
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(end(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(sumto(Ar_0 + 1, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1) -> Com_1(sumto(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: ?, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(end(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(sumto(Ar_0 + 1, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1) -> Com_1(sumto(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(sumto) = 1
	Pol(end) = 0
	Pol(start) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	sumto(Ar_0, Ar_1) -> Com_1(end(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(end(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(sumto(Ar_0 + 1, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1) -> Com_1(sumto(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(sumto) = -V_1 + V_2 + 1
	Pol(end) = -V_1 + V_2
	Pol(start) = -V_1 + V_2 + 1
	Pol(koat_start) = -V_1 + V_2 + 1
orients all transitions weakly and the transition
	sumto(Ar_0, Ar_1) -> Com_1(sumto(Ar_0 + 1, Ar_1)) [ Ar_1 >= Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)                  sumto(Ar_0, Ar_1) -> Com_1(end(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    sumto(Ar_0, Ar_1) -> Com_1(sumto(Ar_0 + 1, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 1)                  start(Ar_0, Ar_1) -> Com_1(sumto(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)                  koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound Ar_0 + Ar_1 + 3

Time: 0.012 sec (SMT: 0.010 sec)
