MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f1(a, b) -> f0(a, b)
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_1
and size complexities
	S("f0(a, b) -> f0(a + b, b) [ a >= 1 /\\ 0 >= b + 1 ]", 0-0) = a + b
	S("f0(a, b) -> f0(a + b, b) [ a >= 1 /\\ 0 >= b + 1 ]", 0-1) = b
	S("f0(a, b) -> f0(a + b, b) [ a >= 1 /\\ b >= 1 ]", 0-0) = ?
	S("f0(a, b) -> f0(a + b, b) [ a >= 1 /\\ b >= 1 ]", 0-1) = b
	S("f1(a, b) -> f0(a, b)", 0-0) = a
	S("f1(a, b) -> f0(a, b)", 0-1) = b
orients the transition
	f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
weakly and the transition
	f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
strictly and produces the following problem:
2:	T:
		(1, 1)    f1(a, b) -> f0(a, b)
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a, b) with all transitions in problem 2, the following new transitions are obtained:
	f1(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
We thus obtain the following problem:
3:	T:
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ] with all transitions in problem 3, the following new transition is obtained:
	f1(a, b) -> f0(a + 2*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 ]
We thus obtain the following problem:
4:	T:
		(1, 3)    f1(a, b) -> f0(a + 2*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 2*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 ] with all transitions in problem 4, the following new transition is obtained:
	f1(a, b) -> f0(a + 3*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 ]
We thus obtain the following problem:
5:	T:
		(1, 4)    f1(a, b) -> f0(a + 3*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 3*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 ] with all transitions in problem 5, the following new transition is obtained:
	f1(a, b) -> f0(a + 4*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 ]
We thus obtain the following problem:
6:	T:
		(1, 5)    f1(a, b) -> f0(a + 4*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 4*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 ] with all transitions in problem 6, the following new transition is obtained:
	f1(a, b) -> f0(a + 5*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 ]
We thus obtain the following problem:
7:	T:
		(1, 6)    f1(a, b) -> f0(a + 5*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 5*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 ] with all transitions in problem 7, the following new transition is obtained:
	f1(a, b) -> f0(a + 6*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 ]
We thus obtain the following problem:
8:	T:
		(1, 7)    f1(a, b) -> f0(a + 6*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 6*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 ] with all transitions in problem 8, the following new transition is obtained:
	f1(a, b) -> f0(a + 7*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 ]
We thus obtain the following problem:
9:	T:
		(1, 8)    f1(a, b) -> f0(a + 7*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 7*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 ] with all transitions in problem 9, the following new transition is obtained:
	f1(a, b) -> f0(a + 8*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 ]
We thus obtain the following problem:
10:	T:
		(1, 9)    f1(a, b) -> f0(a + 8*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 ]
		(1, 2)    f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)    f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 8*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 ] with all transitions in problem 10, the following new transition is obtained:
	f1(a, b) -> f0(a + 9*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 ]
We thus obtain the following problem:
11:	T:
		(1, 10)    f1(a, b) -> f0(a + 9*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 9*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 ] with all transitions in problem 11, the following new transition is obtained:
	f1(a, b) -> f0(a + 10*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 ]
We thus obtain the following problem:
12:	T:
		(1, 11)    f1(a, b) -> f0(a + 10*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 10*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 ] with all transitions in problem 12, the following new transition is obtained:
	f1(a, b) -> f0(a + 11*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 ]
We thus obtain the following problem:
13:	T:
		(1, 12)    f1(a, b) -> f0(a + 11*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 11*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 ] with all transitions in problem 13, the following new transition is obtained:
	f1(a, b) -> f0(a + 12*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 ]
We thus obtain the following problem:
14:	T:
		(1, 13)    f1(a, b) -> f0(a + 12*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 12*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 ] with all transitions in problem 14, the following new transition is obtained:
	f1(a, b) -> f0(a + 13*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 ]
We thus obtain the following problem:
15:	T:
		(1, 14)    f1(a, b) -> f0(a + 13*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 13*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 ] with all transitions in problem 15, the following new transition is obtained:
	f1(a, b) -> f0(a + 14*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 /\ a + 13*b >= 1 ]
We thus obtain the following problem:
16:	T:
		(1, 15)    f1(a, b) -> f0(a + 14*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 /\ a + 13*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

By chaining the transition f1(a, b) -> f0(a + 14*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 /\ a + 13*b >= 1 ] with all transitions in problem 16, the following new transition is obtained:
	f1(a, b) -> f0(a + 15*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 /\ a + 13*b >= 1 /\ a + 14*b >= 1 ]
We thus obtain the following problem:
17:	T:
		(1, 16)    f1(a, b) -> f0(a + 15*b, b) [ a >= 1 /\ 0 >= b + 1 /\ a + b >= 1 /\ a + 2*b >= 1 /\ a + 3*b >= 1 /\ a + 4*b >= 1 /\ a + 5*b >= 1 /\ a + 6*b >= 1 /\ a + 7*b >= 1 /\ a + 8*b >= 1 /\ a + 9*b >= 1 /\ a + 10*b >= 1 /\ a + 11*b >= 1 /\ a + 12*b >= 1 /\ a + 13*b >= 1 /\ a + 14*b >= 1 ]
		(1, 2)     f1(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(?, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ b >= 1 ]
		(a, 1)     f0(a, b) -> f0(a + b, b) [ a >= 1 /\ 0 >= b + 1 ]
	start location:	f1
	leaf cost:	0

Complexity upper bound ?

Time: 1.630 sec (SMT: 1.537 sec)