2.98/1.92	WORST_CASE(?, O(n^1))
2.98/1.93	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.98/1.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.98/1.93	
2.98/1.93	
2.98/1.93	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.98/1.93	
2.98/1.93	(0) CpxIntTrs
2.98/1.93	(1) Koat Proof [FINISHED, 779 ms]
2.98/1.93	(2) BOUNDS(1, n^1)
2.98/1.93	
2.98/1.93	
2.98/1.93	----------------------------------------
2.98/1.93	
2.98/1.93	(0)
2.98/1.93	Obligation:
2.98/1.93	Complexity Int TRS consisting of the following rules:
2.98/1.93	eval_foo_start(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: TRUE
2.98/1.93	eval_foo_bb0_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.1, v_.2, v_c, v_x, v_y)) :|: TRUE
2.98/1.93	eval_foo_bb1_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: v_.01 > 0
2.98/1.93	eval_foo_bb1_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: v_.02 > 0
2.98/1.93	eval_foo_bb1_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: v_.01 <= 0 && v_.02 <= 0
2.98/1.93	eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: v_.01 > 0
2.98/1.93	eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: v_.01 <= 0
2.98/1.93	eval_foo_bb3_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01 - 1, v_.02, v_c, v_x, v_y)) :|: TRUE
2.98/1.93	eval_foo_bb4_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02 - 1, v_c, v_x, v_y)) :|: v_.02 > 0
2.98/1.93	eval_foo_bb4_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02, v_c, v_x, v_y)) :|: v_.02 <= 0
2.98/1.93	eval_foo_bb5_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.1, v_.2, v_.1, v_.2, v_c, v_x, v_y)) :|: TRUE
2.98/1.93	eval_foo_bb6_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y)) :|: TRUE
2.98/1.93	
2.98/1.93	The start-symbols are:[eval_foo_start_7]
2.98/1.93	
2.98/1.93	
2.98/1.93	----------------------------------------
2.98/1.93	
2.98/1.93	(1) Koat Proof (FINISHED)
2.98/1.93	YES(?, 8*ar_1 + 6*ar_3 + 11)
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	Initial complexity problem:
2.98/1.93	
2.98/1.93	1:	T:
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb6in(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))
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.98/1.93	
2.98/1.93	2:	T:
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb6in(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))
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	A polynomial rank function with
2.98/1.93	
2.98/1.93		Pol(evalfoostart) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoobb0in) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoobb1in) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoobb2in) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoobb6in) = 1
2.98/1.93	
2.98/1.93		Pol(evalfoobb3in) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoobb4in) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoobb5in) = 2
2.98/1.93	
2.98/1.93		Pol(evalfoostop) = 0
2.98/1.93	
2.98/1.93		Pol(koat_start) = 2
2.98/1.93	
2.98/1.93	orients all transitions weakly and the transitions
2.98/1.93	
2.98/1.93		evalfoobb6in(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))
2.98/1.93	
2.98/1.93		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93	strictly and produces the following problem:
2.98/1.93	
2.98/1.93	3:	T:
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)    evalfoobb6in(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))
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	A polynomial rank function with
2.98/1.93	
2.98/1.93		Pol(evalfoostart) = V_2
2.98/1.93	
2.98/1.93		Pol(evalfoobb0in) = V_2
2.98/1.93	
2.98/1.93		Pol(evalfoobb1in) = V_1
2.98/1.93	
2.98/1.93		Pol(evalfoobb2in) = V_1
2.98/1.93	
2.98/1.93		Pol(evalfoobb6in) = V_1
2.98/1.93	
2.98/1.93		Pol(evalfoobb3in) = V_1 - 1
2.98/1.93	
2.98/1.93		Pol(evalfoobb4in) = V_1
2.98/1.93	
2.98/1.93		Pol(evalfoobb5in) = V_5
2.98/1.93	
2.98/1.93		Pol(evalfoostop) = V_1
2.98/1.93	
2.98/1.93		Pol(koat_start) = V_2
2.98/1.93	
2.98/1.93	orients all transitions weakly and the transition
2.98/1.93	
2.98/1.93		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93	strictly and produces the following problem:
2.98/1.93	
2.98/1.93	4:	T:
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb6in(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))
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.98/1.93	
2.98/1.93	5:	T:
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb6in(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))
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	A polynomial rank function with
2.98/1.93	
2.98/1.93		Pol(evalfoostart) = V_4
2.98/1.93	
2.98/1.93		Pol(evalfoobb0in) = V_4
2.98/1.93	
2.98/1.93		Pol(evalfoobb1in) = V_3
2.98/1.93	
2.98/1.93		Pol(evalfoobb2in) = V_3
2.98/1.93	
2.98/1.93		Pol(evalfoobb6in) = V_3
2.98/1.93	
2.98/1.93		Pol(evalfoobb3in) = V_3
2.98/1.93	
2.98/1.93		Pol(evalfoobb4in) = V_3
2.98/1.93	
2.98/1.93		Pol(evalfoobb5in) = V_6
2.98/1.93	
2.98/1.93		Pol(evalfoostop) = V_3
2.98/1.93	
2.98/1.93		Pol(koat_start) = V_4
2.98/1.93	
2.98/1.93	orients all transitions weakly and the transition
2.98/1.93	
2.98/1.93		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93	strictly and produces the following problem:
2.98/1.93	
2.98/1.93	6:	T:
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(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 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.98/1.93	
2.98/1.93			(Comp: ar_3, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb6in(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))
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	Applied AI with 'oct' on problem 6 to obtain the following invariants:
2.98/1.93	
2.98/1.93	  For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.98/1.93	
2.98/1.93	  For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.98/1.93	
2.98/1.93	  For symbol evalfoobb3in: -X_3 + X_4 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0
2.98/1.93	
2.98/1.93	  For symbol evalfoobb4in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 >= 0
2.98/1.93	
2.98/1.93	  For symbol evalfoobb5in: X_4 - X_6 >= 0 /\ X_3 - X_6 >= 0 /\ -X_3 + X_6 + 1 >= 0 /\ X_2 - X_5 >= 0 /\ X_1 - X_5 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.98/1.93	
2.98/1.93	  For symbol evalfoobb6in: -X_3 + X_4 >= 0 /\ -X_3 >= 0 /\ -X_1 - X_3 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 >= 0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	This yielded the following problem:
2.98/1.93	
2.98/1.93	7:	T:
2.98/1.93	
2.98/1.93			(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 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ar_3, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	By chaining the transition 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 ] with all transitions in problem 7, the following new transition is obtained:
2.98/1.93	
2.98/1.93		koat_start(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)) [ 0 <= 0 ]
2.98/1.93	
2.98/1.93	We thus obtain the following problem:
2.98/1.93	
2.98/1.93	8:	T:
2.98/1.93	
2.98/1.93			(Comp: 1, Cost: 1)       koat_start(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)) [ 0 <= 0 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(Comp: ar_3, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ]
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.93	
2.98/1.93			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.93	
2.98/1.93			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.93	
2.98/1.93			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93			(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))
2.98/1.93	
2.98/1.93		start location:	koat_start
2.98/1.93	
2.98/1.93		leaf cost:	0
2.98/1.93	
2.98/1.93	
2.98/1.93	
2.98/1.93	Testing for reachability in the complexity graph removes the following transition from problem 8:
2.98/1.93	
2.98/1.93		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))
2.98/1.93	
2.98/1.93	We thus obtain the following problem:
2.98/1.93	
2.98/1.93	9:	T:
2.98/1.93	
2.98/1.93			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(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))
2.98/1.94	
2.98/1.94			(Comp: 1, Cost: 1)       koat_start(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)) [ 0 <= 0 ]
2.98/1.94	
2.98/1.94		start location:	koat_start
2.98/1.94	
2.98/1.94		leaf cost:	0
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	By chaining the transition evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
2.98/1.94	
2.98/1.94		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 + 1 >= 0 ]
2.98/1.94	
2.98/1.94	We thus obtain the following problem:
2.98/1.94	
2.98/1.94	10:	T:
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 2)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 + 1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(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))
2.98/1.94	
2.98/1.94			(Comp: 1, Cost: 1)       koat_start(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)) [ 0 <= 0 ]
2.98/1.94	
2.98/1.94		start location:	koat_start
2.98/1.94	
2.98/1.94		leaf cost:	0
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	By chaining the transition evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 ] with all transitions in problem 10, the following new transition is obtained:
2.98/1.94	
2.98/1.94		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 /\ ar_3 - ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94	We thus obtain the following problem:
2.98/1.94	
2.98/1.94	11:	T:
2.98/1.94	
2.98/1.94			(Comp: ar_3, Cost: 2)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 /\ ar_3 - ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 2)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 + 1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(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))
2.98/1.94	
2.98/1.94			(Comp: 1, Cost: 1)       koat_start(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)) [ 0 <= 0 ]
2.98/1.94	
2.98/1.94		start location:	koat_start
2.98/1.94	
2.98/1.94		leaf cost:	0
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	By chaining the transition evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 ] with all transitions in problem 11, the following new transition is obtained:
2.98/1.94	
2.98/1.94		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94	We thus obtain the following problem:
2.98/1.94	
2.98/1.94	12:	T:
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 2)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3, Cost: 2)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 /\ ar_3 - ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 2)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 + 1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(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))
2.98/1.94	
2.98/1.94			(Comp: 1, Cost: 1)       koat_start(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)) [ 0 <= 0 ]
2.98/1.94	
2.98/1.94		start location:	koat_start
2.98/1.94	
2.98/1.94		leaf cost:	0
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	Testing for reachability in the complexity graph removes the following transition from problem 12:
2.98/1.94	
2.98/1.94		evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5)) [ ar_3 - ar_5 >= 0 /\ ar_2 - ar_5 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.98/1.94	
2.98/1.94	We thus obtain the following problem:
2.98/1.94	
2.98/1.94	13:	T:
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 2)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 + 1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 2)       evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3, Cost: 2)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 /\ ar_3 - ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ?, Cost: 1)       evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)       evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(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))
2.98/1.94	
2.98/1.94			(Comp: 1, Cost: 1)       koat_start(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)) [ 0 <= 0 ]
2.98/1.94	
2.98/1.94		start location:	koat_start
2.98/1.94	
2.98/1.94		leaf cost:	0
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	Repeatedly propagating knowledge in problem 13 produces the following problem:
2.98/1.94	
2.98/1.94	14:	T:
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 2)               evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 + 1 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3 + ar_1 + 1, Cost: 2)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ 0 >= ar_2 /\ ar_3 - ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3, Cost: 2)               evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3, ar_0, ar_2 - 1)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 /\ ar_2 >= 1 /\ ar_3 - ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ ar_1 - ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1, Cost: 1)               evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3 + ar_1 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)                  evalfoobb6in(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 /\ -ar_2 >= 0 /\ -ar_0 - ar_2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.98/1.94	
2.98/1.94			(Comp: ar_1 + 1, 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 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: ar_3 + ar_1 + 1, 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 + ar_1 >= 0 /\ ar_2 >= 1 ]
2.98/1.94	
2.98/1.94			(Comp: 2, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ 0 >= ar_2 ]
2.98/1.94	
2.98/1.94			(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))
2.98/1.94	
2.98/1.94			(Comp: 1, Cost: 1)                  koat_start(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)) [ 0 <= 0 ]
2.98/1.94	
2.98/1.94		start location:	koat_start
2.98/1.94	
2.98/1.94		leaf cost:	0
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	Complexity upper bound 8*ar_1 + 6*ar_3 + 11
2.98/1.94	
2.98/1.94	
2.98/1.94	
2.98/1.94	Time: 0.751 sec (SMT: 0.574 sec)
2.98/1.94	
2.98/1.94	
2.98/1.94	----------------------------------------
2.98/1.94	
2.98/1.94	(2)
2.98/1.94	BOUNDS(1, n^1)
2.98/1.96	EOF