2.24/1.71	WORST_CASE(?, O(n^1))
2.24/1.72	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.24/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.24/1.72	
2.24/1.72	
2.24/1.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.24/1.72	
2.24/1.72	(0) CpxIntTrs
2.24/1.72	(1) Koat Proof [FINISHED, 480 ms]
2.24/1.72	(2) BOUNDS(1, n^1)
2.24/1.72	
2.24/1.72	
2.24/1.72	----------------------------------------
2.24/1.72	
2.24/1.72	(0)
2.24/1.72	Obligation:
2.24/1.72	Complexity Int TRS consisting of the following rules:
2.24/1.72	eval_foo_start(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: TRUE
2.24/1.72	eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_3, v_4, v_x, v_y)) :|: TRUE
2.24/1.72	eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.0 >= 0 && v_.01 >= 1
2.24/1.72	eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.0 < 0
2.24/1.72	eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.01 < 1
2.24/1.72	eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_1(v_.0, v_.01, v_.0 - v_.01, v_4, v_x, v_y)) :|: TRUE
2.24/1.72	eval_foo_1(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_4, v_x, v_y), eval_foo_2(v_.0, v_.01, v_3, nondef.0, v_x, v_y)) :|: TRUE
2.24/1.72	eval_foo_2(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_3, v_4, v_3, v_4, v_x, v_y)) :|: TRUE
2.24/1.72	eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: TRUE
2.24/1.72	
2.24/1.72	The start-symbols are:[eval_foo_start_6]
2.24/1.72	
2.24/1.72	
2.24/1.72	----------------------------------------
2.24/1.72	
2.24/1.72	(1) Koat Proof (FINISHED)
2.24/1.72	YES(?, 36*ar_1 + 44)
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	Initial complexity problem:
2.24/1.72	
2.24/1.72	1:	T:
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 0 /\ ar_2 >= 1 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 + 1 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ]
2.24/1.72	
2.24/1.72		start location:	koat_start
2.24/1.72	
2.24/1.72		leaf cost:	0
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.24/1.72	
2.24/1.72	2:	T:
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 0 /\ ar_2 >= 1 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 + 1 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ]
2.24/1.72	
2.24/1.72		start location:	koat_start
2.24/1.72	
2.24/1.72		leaf cost:	0
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	A polynomial rank function with
2.24/1.72	
2.24/1.72		Pol(evalfoostart) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoobb0in) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoobb1in) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoobb2in) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoobb3in) = 1
2.24/1.72	
2.24/1.72		Pol(evalfoo1) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoo10) = 0
2.24/1.72	
2.24/1.72		Pol(evalVERIFIERnondetintstart) = 0
2.24/1.72	
2.24/1.72		Pol(evalfoo11) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoo2) = 2
2.24/1.72	
2.24/1.72		Pol(evalfoostop) = 0
2.24/1.72	
2.24/1.72		Pol(koat_start) = 2
2.24/1.72	
2.24/1.72	orients all transitions weakly and the transitions
2.24/1.72	
2.24/1.72		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 + 1 ]
2.24/1.72	
2.24/1.72		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ]
2.24/1.72	
2.24/1.72	strictly and produces the following problem:
2.24/1.72	
2.24/1.72	3:	T:
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 0 /\ ar_2 >= 1 ]
2.24/1.72	
2.24/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 + 1 ]
2.24/1.72	
2.24/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h))
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ]
2.24/1.72	
2.24/1.72		start location:	koat_start
2.24/1.72	
2.24/1.72		leaf cost:	0
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.24/1.72	
2.24/1.72	  For symbol evalfoo1: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
2.24/1.72	
2.24/1.72	  For symbol evalfoo10: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
2.24/1.72	
2.24/1.72	  For symbol evalfoo11: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
2.24/1.72	
2.24/1.72	  For symbol evalfoo2: X_6 - X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
2.24/1.72	
2.24/1.72	  For symbol evalfoobb1in: -X_1 + X_2 >= 0
2.24/1.72	
2.24/1.72	  For symbol evalfoobb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
2.24/1.72	
2.24/1.72	  For symbol evalfoobb3in: -X_1 + X_2 >= 0
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	This yielded the following problem:
2.24/1.72	
2.24/1.72	4:	T:
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ]
2.24/1.72	
2.24/1.72			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.72	
2.24/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.24/1.72	
2.24/1.72			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.24/1.72	
2.24/1.72			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.72	
2.24/1.72		start location:	koat_start
2.24/1.72	
2.24/1.72		leaf cost:	0
2.24/1.72	
2.24/1.72	
2.24/1.72	
2.24/1.72	A polynomial rank function with
2.24/1.72	
2.24/1.72		Pol(koat_start) = 6*V_2 + 6
2.24/1.72	
2.24/1.72		Pol(evalfoostart) = 6*V_2 + 6
2.24/1.72	
2.24/1.72		Pol(evalfoobb3in) = 6*V_1
2.24/1.72	
2.24/1.72		Pol(evalfoostop) = 6*V_1
2.24/1.72	
2.24/1.72		Pol(evalfoo2) = 6*V_3 + 6*V_5 + 1
2.24/1.72	
2.24/1.72		Pol(evalfoobb1in) = 6*V_1 + 6
2.24/1.72	
2.24/1.72		Pol(evalfoo1) = 6*V_3 + 6*V_5 + 4
2.24/1.72	
2.24/1.72		Pol(evalfoo10) = 1
2.24/1.72	
2.24/1.72		Pol(evalfoo11) = 6*V_3 + 6*V_5 + 2
2.24/1.72	
2.24/1.72		Pol(evalVERIFIERnondetintstart) = 0
2.24/1.72	
2.24/1.72		Pol(evalfoobb2in) = 6*V_1 + 5
2.24/1.72	
2.24/1.72		Pol(evalfoobb0in) = 6*V_2 + 6
2.24/1.72	
2.24/1.72	orients all transitions weakly and the transitions
2.24/1.72	
2.24/1.72		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.72	
2.24/1.72		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
2.24/1.73	
2.24/1.73		evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73		evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73		evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73		evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73	strictly and produces the following problem:
2.24/1.73	
2.24/1.73	5:	T:
2.24/1.73	
2.24/1.73			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 2, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 6*ar_1 + 6, Cost: 1)    evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 6*ar_1 + 6, Cost: 1)    evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 6*ar_1 + 6, Cost: 1)    evalfoo11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 6*ar_1 + 6, Cost: 1)    evalfoo10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 6*ar_1 + 6, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoo1(ar_0, ar_1, ar_2, ar_3, ar_0 - ar_2, ar_5, ar_6)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.24/1.73	
2.24/1.73			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.24/1.73	
2.24/1.73			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.24/1.73	
2.24/1.73			(Comp: 6*ar_1 + 6, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
2.24/1.73	
2.24/1.73			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6))
2.24/1.73	
2.24/1.73			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6))
2.24/1.73	
2.24/1.73		start location:	koat_start
2.24/1.73	
2.24/1.73		leaf cost:	0
2.24/1.73	
2.24/1.73	
2.24/1.73	
2.24/1.73	Complexity upper bound 36*ar_1 + 44
2.24/1.73	
2.24/1.73	
2.24/1.73	
2.24/1.73	Time: 0.449 sec (SMT: 0.339 sec)
2.24/1.73	
2.24/1.73	
2.24/1.73	----------------------------------------
2.24/1.73	
2.24/1.73	(2)
2.24/1.73	BOUNDS(1, n^1)
2.24/1.76	EOF