MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f0(a, b, c) -> f2(a, b, c) [ a >= 0 /\ b >= c ]
		(?, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ a >= 1 /\ b + 1 >= c ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= 0 ]
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_1
	Pol(f2) = V_1
orients all transitions weakly and the transition
	f2(a, b, c) -> f2(a - 1, b, c - 1) [ a >= 1 /\ b + 1 >= c ]
strictly and produces the following problem:
2:	T:
		(1, 1)    f0(a, b, c) -> f2(a, b, c) [ a >= 0 /\ b >= c ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ a >= 1 /\ b + 1 >= c ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= 0 ]
	start location:	f0
	leaf cost:	0

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f2: X_2 - X_3 >= 0 /\ X_1 >= 0


This yielded the following problem:
3:	T:
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
		(1, 1)    f0(a, b, c) -> f2(a, b, c) [ a >= 0 /\ b >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a, b, c) [ a >= 0 /\ b >= c ] with all transitions in problem 3, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 1, b, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c ]
	f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f0(a, b, c) -> f2(a - 1, b, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 1, b, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c ] with all transitions in problem 4, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 2, b, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 ]
	f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f0(a, b, c) -> f2(a - 2, b, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 2, b, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 ] with all transitions in problem 5, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 3, b, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 ]
	f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f0(a, b, c) -> f2(a - 3, b, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 ]
		(1, 4)    f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 3, b, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 ] with all transitions in problem 6, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 4, b, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 ]
	f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f0(a, b, c) -> f2(a - 4, b, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 ]
		(1, 5)    f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)    f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 4, b, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 ] with all transitions in problem 7, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 5, b, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 ]
	f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 6)    f0(a, b, c) -> f2(a - 5, b, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 ]
		(1, 6)    f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)    f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)    f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 5, b, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 ] with all transitions in problem 8, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 6, b, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 ]
	f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 7)    f0(a, b, c) -> f2(a - 6, b, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 ]
		(1, 7)    f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)    f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)    f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)    f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 6, b, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 ] with all transitions in problem 9, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 7, b, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 ]
	f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 8)    f0(a, b, c) -> f2(a - 7, b, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 ]
		(1, 8)    f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)    f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)    f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)    f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)    f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 7, b, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 ] with all transitions in problem 10, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 8, b, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 ]
	f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 9)    f0(a, b, c) -> f2(a - 8, b, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 ]
		(1, 9)    f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)    f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)    f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)    f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)    f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)    f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)    f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)    f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)    f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)    f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 8, b, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 ] with all transitions in problem 11, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 9, b, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 ]
	f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 10)    f0(a, b, c) -> f2(a - 9, b, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 9, b, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 ] with all transitions in problem 12, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 10, b, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 ]
	f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 11)    f0(a, b, c) -> f2(a - 10, b, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 ]
		(1, 11)    f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 10, b, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 ] with all transitions in problem 13, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 11, b, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 ]
	f0(a, b, c) -> f2(a - 10, b + c - 11, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 12)    f0(a, b, c) -> f2(a - 11, b, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 ]
		(1, 12)    f0(a, b, c) -> f2(a - 10, b + c - 11, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ b >= 0 ]
		(1, 11)    f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 11, b, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 ] with all transitions in problem 14, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 12, b, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 ]
	f0(a, b, c) -> f2(a - 11, b + c - 12, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 13)    f0(a, b, c) -> f2(a - 12, b, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 ]
		(1, 13)    f0(a, b, c) -> f2(a - 11, b + c - 12, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ b >= 0 ]
		(1, 12)    f0(a, b, c) -> f2(a - 10, b + c - 11, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ b >= 0 ]
		(1, 11)    f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 12, b, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 ] with all transitions in problem 15, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 13, b, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 ]
	f0(a, b, c) -> f2(a - 12, b + c - 13, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 14)    f0(a, b, c) -> f2(a - 13, b, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 ]
		(1, 14)    f0(a, b, c) -> f2(a - 12, b + c - 13, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ b >= 0 ]
		(1, 13)    f0(a, b, c) -> f2(a - 11, b + c - 12, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ b >= 0 ]
		(1, 12)    f0(a, b, c) -> f2(a - 10, b + c - 11, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ b >= 0 ]
		(1, 11)    f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 13, b, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 ] with all transitions in problem 16, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 14, b, c - 14) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 ]
	f0(a, b, c) -> f2(a - 13, b + c - 14, c - 14) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 15)    f0(a, b, c) -> f2(a - 14, b, c - 14) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 ]
		(1, 15)    f0(a, b, c) -> f2(a - 13, b + c - 14, c - 14) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ b >= 0 ]
		(1, 14)    f0(a, b, c) -> f2(a - 12, b + c - 13, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ b >= 0 ]
		(1, 13)    f0(a, b, c) -> f2(a - 11, b + c - 12, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ b >= 0 ]
		(1, 12)    f0(a, b, c) -> f2(a - 10, b + c - 11, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ b >= 0 ]
		(1, 11)    f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b, c) -> f2(a - 14, b, c - 14) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 ] with all transitions in problem 17, the following new transitions are obtained:
	f0(a, b, c) -> f2(a - 15, b, c - 15) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 /\ b - c + 14 >= 0 /\ a - 14 >= 0 /\ a - 14 >= 1 /\ b + 1 >= c - 14 ]
	f0(a, b, c) -> f2(a - 14, b + c - 15, c - 15) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 /\ b - c + 14 >= 0 /\ a - 14 >= 0 /\ b >= 0 ]
We thus obtain the following problem:
18:	T:
		(1, 16)    f0(a, b, c) -> f2(a - 15, b, c - 15) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 /\ b - c + 14 >= 0 /\ a - 14 >= 0 /\ a - 14 >= 1 /\ b + 1 >= c - 14 ]
		(1, 16)    f0(a, b, c) -> f2(a - 14, b + c - 15, c - 15) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ a - 13 >= 1 /\ b + 1 >= c - 13 /\ b - c + 14 >= 0 /\ a - 14 >= 0 /\ b >= 0 ]
		(1, 15)    f0(a, b, c) -> f2(a - 13, b + c - 14, c - 14) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ a - 12 >= 1 /\ b + 1 >= c - 12 /\ b - c + 13 >= 0 /\ a - 13 >= 0 /\ b >= 0 ]
		(1, 14)    f0(a, b, c) -> f2(a - 12, b + c - 13, c - 13) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ a - 11 >= 1 /\ b + 1 >= c - 11 /\ b - c + 12 >= 0 /\ a - 12 >= 0 /\ b >= 0 ]
		(1, 13)    f0(a, b, c) -> f2(a - 11, b + c - 12, c - 12) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ a - 10 >= 1 /\ b + 1 >= c - 10 /\ b - c + 11 >= 0 /\ a - 11 >= 0 /\ b >= 0 ]
		(1, 12)    f0(a, b, c) -> f2(a - 10, b + c - 11, c - 11) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ a - 9 >= 1 /\ b + 1 >= c - 9 /\ b - c + 10 >= 0 /\ a - 10 >= 0 /\ b >= 0 ]
		(1, 11)    f0(a, b, c) -> f2(a - 9, b + c - 10, c - 10) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ a - 8 >= 1 /\ b + 1 >= c - 8 /\ b - c + 9 >= 0 /\ a - 9 >= 0 /\ b >= 0 ]
		(1, 10)    f0(a, b, c) -> f2(a - 8, b + c - 9, c - 9) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ a - 7 >= 1 /\ b + 1 >= c - 7 /\ b - c + 8 >= 0 /\ a - 8 >= 0 /\ b >= 0 ]
		(1, 9)     f0(a, b, c) -> f2(a - 7, b + c - 8, c - 8) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ a - 6 >= 1 /\ b + 1 >= c - 6 /\ b - c + 7 >= 0 /\ a - 7 >= 0 /\ b >= 0 ]
		(1, 8)     f0(a, b, c) -> f2(a - 6, b + c - 7, c - 7) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ a - 5 >= 1 /\ b + 1 >= c - 5 /\ b - c + 6 >= 0 /\ a - 6 >= 0 /\ b >= 0 ]
		(1, 7)     f0(a, b, c) -> f2(a - 5, b + c - 6, c - 6) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ a - 4 >= 1 /\ b + 1 >= c - 4 /\ b - c + 5 >= 0 /\ a - 5 >= 0 /\ b >= 0 ]
		(1, 6)     f0(a, b, c) -> f2(a - 4, b + c - 5, c - 5) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ a - 3 >= 1 /\ b + 1 >= c - 3 /\ b - c + 4 >= 0 /\ a - 4 >= 0 /\ b >= 0 ]
		(1, 5)     f0(a, b, c) -> f2(a - 3, b + c - 4, c - 4) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ a - 2 >= 1 /\ b + 1 >= c - 2 /\ b - c + 3 >= 0 /\ a - 3 >= 0 /\ b >= 0 ]
		(1, 4)     f0(a, b, c) -> f2(a - 2, b + c - 3, c - 3) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ a - 1 >= 1 /\ b + 1 >= c - 1 /\ b - c + 2 >= 0 /\ a - 2 >= 0 /\ b >= 0 ]
		(1, 3)     f0(a, b, c) -> f2(a - 1, b + c - 2, c - 2) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ a >= 1 /\ b + 1 >= c /\ b - c + 1 >= 0 /\ a - 1 >= 0 /\ b >= 0 ]
		(1, 2)     f0(a, b, c) -> f2(a, b + c - 1, c - 1) [ a >= 0 /\ b >= c /\ b - c >= 0 /\ b >= 0 ]
		(?, 1)     f2(a, b, c) -> f2(a, b + c - 1, c - 1) [ b - c >= 0 /\ a >= 0 /\ b >= 0 ]
		(a, 1)     f2(a, b, c) -> f2(a - 1, b, c - 1) [ b - c >= 0 /\ a >= 0 /\ a >= 1 /\ b + 1 >= c ]
	start location:	f0
	leaf cost:	0

Complexity upper bound ?

Time: 5.305 sec (SMT: 4.746 sec)