MAYBE

Initial complexity problem:
1:	T:
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d)
		(1, 1)    f1(a, b, c, d) -> f2(a, b, c, d) [ a >= c /\ b >= a /\ c >= b ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
	start location:	f1
	leaf cost:	0

Applied AI with 'oct' on problem 1 to obtain the following invariants:
  For symbol f2: X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0


This yielded the following problem:
2:	T:
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(1, 1)    f1(a, b, c, d) -> f2(a, b, c, d) [ a >= c /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a, b, c, d) [ a >= c /\ b >= a /\ c >= b ] with all transitions in problem 2, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
We thus obtain the following problem:
3:	T:
		(1, 2)    f1(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ] with all transitions in problem 3, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 2, b + 2, c - 2, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 3)    f1(a, b, c, d) -> f2(a + 2, b + 2, c - 2, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 2, b + 2, c - 2, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 ] with all transitions in problem 4, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 3, b + 3, c - 3, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 4)    f1(a, b, c, d) -> f2(a + 3, b + 3, c - 3, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 3, b + 3, c - 3, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 4, b + 4, c - 4, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 5)    f1(a, b, c, d) -> f2(a + 4, b + 4, c - 4, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 4, b + 4, c - 4, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 5, b + 5, c - 5, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 6)    f1(a, b, c, d) -> f2(a + 5, b + 5, c - 5, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 5, b + 5, c - 5, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 6, b + 6, c - 6, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 7)    f1(a, b, c, d) -> f2(a + 6, b + 6, c - 6, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 6, b + 6, c - 6, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 7, b + 7, c - 7, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 8)    f1(a, b, c, d) -> f2(a + 7, b + 7, c - 7, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 7, b + 7, c - 7, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 8, b + 8, c - 8, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 9)    f1(a, b, c, d) -> f2(a + 8, b + 8, c - 8, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)    f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 8, b + 8, c - 8, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 9, b + 9, c - 9, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 10)    f1(a, b, c, d) -> f2(a + 9, b + 9, c - 9, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 9, b + 9, c - 9, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 10, b + 10, c - 10, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 11)    f1(a, b, c, d) -> f2(a + 10, b + 10, c - 10, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 10, b + 10, c - 10, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 11, b + 11, c - 11, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 12)    f1(a, b, c, d) -> f2(a + 11, b + 11, c - 11, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 11, b + 11, c - 11, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 12, b + 12, c - 12, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 13)    f1(a, b, c, d) -> f2(a + 12, b + 12, c - 12, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 12, b + 12, c - 12, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 13, b + 13, c - 13, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 14)    f1(a, b, c, d) -> f2(a + 13, b + 13, c - 13, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 13, b + 13, c - 13, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 14, b + 14, c - 14, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 /\ b - c + 26 >= 0 /\ a - c + 26 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 15)    f1(a, b, c, d) -> f2(a + 14, b + 14, c - 14, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 /\ b - c + 26 >= 0 /\ a - c + 26 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b, c, d) -> f2(a + 14, b + 14, c - 14, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 /\ b - c + 26 >= 0 /\ a - c + 26 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f1(a, b, c, d) -> f2(a + 15, b + 15, c - 15, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 /\ b - c + 26 >= 0 /\ a - c + 26 >= 0 /\ b - c + 28 >= 0 /\ a - c + 28 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 16)    f1(a, b, c, d) -> f2(a + 15, b + 15, c - 15, d) [ a >= c /\ b >= a /\ c >= b /\ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ b - c + 2 >= 0 /\ a - c + 2 >= 0 /\ b - c + 4 >= 0 /\ a - c + 4 >= 0 /\ b - c + 6 >= 0 /\ a - c + 6 >= 0 /\ b - c + 8 >= 0 /\ a - c + 8 >= 0 /\ b - c + 10 >= 0 /\ a - c + 10 >= 0 /\ b - c + 12 >= 0 /\ a - c + 12 >= 0 /\ b - c + 14 >= 0 /\ a - c + 14 >= 0 /\ b - c + 16 >= 0 /\ a - c + 16 >= 0 /\ b - c + 18 >= 0 /\ a - c + 18 >= 0 /\ b - c + 20 >= 0 /\ a - c + 20 >= 0 /\ b - c + 22 >= 0 /\ a - c + 22 >= 0 /\ b - c + 24 >= 0 /\ a - c + 24 >= 0 /\ b - c + 26 >= 0 /\ a - c + 26 >= 0 /\ b - c + 28 >= 0 /\ a - c + 28 >= 0 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ b >= a /\ b >= c + 1 ]
		(1, 1)     f1(a, b, c, d) -> f300(a, b, c, e) [ c >= a + 1 /\ b >= a /\ c >= b ]
		(?, 1)     f2(a, b, c, d) -> f2(a + 1, b + 1, c - 1, d) [ b - c >= 0 /\ a - c >= 0 /\ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f1
	leaf cost:	0

Complexity upper bound ?

Time: 2.174 sec (SMT: 2.012 sec)