 sec (SMT: 1.129 sec)