2.51/1.53	WORST_CASE(?, O(n^1))
2.51/1.54	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.51/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.51/1.54	
2.51/1.54	
2.51/1.54	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.51/1.54	
2.51/1.54	(0) CpxIntTrs
2.51/1.54	(1) Koat Proof [FINISHED, 378 ms]
2.51/1.54	(2) BOUNDS(1, n^1)
2.51/1.54	
2.51/1.54	
2.51/1.54	----------------------------------------
2.51/1.54	
2.51/1.54	(0)
2.51/1.54	Obligation:
2.51/1.54	Complexity Int TRS consisting of the following rules:
2.51/1.54	eval_foo_start(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: TRUE
2.51/1.54	eval_foo_bb0_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb1_in(v_x, v_oldx, v_3, v_oldx, v_x)) :|: TRUE
2.51/1.54	eval_foo_bb1_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: v_.0 > 1 && 2 * v_.0 <= v_.01
2.51/1.54	eval_foo_bb1_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: v_.0 <= 1
2.51/1.54	eval_foo_bb1_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_3, v_oldx, v_x)) :|: 2 * v_.0 > v_.01
2.51/1.54	eval_foo_bb2_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_2(v_.0, v_.01, v_3, v_oldx, v_x)) :|: TRUE
2.51/1.54	eval_foo_2(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_oldx, v_x), eval_foo_3(v_.0, v_.01, nondef.0, v_oldx, v_x)) :|: TRUE
2.51/1.54	eval_foo_3(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_bb1_in(v_3, v_.0, v_3, v_oldx, v_x)) :|: TRUE
2.51/1.54	eval_foo_.critedge_in(v_.0, v_.01, v_3, v_oldx, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_oldx, v_x)) :|: TRUE
2.51/1.54	
2.51/1.54	The start-symbols are:[eval_foo_start_5]
2.51/1.54	
2.51/1.54	
2.51/1.54	----------------------------------------
2.51/1.54	
2.51/1.54	(1) Koat Proof (FINISHED)
2.51/1.54	YES(?, 18*ar_3 + 8)
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	Initial complexity problem:
2.51/1.54	
2.51/1.54	1:	T:
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_2 >= 2*ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 2*ar_0 >= ar_2 + 1 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_0, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.51/1.54	
2.51/1.54		start location:	koat_start
2.51/1.54	
2.51/1.54		leaf cost:	0
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.51/1.54	
2.51/1.54	2:	T:
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_2 >= 2*ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 2*ar_0 >= ar_2 + 1 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_0, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.51/1.54	
2.51/1.54		start location:	koat_start
2.51/1.54	
2.51/1.54		leaf cost:	0
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	A polynomial rank function with
2.51/1.54	
2.51/1.54		Pol(evalfoostart) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoobb0in) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoobb1in) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoobb2in) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoocritedgein) = 1
2.51/1.54	
2.51/1.54		Pol(evalfoo2) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoo20) = 0
2.51/1.54	
2.51/1.54		Pol(evalVERIFIERnondetintstart) = 0
2.51/1.54	
2.51/1.54		Pol(evalfoo21) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoo3) = 2
2.51/1.54	
2.51/1.54		Pol(evalfoostop) = 0
2.51/1.54	
2.51/1.54		Pol(koat_start) = 2
2.51/1.54	
2.51/1.54	orients all transitions weakly and the transitions
2.51/1.54	
2.51/1.54		evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ]
2.51/1.54	
2.51/1.54		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 2*ar_0 >= ar_2 + 1 ]
2.51/1.54	
2.51/1.54	strictly and produces the following problem:
2.51/1.54	
2.51/1.54	3:	T:
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_2 >= 2*ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 2*ar_0 >= ar_2 + 1 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, g))
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_0, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.51/1.54	
2.51/1.54		start location:	koat_start
2.51/1.54	
2.51/1.54		leaf cost:	0
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.51/1.54	
2.51/1.54	  For symbol evalfoo2: X_4 - 4 >= 0 /\ X_3 + X_4 - 8 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 6 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_3 - 4 >= 0 /\ X_1 + X_3 - 6 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_1 - 2 >= 0
2.51/1.54	
2.51/1.54	  For symbol evalfoo20: X_4 - 4 >= 0 /\ X_3 + X_4 - 8 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 6 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_3 - 4 >= 0 /\ X_1 + X_3 - 6 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_1 - 2 >= 0
2.51/1.54	
2.51/1.54	  For symbol evalfoo21: X_4 - 4 >= 0 /\ X_3 + X_4 - 8 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 6 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_3 - 4 >= 0 /\ X_1 + X_3 - 6 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_1 - 2 >= 0
2.51/1.54	
2.51/1.54	  For symbol evalfoo3: X_5 - X_6 >= 0 /\ -X_5 + X_6 >= 0 /\ X_4 - 4 >= 0 /\ X_3 + X_4 - 8 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 6 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_3 - 4 >= 0 /\ X_1 + X_3 - 6 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_1 - 2 >= 0
2.51/1.54	
2.51/1.54	  For symbol evalfoobb1in: -X_3 + X_4 >= 0
2.51/1.54	
2.51/1.54	  For symbol evalfoobb2in: X_4 - 4 >= 0 /\ X_3 + X_4 - 8 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 6 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_3 - 4 >= 0 /\ X_1 + X_3 - 6 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_1 - 2 >= 0
2.51/1.54	
2.51/1.54	  For symbol evalfoocritedgein: -X_3 + X_4 >= 0
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	This yielded the following problem:
2.51/1.54	
2.51/1.54	4:	T:
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)    evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_0, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, g)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ 2*ar_0 >= ar_2 + 1 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ 1 >= ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 2 /\ ar_2 >= 2*ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54		start location:	koat_start
2.51/1.54	
2.51/1.54		leaf cost:	0
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	A polynomial rank function with
2.51/1.54	
2.51/1.54		Pol(koat_start) = 3*V_4
2.51/1.54	
2.51/1.54		Pol(evalfoostart) = 3*V_4
2.51/1.54	
2.51/1.54		Pol(evalfoocritedgein) = 3*V_3
2.51/1.54	
2.51/1.54		Pol(evalfoostop) = 3*V_3
2.51/1.54	
2.51/1.54		Pol(evalfoo3) = 3*V_1 + 1
2.51/1.54	
2.51/1.54		Pol(evalfoobb1in) = 3*V_3
2.51/1.54	
2.51/1.54		Pol(evalfoo2) = 5*V_1
2.51/1.54	
2.51/1.54		Pol(evalfoo20) = 2*V_1 - 3
2.51/1.54	
2.51/1.54		Pol(evalfoo21) = 3*V_1 + 2
2.51/1.54	
2.51/1.54		Pol(evalVERIFIERnondetintstart) = 2*V_1 - 4
2.51/1.54	
2.51/1.54		Pol(evalfoobb2in) = 6*V_1 - 1
2.51/1.54	
2.51/1.54		Pol(evalfoobb0in) = 3*V_4
2.51/1.54	
2.51/1.54	orients all transitions weakly and the transitions
2.51/1.54	
2.51/1.54		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 2 /\ ar_2 >= 2*ar_0 ]
2.51/1.54	
2.51/1.54		evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_0, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54		evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54		evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54		evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, g)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54	strictly and produces the following problem:
2.51/1.54	
2.51/1.54	5:	T:
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)         evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 3*ar_3, Cost: 1)    evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_0, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_4 + ar_5 >= 0 /\ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 3*ar_3, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, g)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 3*ar_3, Cost: 1)    evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 3*ar_3, Cost: 1)    evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 3*ar_3, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 - 4 >= 0 /\ ar_2 + ar_3 - 8 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 6 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 4 >= 0 /\ ar_0 + ar_2 - 6 >= 0 /\ -ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 2 >= 0 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)         evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ 2*ar_0 >= ar_2 + 1 ]
2.51/1.54	
2.51/1.54			(Comp: 2, Cost: 1)         evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ 1 >= ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: 3*ar_3, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 2 /\ ar_2 >= 2*ar_0 ]
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)         evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54			(Comp: 1, Cost: 1)         evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.51/1.54	
2.51/1.54		start location:	koat_start
2.51/1.54	
2.51/1.54		leaf cost:	0
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	Complexity upper bound 18*ar_3 + 8
2.51/1.54	
2.51/1.54	
2.51/1.54	
2.51/1.54	Time: 0.336 sec (SMT: 0.256 sec)
2.51/1.54	
2.51/1.54	
2.51/1.54	----------------------------------------
2.51/1.54	
2.51/1.54	(2)
2.51/1.54	BOUNDS(1, n^1)
2.51/1.57	EOF