MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, f) [ 1023 >= e /\ e >= 1 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ e >= c + 1 ]
		(?, 1)    f14(a, b, c, d) -> f22(a, b, c, d) [ c >= e ]
	start location:	f0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, f) [ 1023 >= e /\ e >= 1 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ e >= c + 1 ]
	start location:	f0
	leaf cost:	1

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f14: X_3 >= 0


This yielded the following problem:
3:	T:
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, f) [ 1023 >= e /\ e >= 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 0, f) [ 1023 >= e /\ e >= 1 ] with all transitions in problem 3, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 1, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f0(a, b, c, d) -> f14(e, e, 1, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 1, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 ] with all transitions in problem 4, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 2, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f0(a, b, c, d) -> f14(e, e, 2, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 2, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 ] with all transitions in problem 5, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 3, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f0(a, b, c, d) -> f14(e, e, 3, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 3, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 ] with all transitions in problem 6, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 4, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f0(a, b, c, d) -> f14(e, e, 4, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 4, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 ] with all transitions in problem 7, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 5, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 ]
We thus obtain the following problem:
8:	T:
		(1, 6)    f0(a, b, c, d) -> f14(e, e, 5, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 5, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 ] with all transitions in problem 8, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 6, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 ]
We thus obtain the following problem:
9:	T:
		(1, 7)    f0(a, b, c, d) -> f14(e, e, 6, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 6, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 ] with all transitions in problem 9, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 7, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 ]
We thus obtain the following problem:
10:	T:
		(1, 8)    f0(a, b, c, d) -> f14(e, e, 7, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 7, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 ] with all transitions in problem 10, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 8, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 ]
We thus obtain the following problem:
11:	T:
		(1, 9)    f0(a, b, c, d) -> f14(e, e, 8, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 ]
		(?, 1)    f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)    f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 8, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 ] with all transitions in problem 11, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 9, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 ]
We thus obtain the following problem:
12:	T:
		(1, 10)    f0(a, b, c, d) -> f14(e, e, 9, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 9, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 ] with all transitions in problem 12, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 10, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 ]
We thus obtain the following problem:
13:	T:
		(1, 11)    f0(a, b, c, d) -> f14(e, e, 10, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 10, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 ] with all transitions in problem 13, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 11, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 ]
We thus obtain the following problem:
14:	T:
		(1, 12)    f0(a, b, c, d) -> f14(e, e, 11, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 11, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 ] with all transitions in problem 14, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 12, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 ]
We thus obtain the following problem:
15:	T:
		(1, 13)    f0(a, b, c, d) -> f14(e, e, 12, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 12, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 ] with all transitions in problem 15, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 13, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 ]
We thus obtain the following problem:
16:	T:
		(1, 14)    f0(a, b, c, d) -> f14(e, e, 13, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 13, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 ] with all transitions in problem 16, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 14, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 /\ 13 >= 0 /\ e'''''''''''''' >= 14 ]
We thus obtain the following problem:
17:	T:
		(1, 15)    f0(a, b, c, d) -> f14(e, e, 14, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 /\ 13 >= 0 /\ e'''''''''''''' >= 14 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a, b, c, d) -> f14(e, e, 14, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 /\ 13 >= 0 /\ e'''''''''''''' >= 14 ] with all transitions in problem 17, the following new transition is obtained:
	f0(a, b, c, d) -> f14(e, e, 15, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 /\ 13 >= 0 /\ e'''''''''''''' >= 14 /\ 14 >= 0 /\ e''''''''''''''' >= 15 ]
We thus obtain the following problem:
18:	T:
		(1, 16)    f0(a, b, c, d) -> f14(e, e, 15, f) [ 1023 >= e /\ e >= 1 /\ 0 >= 0 /\ e' >= 1 /\ 1 >= 0 /\ e'' >= 2 /\ 2 >= 0 /\ e''' >= 3 /\ 3 >= 0 /\ e'''' >= 4 /\ 4 >= 0 /\ e''''' >= 5 /\ 5 >= 0 /\ e'''''' >= 6 /\ 6 >= 0 /\ e''''''' >= 7 /\ 7 >= 0 /\ e'''''''' >= 8 /\ 8 >= 0 /\ e''''''''' >= 9 /\ 9 >= 0 /\ e'''''''''' >= 10 /\ 10 >= 0 /\ e''''''''''' >= 11 /\ 11 >= 0 /\ e'''''''''''' >= 12 /\ 12 >= 0 /\ e''''''''''''' >= 13 /\ 13 >= 0 /\ e'''''''''''''' >= 14 /\ 14 >= 0 /\ e''''''''''''''' >= 15 ]
		(?, 1)     f14(a, b, c, d) -> f14(a, b, c + 1, d) [ c >= 0 /\ e >= c + 1 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ e >= 1024 ]
		(1, 1)     f0(a, b, c, d) -> f14(e, e, 0, d) [ 0 >= e ]
	start location:	f0
	leaf cost:	1

Complexity upper bound ?

Time: 2.242 sec (SMT: 2.106 sec)