MAYBE

Initial complexity problem:
1:	T:
		(?, 1)    f4(a, b) -> f5(a, b) [ 0 >= a + 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ a >= 1 ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ 3 >= b ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, 1) [ b = 4 ]
		(?, 1)    f4(a, b) -> f12(0, b) [ a = 0 ]
	start location:	f0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(?, 1)    f4(a, b) -> f5(a, b) [ 0 >= a + 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ a >= 1 ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ 3 >= b ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, 1) [ b = 4 ]
	start location:	f0
	leaf cost:	1

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f4: X_2 >= 0
  For symbol f5: X_2 >= 0


This yielded the following problem:
3:	T:
		(?, 1)    f5(a, b) -> f4(c, 1) [ b >= 0 /\ b = 4 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c, 1) [ b >= 0 /\ b = 4 ] with all transitions in problem 3, the following new transitions are obtained:
	f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 ]
	f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 ]
We thus obtain the following problem:
4:	T:
		(?, 2)    f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 ]
		(?, 2)    f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 ] with all transitions in problem 4, the following new transition is obtained:
	f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
We thus obtain the following problem:
5:	T:
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 2)    f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c, 1) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 ] with all transitions in problem 5, the following new transition is obtained:
	f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 ]
We thus obtain the following problem:
6:	T:
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 ] with all transitions in problem 6, the following new transitions are obtained:
	f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 ]
	f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 ]
We thus obtain the following problem:
7:	T:
		(?, 4)    f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 ]
		(?, 4)    f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 ] with all transitions in problem 7, the following new transition is obtained:
	f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
We thus obtain the following problem:
8:	T:
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 4)    f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 ] with all transitions in problem 8, the following new transition is obtained:
	f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 ]
We thus obtain the following problem:
9:	T:
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 ]
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 ] with all transitions in problem 9, the following new transitions are obtained:
	f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 ]
	f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ]
We thus obtain the following problem:
10:	T:
		(?, 6)    f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 ]
		(?, 6)    f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ]
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 ] with all transitions in problem 10, the following new transition is obtained:
	f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
We thus obtain the following problem:
11:	T:
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
		(?, 6)    f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ]
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ] with all transitions in problem 11, the following new transition is obtained:
	f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 ]
We thus obtain the following problem:
12:	T:
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 ]
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 ] with all transitions in problem 12, the following new transitions are obtained:
	f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
	f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
We thus obtain the following problem:
13:	T:
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ] with all transitions in problem 13, the following new transitions are obtained:
	f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
	f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
We thus obtain the following problem:
14:	T:
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 5)    f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 ] with all transitions in problem 14, the following new transitions are obtained:
	f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 ]
	f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ]
We thus obtain the following problem:
15:	T:
		(?, 6)    f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 ]
		(?, 6)    f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 ] with all transitions in problem 15, the following new transition is obtained:
	f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
We thus obtain the following problem:
16:	T:
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
		(?, 6)    f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f5(c'', 3) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 ] with all transitions in problem 16, the following new transition is obtained:
	f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 ]
We thus obtain the following problem:
17:	T:
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 ]
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 ] with all transitions in problem 17, the following new transitions are obtained:
	f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
	f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
We thus obtain the following problem:
18:	T:
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 7)    f5(a, b) -> f4(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ 0 >= c' + 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ 0 >= c'' + 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ 0 >= c''' + 1 ]
		(?, 8)    f5(a, b) -> f5(c''', 4) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ c >= 1 /\ 3 >= 1 /\ 2 >= 0 /\ c' >= 1 /\ 3 >= 2 /\ 3 >= 0 /\ c'' >= 1 /\ 3 >= 3 /\ 4 >= 0 /\ c''' >= 1 ]
		(?, 3)    f5(a, b) -> f4(c', 2) [ b >= 0 /\ b = 4 /\ 1 >= 0 /\ 0 >= c + 1 /\ 3 >= 1 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ b >= 5 ]
		(?, 1)    f5(a, b) -> f4(c, b + 1) [ b >= 0 /\ 3 >= b ]
		(1, 1)    f0(a, b) -> f4(c, 0)
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ a >= 1 ]
		(?, 1)    f4(a, b) -> f5(a, b) [ b >= 0 /\ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

Complexity upper bound ?

Time: 1.999 sec (SMT: 1.813 sec)