MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f3(a, b, c, d) -> f1(0, b, c, d)
		(?, 1)    f1(a, b, c, d) -> f2(a, b, c, e) [ b >= c ]
		(?, 1)    f1(a, b, c, d) -> f2(1, b + 1, c, e) [ b + 1 = c /\ a = 0 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(1, 1)    f3(a, b, c, d) -> f1(0, b, c, d)
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f1: -X_1 >= 0 /\ X_1 >= 0


This yielded the following problem:
3:	T:
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
		(1, 1)    f3(a, b, c, d) -> f1(0, b, c, d)
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b, c, d) with all transitions in problem 3, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f3(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 ] with all transitions in problem 4, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 2, c + 2, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f3(a, b, c, d) -> f1(0, b + 2, c + 2, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 2, c + 2, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 ] with all transitions in problem 5, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 3, c + 3, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f3(a, b, c, d) -> f1(0, b + 3, c + 3, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 3, c + 3, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 ] with all transitions in problem 6, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 4, c + 4, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f3(a, b, c, d) -> f1(0, b + 4, c + 4, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 4, c + 4, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 ] with all transitions in problem 7, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 5, c + 5, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 ]
We thus obtain the following problem:
8:	T:
		(1, 6)    f3(a, b, c, d) -> f1(0, b + 5, c + 5, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 5, c + 5, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 ] with all transitions in problem 8, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 6, c + 6, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 ]
We thus obtain the following problem:
9:	T:
		(1, 7)    f3(a, b, c, d) -> f1(0, b + 6, c + 6, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 6, c + 6, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 ] with all transitions in problem 9, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 7, c + 7, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 ]
We thus obtain the following problem:
10:	T:
		(1, 8)    f3(a, b, c, d) -> f1(0, b + 7, c + 7, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 7, c + 7, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 ] with all transitions in problem 10, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 8, c + 8, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 ]
We thus obtain the following problem:
11:	T:
		(1, 9)    f3(a, b, c, d) -> f1(0, b + 8, c + 8, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 ]
		(?, 1)    f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 8, c + 8, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 ] with all transitions in problem 11, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 9, c + 9, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 ]
We thus obtain the following problem:
12:	T:
		(1, 10)    f3(a, b, c, d) -> f1(0, b + 9, c + 9, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 9, c + 9, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 ] with all transitions in problem 12, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 10, c + 10, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 ]
We thus obtain the following problem:
13:	T:
		(1, 11)    f3(a, b, c, d) -> f1(0, b + 10, c + 10, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 10, c + 10, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 ] with all transitions in problem 13, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 11, c + 11, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 ]
We thus obtain the following problem:
14:	T:
		(1, 12)    f3(a, b, c, d) -> f1(0, b + 11, c + 11, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 11, c + 11, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 ] with all transitions in problem 14, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 12, c + 12, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 ]
We thus obtain the following problem:
15:	T:
		(1, 13)    f3(a, b, c, d) -> f1(0, b + 12, c + 12, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 12, c + 12, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 ] with all transitions in problem 15, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 13, c + 13, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 ]
We thus obtain the following problem:
16:	T:
		(1, 14)    f3(a, b, c, d) -> f1(0, b + 13, c + 13, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 13, c + 13, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 ] with all transitions in problem 16, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 14, c + 14, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 /\ c + 13 >= b + 15 /\ c + 13 >= b + 14 ]
We thus obtain the following problem:
17:	T:
		(1, 15)    f3(a, b, c, d) -> f1(0, b + 14, c + 14, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 /\ c + 13 >= b + 15 /\ c + 13 >= b + 14 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

By chaining the transition f3(a, b, c, d) -> f1(0, b + 14, c + 14, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 /\ c + 13 >= b + 15 /\ c + 13 >= b + 14 ] with all transitions in problem 17, the following new transition is obtained:
	f3(a, b, c, d) -> f1(0, b + 15, c + 15, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 /\ c + 13 >= b + 15 /\ c + 13 >= b + 14 /\ c + 14 >= b + 16 /\ c + 14 >= b + 15 ]
We thus obtain the following problem:
18:	T:
		(1, 16)    f3(a, b, c, d) -> f1(0, b + 15, c + 15, d) [ 0 >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ 0 = 0 /\ c + 1 >= b + 3 /\ c + 1 >= b + 2 /\ c + 2 >= b + 4 /\ c + 2 >= b + 3 /\ c + 3 >= b + 5 /\ c + 3 >= b + 4 /\ c + 4 >= b + 6 /\ c + 4 >= b + 5 /\ c + 5 >= b + 7 /\ c + 5 >= b + 6 /\ c + 6 >= b + 8 /\ c + 6 >= b + 7 /\ c + 7 >= b + 9 /\ c + 7 >= b + 8 /\ c + 8 >= b + 10 /\ c + 8 >= b + 9 /\ c + 9 >= b + 11 /\ c + 9 >= b + 10 /\ c + 10 >= b + 12 /\ c + 10 >= b + 11 /\ c + 11 >= b + 13 /\ c + 11 >= b + 12 /\ c + 12 >= b + 14 /\ c + 12 >= b + 13 /\ c + 13 >= b + 15 /\ c + 13 >= b + 14 /\ c + 14 >= b + 16 /\ c + 14 >= b + 15 ]
		(?, 1)     f1(a, b, c, d) -> f1(0, b + 1, c + 1, d) [ -a >= 0 /\ a >= 0 /\ c >= b + 2 /\ c >= b + 1 /\ a = 0 ]
	start location:	f3
	leaf cost:	2

Complexity upper bound ?

Time: 1.522 sec (SMT: 1.409 sec)