2.18/1.32	WORST_CASE(?, O(n^1))
2.18/1.33	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.18/1.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.18/1.33	
2.18/1.33	
2.18/1.33	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.18/1.33	
2.18/1.33	(0) CpxIntTrs
2.18/1.33	(1) Koat Proof [FINISHED, 76 ms]
2.18/1.33	(2) BOUNDS(1, n^1)
2.18/1.33	
2.18/1.33	
2.18/1.33	----------------------------------------
2.18/1.33	
2.18/1.33	(0)
2.18/1.33	Obligation:
2.18/1.33	Complexity Int TRS consisting of the following rules:
2.18/1.33	eval_foo_start(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_i, v_x, v_y)) :|: TRUE
2.18/1.33	eval_foo_bb0_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_i, v_x, v_y)) :|: v_x < 0
2.18/1.33	eval_foo_bb0_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_i, v_x, v_y)) :|: v_x > 0
2.18/1.33	eval_foo_bb0_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_i, v_x, v_y)) :|: v_x >= 0 && v_x <= 0
2.18/1.33	eval_foo_bb1_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_i, v_x, v_y)) :|: v_.01 > 0 && v_y > 0
2.18/1.33	eval_foo_bb1_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_i, v_x, v_y)) :|: v_.01 <= 0
2.18/1.33	eval_foo_bb1_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_i, v_x, v_y)) :|: v_y <= 0
2.18/1.33	eval_foo_bb2_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 - v_y, v_i, v_x, v_y)) :|: TRUE
2.18/1.33	eval_foo_bb3_in(v_.01, v_i, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_i, v_x, v_y)) :|: TRUE
2.18/1.33	
2.18/1.33	The start-symbols are:[eval_foo_start_4]
2.18/1.33	
2.18/1.33	
2.18/1.33	----------------------------------------
2.18/1.33	
2.18/1.33	(1) Koat Proof (FINISHED)
2.18/1.33	YES(?, 2*ar_0 + 10)
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	Initial complexity problem:
2.18/1.33	
2.18/1.33	1:	T:
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.33	
2.18/1.33		start location:	koat_start
2.18/1.33	
2.18/1.33		leaf cost:	0
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.18/1.33	
2.18/1.33	2:	T:
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.33	
2.18/1.33		start location:	koat_start
2.18/1.33	
2.18/1.33		leaf cost:	0
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	A polynomial rank function with
2.18/1.33	
2.18/1.33		Pol(evalfoostart) = 2
2.18/1.33	
2.18/1.33		Pol(evalfoobb0in) = 2
2.18/1.33	
2.18/1.33		Pol(evalfoobb1in) = 2
2.18/1.33	
2.18/1.33		Pol(evalfoobb3in) = 1
2.18/1.33	
2.18/1.33		Pol(evalfoobb2in) = 2
2.18/1.33	
2.18/1.33		Pol(evalfoostop) = 0
2.18/1.33	
2.18/1.33		Pol(koat_start) = 2
2.18/1.33	
2.18/1.33	orients all transitions weakly and the transitions
2.18/1.33	
2.18/1.33		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.18/1.33	
2.18/1.33		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.18/1.33	
2.18/1.33	strictly and produces the following problem:
2.18/1.33	
2.18/1.33	3:	T:
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.33	
2.18/1.33		start location:	koat_start
2.18/1.33	
2.18/1.33		leaf cost:	0
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	A polynomial rank function with
2.18/1.33	
2.18/1.33		Pol(evalfoobb2in) = V_2 - V_3
2.18/1.33	
2.18/1.33		Pol(evalfoobb1in) = V_2
2.18/1.33	
2.18/1.33	and size complexities
2.18/1.33	
2.18/1.33		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.18/1.33	
2.18/1.33		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.18/1.33	
2.18/1.33		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))", 0-1) = ?
2.18/1.33	
2.18/1.33		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-1) = ?
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-1) = ?
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\\ ar_2 >= 1 ]", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\\ ar_2 >= 1 ]", 0-1) = ?
2.18/1.33	
2.18/1.33		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\\ ar_2 >= 1 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]", 0-0) = 0
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]", 0-1) = ar_1
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
2.18/1.33	
2.18/1.33		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.18/1.33	
2.18/1.33		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.18/1.33	
2.18/1.33		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.18/1.33	
2.18/1.33	orients the transitions
2.18/1.33	
2.18/1.33		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))
2.18/1.33	
2.18/1.33		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33	weakly and the transition
2.18/1.33	
2.18/1.33		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33	strictly and produces the following problem:
2.18/1.33	
2.18/1.33	4:	T:
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]
2.18/1.33	
2.18/1.33			(Comp: ar_0, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.18/1.33	
2.18/1.33			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)       evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.33	
2.18/1.33		start location:	koat_start
2.18/1.33	
2.18/1.33		leaf cost:	0
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.18/1.33	
2.18/1.33	5:	T:
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ 0 >= ar_0 + 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 = 0 ]
2.18/1.33	
2.18/1.33			(Comp: ar_0, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 /\ ar_2 >= 1 ]
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.18/1.33	
2.18/1.33			(Comp: ar_0, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - ar_2, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 2, Cost: 1)       evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.18/1.33	
2.18/1.33			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.33	
2.18/1.33		start location:	koat_start
2.18/1.33	
2.18/1.33		leaf cost:	0
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	Complexity upper bound 2*ar_0 + 10
2.18/1.33	
2.18/1.33	
2.18/1.33	
2.18/1.33	Time: 0.108 sec (SMT: 0.099 sec)
2.18/1.33	
2.18/1.33	
2.18/1.33	----------------------------------------
2.18/1.33	
2.18/1.33	(2)
2.18/1.33	BOUNDS(1, n^1)
2.34/1.35	EOF