2.19/1.41	WORST_CASE(?, O(n^1))
2.19/1.42	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.19/1.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.19/1.42	
2.19/1.42	
2.19/1.42	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.19/1.42	
2.19/1.42	(0) CpxIntTrs
2.19/1.42	(1) Koat Proof [FINISHED, 174 ms]
2.19/1.42	(2) BOUNDS(1, n^1)
2.19/1.42	
2.19/1.42	
2.19/1.42	----------------------------------------
2.19/1.42	
2.19/1.42	(0)
2.19/1.42	Obligation:
2.19/1.42	Complexity Int TRS consisting of the following rules:
2.19/1.42	eval_foo_start(v_.0, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_x, v_y)) :|: TRUE
2.19/1.42	eval_foo_bb0_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_y, v_x, v_y)) :|: v_x > 0
2.19/1.42	eval_foo_bb0_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_x, v_y)) :|: v_x <= 0
2.19/1.42	eval_foo_bb1_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_x, v_y)) :|: v_x > v_.0
2.19/1.42	eval_foo_bb1_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_x, v_y)) :|: v_x <= v_.0
2.19/1.42	eval_foo_bb2_in(v_.0, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x + v_.0, v_x, v_y)) :|: TRUE
2.19/1.42	eval_foo_bb3_in(v_.0, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_x, v_y)) :|: TRUE
2.19/1.42	
2.19/1.42	The start-symbols are:[eval_foo_start_3]
2.19/1.42	
2.19/1.42	
2.19/1.42	----------------------------------------
2.19/1.42	
2.19/1.42	(1) Koat Proof (FINISHED)
2.19/1.42	YES(?, 4*ar_0 + 4*ar_2 + 7)
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	Initial complexity problem:
2.19/1.42	
2.19/1.42	1:	T:
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.42	
2.19/1.42		start location:	koat_start
2.19/1.42	
2.19/1.42		leaf cost:	0
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.19/1.42	
2.19/1.42	2:	T:
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.42	
2.19/1.42		start location:	koat_start
2.19/1.42	
2.19/1.42		leaf cost:	0
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	A polynomial rank function with
2.19/1.42	
2.19/1.42		Pol(evalfoostart) = 2
2.19/1.42	
2.19/1.42		Pol(evalfoobb0in) = 2
2.19/1.42	
2.19/1.42		Pol(evalfoobb1in) = 2
2.19/1.42	
2.19/1.42		Pol(evalfoobb3in) = 1
2.19/1.42	
2.19/1.42		Pol(evalfoobb2in) = 2
2.19/1.42	
2.19/1.42		Pol(evalfoostop) = 0
2.19/1.42	
2.19/1.42		Pol(koat_start) = 2
2.19/1.42	
2.19/1.42	orients all transitions weakly and the transitions
2.19/1.42	
2.19/1.42		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 ]
2.19/1.42	
2.19/1.42	strictly and produces the following problem:
2.19/1.42	
2.19/1.42	3:	T:
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.42	
2.19/1.42		start location:	koat_start
2.19/1.42	
2.19/1.42		leaf cost:	0
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.19/1.42	
2.19/1.42	  For symbol evalfoobb1in: X_2 - X_3 >= 0 /\ X_1 - 1 >= 0
2.19/1.42	
2.19/1.42	  For symbol evalfoobb2in: X_2 - X_3 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	This yielded the following problem:
2.19/1.42	
2.19/1.42	4:	T:
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.42	
2.19/1.42			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.19/1.42	
2.19/1.42			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42		start location:	koat_start
2.19/1.42	
2.19/1.42		leaf cost:	0
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	A polynomial rank function with
2.19/1.42	
2.19/1.42		Pol(evalfoobb2in) = 2*V_1 - 2*V_2 - 1
2.19/1.42	
2.19/1.42		Pol(evalfoobb1in) = 2*V_1 - 2*V_2
2.19/1.42	
2.19/1.42	and size complexities
2.19/1.42	
2.19/1.42		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.19/1.42	
2.19/1.42		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.19/1.42	
2.19/1.42		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-1) = ?
2.19/1.42	
2.19/1.42		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 ]", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 ]", 0-1) = ?
2.19/1.42	
2.19/1.42		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 ]", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ?
2.19/1.42	
2.19/1.42		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.19/1.42	
2.19/1.42		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.19/1.42	
2.19/1.42		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.19/1.42	
2.19/1.42		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.19/1.42	
2.19/1.42		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.19/1.42	
2.19/1.42	orients the transitions
2.19/1.42	
2.19/1.42		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.19/1.42	
2.19/1.42		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42	weakly and the transitions
2.19/1.42	
2.19/1.42		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.19/1.42	
2.19/1.42		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42	strictly and produces the following problem:
2.19/1.42	
2.19/1.42	5:	T:
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.19/1.42	
2.19/1.42			(Comp: 2, Cost: 1)                  evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42			(Comp: 2*ar_0 + 2*ar_2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0 + ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.19/1.42	
2.19/1.42			(Comp: 2, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: 2*ar_0 + 2*ar_2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.19/1.42	
2.19/1.42			(Comp: 1, Cost: 1)                  evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.19/1.42	
2.19/1.42		start location:	koat_start
2.19/1.42	
2.19/1.42		leaf cost:	0
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	Complexity upper bound 4*ar_0 + 4*ar_2 + 7
2.19/1.42	
2.19/1.42	
2.19/1.42	
2.19/1.42	Time: 0.184 sec (SMT: 0.165 sec)
2.19/1.42	
2.19/1.42	
2.19/1.42	----------------------------------------
2.19/1.42	
2.19/1.42	(2)
2.19/1.42	BOUNDS(1, n^1)
2.19/1.44	EOF