2.41/1.73	WORST_CASE(?, O(n^2))
2.41/1.74	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.41/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.41/1.74	
2.41/1.74	
2.41/1.74	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.41/1.74	
2.41/1.74	(0) CpxIntTrs
2.41/1.74	(1) Koat Proof [FINISHED, 281 ms]
2.41/1.74	(2) BOUNDS(1, n^2)
2.41/1.74	
2.41/1.74	
2.41/1.74	----------------------------------------
2.41/1.74	
2.41/1.74	(0)
2.41/1.74	Obligation:
2.41/1.74	Complexity Int TRS consisting of the following rules:
2.41/1.74	eval_foo_start(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_n, v_x, v_y)) :|: TRUE
2.41/1.74	eval_foo_bb0_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_n, v_.01, v_n, v_x, v_y)) :|: v_n >= 0
2.41/1.74	eval_foo_bb0_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_n, v_x, v_y)) :|: v_n < 0
2.41/1.74	eval_foo_bb1_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_n, v_x, v_y)) :|: v_.0 >= 0
2.41/1.74	eval_foo_bb1_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_n, v_x, v_y)) :|: v_.0 < 0
2.41/1.74	eval_foo_bb2_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, 1, v_n, v_x, v_y)) :|: 1 < v_.0
2.41/1.74	eval_foo_bb2_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_n, v_x, v_y)) :|: 1 >= v_.0
2.41/1.74	eval_foo_bb3_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_n, v_x, v_y)) :|: v_.01 < v_.0
2.41/1.74	eval_foo_bb3_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_n, v_x, v_y)) :|: v_.01 >= v_.0
2.41/1.74	eval_foo_bb4_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, 2 * v_.01, v_n, v_x, v_y)) :|: TRUE
2.41/1.74	eval_foo_bb5_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_n, v_x, v_y)) :|: TRUE
2.41/1.74	eval_foo_bb6_in(v_.0, v_.01, v_n, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_n, v_x, v_y)) :|: TRUE
2.41/1.74	
2.41/1.74	The start-symbols are:[eval_foo_start_5]
2.41/1.74	
2.41/1.74	
2.41/1.74	----------------------------------------
2.41/1.74	
2.41/1.74	(1) Koat Proof (FINISHED)
2.41/1.74	YES(?, 50*ar_0 + 8*ar_0^2 + 49)
2.41/1.74	
2.41/1.74	
2.41/1.74	
2.41/1.74	Initial complexity problem:
2.41/1.74	
2.41/1.74	1:	T:
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.74	
2.41/1.74		start location:	koat_start
2.41/1.74	
2.41/1.74		leaf cost:	0
2.41/1.74	
2.41/1.74	
2.41/1.74	
2.41/1.74	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.41/1.74	
2.41/1.74	2:	T:
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.74	
2.41/1.74		start location:	koat_start
2.41/1.74	
2.41/1.74		leaf cost:	0
2.41/1.74	
2.41/1.74	
2.41/1.74	
2.41/1.74	A polynomial rank function with
2.41/1.74	
2.41/1.74		Pol(evalfoostart) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb0in) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb1in) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb6in) = 1
2.41/1.74	
2.41/1.74		Pol(evalfoobb2in) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb3in) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb5in) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb4in) = 2
2.41/1.74	
2.41/1.74		Pol(evalfoostop) = 0
2.41/1.74	
2.41/1.74		Pol(koat_start) = 2
2.41/1.74	
2.41/1.74	orients all transitions weakly and the transitions
2.41/1.74	
2.41/1.74		evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.74	
2.41/1.74	strictly and produces the following problem:
2.41/1.74	
2.41/1.74	3:	T:
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 2, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.74	
2.41/1.74		start location:	koat_start
2.41/1.74	
2.41/1.74		leaf cost:	0
2.41/1.74	
2.41/1.74	
2.41/1.74	
2.41/1.74	A polynomial rank function with
2.41/1.74	
2.41/1.74		Pol(evalfoobb5in) = 2*V_2
2.41/1.74	
2.41/1.74		Pol(evalfoobb1in) = 2*V_2 + 2
2.41/1.74	
2.41/1.74		Pol(evalfoobb4in) = 2*V_2
2.41/1.74	
2.41/1.74		Pol(evalfoobb3in) = 2*V_2
2.41/1.74	
2.41/1.74		Pol(evalfoobb2in) = 2*V_2 + 1
2.41/1.74	
2.41/1.74	and size complexities
2.41/1.74	
2.41/1.74		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.41/1.74	
2.41/1.74		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.41/1.74	
2.41/1.74		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-2) = 1
2.41/1.74	
2.41/1.74		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-1) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-2) = ?
2.41/1.74	
2.41/1.74		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.41/1.74	
2.41/1.74		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
2.41/1.74	
2.41/1.74		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-1) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-2) = ar_2
2.41/1.74	
2.41/1.74		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.41/1.74	
2.41/1.74		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.41/1.74	
2.41/1.74		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.41/1.74	
2.41/1.74	orients the transitions
2.41/1.74	
2.41/1.74		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.74	
2.41/1.74		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.74	
2.41/1.74		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.74	
2.41/1.74		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.74	
2.41/1.74		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.74	
2.41/1.74		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.74	
2.41/1.74		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.74	
2.41/1.74	weakly and the transitions
2.41/1.74	
2.41/1.74		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.74	
2.41/1.74		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.74	
2.41/1.74	strictly and produces the following problem:
2.41/1.74	
2.41/1.74	4:	T:
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.74	
2.41/1.74			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)             evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.74	
2.41/1.74			(Comp: ?, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.74	
2.41/1.74			(Comp: 2, Cost: 1)             evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.75	
2.41/1.75		start location:	koat_start
2.41/1.75	
2.41/1.75		leaf cost:	0
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.41/1.75	
2.41/1.75	5:	T:
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)             evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.75	
2.41/1.75		start location:	koat_start
2.41/1.75	
2.41/1.75		leaf cost:	0
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	A polynomial rank function with
2.41/1.75	
2.41/1.75		Pol(evalfoobb5in) = 1
2.41/1.75	
2.41/1.75		Pol(evalfoobb1in) = 0
2.41/1.75	
2.41/1.75		Pol(evalfoobb4in) = 2
2.41/1.75	
2.41/1.75		Pol(evalfoobb3in) = 2
2.41/1.75	
2.41/1.75	and size complexities
2.41/1.75	
2.41/1.75		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.41/1.75	
2.41/1.75		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.41/1.75	
2.41/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-2) = 1
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-1) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-2) = ?
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-1) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-2) = ar_2
2.41/1.75	
2.41/1.75		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.41/1.75	
2.41/1.75		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.41/1.75	
2.41/1.75	orients the transitions
2.41/1.75	
2.41/1.75		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.75	
2.41/1.75		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.75	
2.41/1.75		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.75	
2.41/1.75		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75	weakly and the transitions
2.41/1.75	
2.41/1.75		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.75	
2.41/1.75		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.75	
2.41/1.75	strictly and produces the following problem:
2.41/1.75	
2.41/1.75	6:	T:
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 6*ar_0 + 6, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 2*ar_2))
2.41/1.75	
2.41/1.75			(Comp: 6*ar_0 + 6, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)             evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.75	
2.41/1.75		start location:	koat_start
2.41/1.75	
2.41/1.75		leaf cost:	0
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	Applied AI with 'oct' on problem 6 to obtain the following invariants:
2.41/1.75	
2.41/1.75	  For symbol evalfoobb1in: X_1 - X_2 >= 0 /\ X_1 >= 0
2.41/1.75	
2.41/1.75	  For symbol evalfoobb2in: X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.41/1.75	
2.41/1.75	  For symbol evalfoobb3in: X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 2 >= 0
2.41/1.75	
2.41/1.75	  For symbol evalfoobb4in: 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_1 - X_2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 2 >= 0
2.41/1.75	
2.41/1.75	  For symbol evalfoobb5in: X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	This yielded the following problem:
2.41/1.75	
2.41/1.75	7:	T:
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)             evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 6*ar_0 + 6, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 6*ar_0 + 6, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ 1 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 2 ]
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_1 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75		start location:	koat_start
2.41/1.75	
2.41/1.75		leaf cost:	0
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	A polynomial rank function with
2.41/1.75	
2.41/1.75		Pol(evalfoobb4in) = 2*V_2 - 2*V_3 - 1
2.41/1.75	
2.41/1.75		Pol(evalfoobb3in) = 2*V_2 - 2*V_3
2.41/1.75	
2.41/1.75	and size complexities
2.41/1.75	
2.41/1.75		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.41/1.75	
2.41/1.75		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-1) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-2) = ar_2
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.41/1.75	
2.41/1.75		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-2) = 2*ar_0 + 2*ar_2 + 16
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 + 1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 + 1 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 + 1 ]", 0-2) = 2*ar_0 + 2*ar_2 + 32
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 2 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 2 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 2 ]", 0-2) = 1
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 1 >= ar_1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 1 >= ar_1 ]", 0-1) = 1
2.41/1.75	
2.41/1.75		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 1 >= ar_1 ]", 0-2) = 2*ar_0 + 2*ar_2 + 16
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = 2*ar_0 + 10
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = 2*ar_0 + 8
2.41/1.75	
2.41/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-2) = 2*ar_0 + 4
2.41/1.75	
2.41/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = 2*ar_0 + 2*ar_2 + 16
2.41/1.75	
2.41/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-1) = ar_0 + ar_1 + 2
2.41/1.75	
2.41/1.75		S("evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))", 0-2) = 2*ar_0 + 2*ar_2 + 64
2.41/1.75	
2.41/1.75		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.41/1.75	
2.41/1.75		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.41/1.75	
2.41/1.75		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.41/1.75	
2.41/1.75	orients the transitions
2.41/1.75	
2.41/1.75		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
2.41/1.75	
2.41/1.75		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75	weakly and the transitions
2.41/1.75	
2.41/1.75		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
2.41/1.75	
2.41/1.75		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75	strictly and produces the following problem:
2.41/1.75	
2.41/1.75	8:	T:
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 0)                          koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)                          evalfoobb6in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75			(Comp: 6*ar_0 + 6, Cost: 1)                 evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 4*ar_0^2 + 16*ar_0 + 12, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(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_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 6*ar_0 + 6, Cost: 1)                 evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: 4*ar_0^2 + 16*ar_0 + 12, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)                 evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ 1 >= ar_1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)                 evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 2 ]
2.41/1.75	
2.41/1.75			(Comp: 2, Cost: 1)                          evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_1 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 2*ar_0 + 2, Cost: 1)                 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)                          evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)                          evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
2.41/1.75	
2.41/1.75			(Comp: 1, Cost: 1)                          evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.41/1.75	
2.41/1.75		start location:	koat_start
2.41/1.75	
2.41/1.75		leaf cost:	0
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	Complexity upper bound 50*ar_0 + 8*ar_0^2 + 49
2.41/1.75	
2.41/1.75	
2.41/1.75	
2.41/1.75	Time: 0.320 sec (SMT: 0.288 sec)
2.41/1.75	
2.41/1.75	
2.41/1.75	----------------------------------------
2.41/1.75	
2.41/1.75	(2)
2.41/1.75	BOUNDS(1, n^2)
2.41/1.77	EOF