WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 1:
	eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_1 + 1 ]
	eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= Ar_2 ]
	eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 /\ Ar_1 >= Ar_2 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval) = V_1 - V_2
	Pol(start) = V_1 - V_2
	Pol(koat_start) = V_1 - V_2
orients all transitions weakly and the transition
	eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)              eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)              eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval) = -V_2 + V_3
	Pol(start) = -V_2 + V_3
	Pol(koat_start) = -V_2 + V_3
orients all transitions weakly and the transition
	eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
strictly and produces the following problem:
5:	T:
		(Comp: Ar_1 + Ar_2, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)              eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval) = V_1 - V_2
	Pol(start) = V_1 - V_2
	Pol(koat_start) = V_1 - V_2
orients all transitions weakly and the transition
	eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
6:	T:
		(Comp: Ar_1 + Ar_2, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= Ar_1 + 1 /\ Ar_1 >= Ar_0 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)    eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 3*Ar_1 + Ar_2 + 2*Ar_0 + 1

Time: 0.994 sec (SMT: 0.961 sec)