2.11/1.45	WORST_CASE(?, O(n^2))
2.11/1.46	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.11/1.46	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.11/1.46	
2.11/1.46	
2.11/1.46	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.11/1.46	
2.11/1.46	(0) CpxIntTrs
2.11/1.46	(1) Koat Proof [FINISHED, 285 ms]
2.11/1.46	(2) BOUNDS(1, n^2)
2.11/1.46	
2.11/1.46	
2.11/1.46	----------------------------------------
2.11/1.46	
2.11/1.46	(0)
2.11/1.46	Obligation:
2.11/1.46	Complexity Int TRS consisting of the following rules:
2.11/1.46	eval_foo_start(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE
2.11/1.46	eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_.02, v_c, v_x, v_y)) :|: TRUE
2.11/1.46	eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, 1, v_c, v_x, v_y)) :|: v_.01 >= 0
2.11/1.46	eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 < 0
2.11/1.46	eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 > v_.02
2.11/1.46	eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 <= v_.02
2.11/1.46	eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, 2 * v_.02, v_c, v_x, v_y)) :|: TRUE
2.11/1.46	eval_foo_bb4_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 - 1, v_.02, v_c, v_x, v_y)) :|: TRUE
2.11/1.46	eval_foo_bb5_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE
2.11/1.46	
2.11/1.46	The start-symbols are:[eval_foo_start_5]
2.11/1.46	
2.11/1.46	
2.11/1.46	----------------------------------------
2.11/1.46	
2.11/1.46	(1) Koat Proof (FINISHED)
2.11/1.46	YES(?, 13*ar_1 + 4*ar_1^2 + 15)
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	Initial complexity problem:
2.11/1.46	
2.11/1.46	1:	T:
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.46	
2.11/1.46		start location:	koat_start
2.11/1.46	
2.11/1.46		leaf cost:	0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.11/1.46	
2.11/1.46	2:	T:
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.46	
2.11/1.46		start location:	koat_start
2.11/1.46	
2.11/1.46		leaf cost:	0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	A polynomial rank function with
2.11/1.46	
2.11/1.46		Pol(evalfoostart) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoobb0in) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoobb1in) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoobb2in) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoobb5in) = 1
2.11/1.46	
2.11/1.46		Pol(evalfoobb3in) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoobb4in) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoostop) = 0
2.11/1.46	
2.11/1.46		Pol(koat_start) = 2
2.11/1.46	
2.11/1.46	orients all transitions weakly and the transitions
2.11/1.46	
2.11/1.46		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46	strictly and produces the following problem:
2.11/1.46	
2.11/1.46	3:	T:
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.46	
2.11/1.46		start location:	koat_start
2.11/1.46	
2.11/1.46		leaf cost:	0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	A polynomial rank function with
2.11/1.46	
2.11/1.46		Pol(evalfoostart) = V_2 + 1
2.11/1.46	
2.11/1.46		Pol(evalfoobb0in) = V_2 + 1
2.11/1.46	
2.11/1.46		Pol(evalfoobb1in) = V_1 + 1
2.11/1.46	
2.11/1.46		Pol(evalfoobb2in) = V_1
2.11/1.46	
2.11/1.46		Pol(evalfoobb5in) = V_1
2.11/1.46	
2.11/1.46		Pol(evalfoobb3in) = V_1
2.11/1.46	
2.11/1.46		Pol(evalfoobb4in) = V_1
2.11/1.46	
2.11/1.46		Pol(evalfoostop) = V_1
2.11/1.46	
2.11/1.46		Pol(koat_start) = V_2 + 1
2.11/1.46	
2.11/1.46	orients all transitions weakly and the transition
2.11/1.46	
2.11/1.46		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46	strictly and produces the following problem:
2.11/1.46	
2.11/1.46	4:	T:
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ar_1 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)           evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)           evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.46	
2.11/1.46		start location:	koat_start
2.11/1.46	
2.11/1.46		leaf cost:	0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	A polynomial rank function with
2.11/1.46	
2.11/1.46		Pol(evalfoobb4in) = 1
2.11/1.46	
2.11/1.46		Pol(evalfoobb1in) = 0
2.11/1.46	
2.11/1.46		Pol(evalfoobb3in) = 2
2.11/1.46	
2.11/1.46		Pol(evalfoobb2in) = 2
2.11/1.46	
2.11/1.46	and size complexities
2.11/1.46	
2.11/1.46		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.11/1.46	
2.11/1.46		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.11/1.46	
2.11/1.46		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))", 0-2) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))", 0-2) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]", 0-2) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]", 0-0) = ?
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]", 0-2) = 1
2.11/1.46	
2.11/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.11/1.46	
2.11/1.46		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.11/1.46	
2.11/1.46		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.11/1.46	
2.11/1.46	orients the transitions
2.11/1.46	
2.11/1.46		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))
2.11/1.46	
2.11/1.46		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46	weakly and the transitions
2.11/1.46	
2.11/1.46		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46	strictly and produces the following problem:
2.11/1.46	
2.11/1.46	5:	T:
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: ar_1 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2))
2.11/1.46	
2.11/1.46			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.46	
2.11/1.46		start location:	koat_start
2.11/1.46	
2.11/1.46		leaf cost:	0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	Applied AI with 'oct' on problem 5 to obtain the following invariants:
2.11/1.46	
2.11/1.46	  For symbol evalfoobb1in: -X_1 + X_2 >= 0
2.11/1.46	
2.11/1.46	  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
2.11/1.46	
2.11/1.46	  For symbol evalfoobb3in: 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
2.11/1.46	
2.11/1.46	  For symbol evalfoobb4in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
2.11/1.46	
2.11/1.46	  For symbol evalfoobb5in: -X_1 + X_2 >= 0 /\ -X_1 - 1 >= 0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	This yielded the following problem:
2.11/1.46	
2.11/1.46	6:	T:
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]
2.11/1.46	
2.11/1.46			(Comp: 2*ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 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 /\ ar_2 >= ar_0 ]
2.11/1.46	
2.11/1.46			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\ ar_0 >= ar_2 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.11/1.46	
2.11/1.46			(Comp: ar_1 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.46	
2.11/1.46			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.46	
2.11/1.46		start location:	koat_start
2.11/1.46	
2.11/1.46		leaf cost:	0
2.11/1.46	
2.11/1.46	
2.11/1.46	
2.11/1.46	A polynomial rank function with
2.11/1.46	
2.11/1.46		Pol(evalfoobb3in) = 2*V_2 - 2*V_3 - 1
2.11/1.46	
2.11/1.46		Pol(evalfoobb2in) = 2*V_2 - 2*V_3
2.11/1.46	
2.11/1.46	and size complexities
2.11/1.46	
2.11/1.46		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.11/1.46	
2.11/1.46		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.11/1.46	
2.11/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = 1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-2) = 2*ar_1 + 2*ar_2 + 24
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\\ ar_0 >= ar_2 + 1 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\\ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\\ ar_0 >= ar_2 + 1 ]", 0-2) = 2*ar_1 + 6
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 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 /\\ ar_2 >= ar_0 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 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 /\\ ar_2 >= ar_0 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 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 /\\ ar_2 >= ar_0 ]", 0-2) = 2*ar_1 + 6
2.11/1.46	
2.11/1.46		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]", 0-2) = 2*ar_1 + 2
2.11/1.46	
2.11/1.46		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_1
2.11/1.46	
2.11/1.46		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = 2*ar_1 + 12
2.11/1.46	
2.11/1.46		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-0) = ar_1 + 1
2.11/1.46	
2.11/1.46		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-1) = ar_1
2.11/1.47	
2.11/1.47		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-2) = 2*ar_1 + 2*ar_2 + 48
2.11/1.47	
2.11/1.47		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.11/1.47	
2.11/1.47		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.11/1.47	
2.11/1.47		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.11/1.47	
2.11/1.47	orients the transitions
2.11/1.47	
2.11/1.47		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]
2.11/1.47	
2.11/1.47		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\ ar_0 >= ar_2 + 1 ]
2.11/1.47	
2.11/1.47	weakly and the transitions
2.11/1.47	
2.11/1.47		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]
2.11/1.47	
2.11/1.47		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\ ar_0 >= ar_2 + 1 ]
2.11/1.47	
2.11/1.47	strictly and produces the following problem:
2.11/1.47	
2.11/1.47	7:	T:
2.11/1.47	
2.11/1.47			(Comp: 1, Cost: 0)                        koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.11/1.47	
2.11/1.47			(Comp: 2, Cost: 1)                        evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 - 1 >= 0 ]
2.11/1.47	
2.11/1.47			(Comp: 2*ar_1 + 2, Cost: 1)               evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.11/1.47	
2.11/1.47			(Comp: 2*ar_1^2 + 4*ar_1 + 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) [ 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 ]
2.11/1.47	
2.11/1.47			(Comp: 2*ar_1 + 2, Cost: 1)               evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 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 /\ ar_2 >= ar_0 ]
2.11/1.47	
2.11/1.47			(Comp: 2*ar_1^2 + 4*ar_1 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ 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 /\ ar_0 >= ar_2 + 1 ]
2.11/1.47	
2.11/1.47			(Comp: 2, Cost: 1)                        evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 + 1 ]
2.11/1.47	
2.11/1.47			(Comp: ar_1 + 1, Cost: 1)                 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.11/1.47	
2.11/1.47			(Comp: 1, Cost: 1)                        evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.11/1.47	
2.11/1.47			(Comp: 1, Cost: 1)                        evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.11/1.47	
2.11/1.47		start location:	koat_start
2.11/1.47	
2.11/1.47		leaf cost:	0
2.11/1.47	
2.11/1.47	
2.11/1.47	
2.11/1.47	Complexity upper bound 13*ar_1 + 4*ar_1^2 + 15
2.11/1.47	
2.11/1.47	
2.11/1.47	
2.11/1.47	Time: 0.266 sec (SMT: 0.234 sec)
2.11/1.47	
2.11/1.47	
2.11/1.47	----------------------------------------
2.11/1.47	
2.11/1.47	(2)
2.11/1.47	BOUNDS(1, n^2)
2.44/1.48	EOF