2.07/1.67	WORST_CASE(?, O(n^1))
2.07/1.68	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.07/1.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.07/1.68	
2.07/1.68	
2.07/1.68	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.07/1.68	
2.07/1.68	(0) CpxIntTrs
2.07/1.68	(1) Koat Proof [FINISHED, 361 ms]
2.07/1.68	(2) BOUNDS(1, n^1)
2.07/1.68	
2.07/1.68	
2.07/1.68	----------------------------------------
2.07/1.68	
2.07/1.68	(0)
2.07/1.68	Obligation:
2.07/1.68	Complexity Int TRS consisting of the following rules:
2.07/1.68	eval_foo_start(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_p, v_q)) :|: TRUE
2.07/1.68	eval_foo_bb0_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_p, v_q, v_p, v_q)) :|: TRUE
2.07/1.68	eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 > 0 && v_.0 > 0 && v_.0 < v_.01
2.07/1.68	eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 > 0 && v_.0 > 0 && v_.0 > v_.01
2.07/1.68	eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 <= 0
2.07/1.68	eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q)) :|: v_.0 <= 0
2.07/1.68	eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q)) :|: v_.0 >= v_.01 && v_.0 <= v_.01
2.07/1.68	eval_foo_bb2_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 < v_.0
2.07/1.68	eval_foo_bb2_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 >= v_.0
2.07/1.68	eval_foo_bb3_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_p, v_q)) :|: TRUE
2.07/1.68	eval_foo_bb4_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_p, v_q)) :|: v_.0 < v_.01
2.07/1.68	eval_foo_bb4_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_p, v_q)) :|: v_.0 >= v_.01
2.07/1.68	eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_stop(v_.0, v_.01, v_p, v_q)) :|: TRUE
2.07/1.68	
2.07/1.68	The start-symbols are:[eval_foo_start_4]
2.07/1.68	
2.07/1.68	
2.07/1.68	----------------------------------------
2.07/1.68	
2.07/1.68	(1) Koat Proof (FINISHED)
2.07/1.68	YES(?, 7*ar_1 + 14*ar_3 + 14)
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	Initial complexity problem:
2.07/1.68	
2.07/1.68	1:	T:
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.07/1.68	
2.07/1.68		start location:	koat_start
2.07/1.68	
2.07/1.68		leaf cost:	0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.07/1.68	
2.07/1.68	2:	T:
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.07/1.68	
2.07/1.68		start location:	koat_start
2.07/1.68	
2.07/1.68		leaf cost:	0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	A polynomial rank function with
2.07/1.68	
2.07/1.68		Pol(evalfoostart) = 2
2.07/1.68	
2.07/1.68		Pol(evalfoobb0in) = 2
2.07/1.68	
2.07/1.68		Pol(evalfoobb1in) = 2
2.07/1.68	
2.07/1.68		Pol(evalfoobb2in) = 2
2.07/1.68	
2.07/1.68		Pol(evalfoocritedgein) = 1
2.07/1.68	
2.07/1.68		Pol(evalfoobb3in) = 2
2.07/1.68	
2.07/1.68		Pol(evalfoobb4in) = 2
2.07/1.68	
2.07/1.68		Pol(evalfoostop) = 0
2.07/1.68	
2.07/1.68		Pol(koat_start) = 2
2.07/1.68	
2.07/1.68	orients all transitions weakly and the transitions
2.07/1.68	
2.07/1.68		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68	strictly and produces the following problem:
2.07/1.68	
2.07/1.68	3:	T:
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3))
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.07/1.68	
2.07/1.68		start location:	koat_start
2.07/1.68	
2.07/1.68		leaf cost:	0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.07/1.68	
2.07/1.68	  For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.68	
2.07/1.68	  For symbol evalfoobb2in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0
2.07/1.68	
2.07/1.68	  For symbol evalfoobb3in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0
2.07/1.68	
2.07/1.68	  For symbol evalfoobb4in: X_4 - 1 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0
2.07/1.68	
2.07/1.68	  For symbol evalfoocritedgein: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	This yielded the following problem:
2.07/1.68	
2.07/1.68	4:	T:
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68		start location:	koat_start
2.07/1.68	
2.07/1.68		leaf cost:	0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	A polynomial rank function with
2.07/1.68	
2.07/1.68		Pol(koat_start) = V_2 + 2*V_4
2.07/1.68	
2.07/1.68		Pol(evalfoostart) = V_2 + 2*V_4
2.07/1.68	
2.07/1.68		Pol(evalfoocritedgein) = V_1 + 2*V_3
2.07/1.68	
2.07/1.68		Pol(evalfoostop) = V_1 + 2*V_3
2.07/1.68	
2.07/1.68		Pol(evalfoobb4in) = V_1 + 2*V_3
2.07/1.68	
2.07/1.68		Pol(evalfoobb1in) = V_1 + 2*V_3
2.07/1.68	
2.07/1.68		Pol(evalfoobb3in) = V_1 + 2*V_3 - 1
2.07/1.68	
2.07/1.68		Pol(evalfoobb2in) = V_1 + 2*V_3
2.07/1.68	
2.07/1.68		Pol(evalfoobb0in) = V_2 + 2*V_4
2.07/1.68	
2.07/1.68	orients all transitions weakly and the transitions
2.07/1.68	
2.07/1.68		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.07/1.68	
2.07/1.68		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68	strictly and produces the following problem:
2.07/1.68	
2.07/1.68	5:	T:
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 0)                koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)                evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)                evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ?, Cost: 1)                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)                evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)                evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68		start location:	koat_start
2.07/1.68	
2.07/1.68		leaf cost:	0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	Repeatedly propagating knowledge in problem 5 produces the following problem:
2.07/1.68	
2.07/1.68	6:	T:
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 0)                    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3 + 1, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3, Cost: 1)        evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3, Cost: 1)        evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3, Cost: 1)        evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 = ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.07/1.68	
2.07/1.68			(Comp: 2, Cost: 1)                    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: ar_1 + 2*ar_3 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ]
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)                    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.07/1.68	
2.07/1.68			(Comp: 1, Cost: 1)                    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.07/1.68	
2.07/1.68		start location:	koat_start
2.07/1.68	
2.07/1.68		leaf cost:	0
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	Complexity upper bound 7*ar_1 + 14*ar_3 + 14
2.07/1.68	
2.07/1.68	
2.07/1.68	
2.07/1.68	Time: 0.388 sec (SMT: 0.305 sec)
2.07/1.68	
2.07/1.68	
2.07/1.68	----------------------------------------
2.07/1.68	
2.07/1.68	(2)
2.07/1.68	BOUNDS(1, n^1)
2.51/1.72	EOF