2.09/1.38	WORST_CASE(?, ?)
2.09/1.39	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.09/1.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.09/1.39	
2.09/1.39	
2.09/1.39	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, EXP).
2.09/1.39	
2.09/1.39	(0) CpxIntTrs
2.09/1.39	(1) Koat Proof [FINISHED, 178 ms]
2.09/1.39	(2) BOUNDS(1, EXP)
2.09/1.39	
2.09/1.39	
2.09/1.39	----------------------------------------
2.09/1.39	
2.09/1.39	(0)
2.09/1.39	Obligation:
2.09/1.39	Complexity Int TRS consisting of the following rules:
2.09/1.39	eval_foo_start(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE
2.09/1.39	eval_foo_bb0_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE
2.09/1.39	eval_foo_bb1_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.0, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 > 0 && v_.0 > 0
2.09/1.39	eval_foo_bb1_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 <= 0
2.09/1.39	eval_foo_bb1_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.0 <= 0
2.09/1.39	eval_foo_bb2_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.02 >= v_.01 && v_.01 > 0
2.09/1.39	eval_foo_bb2_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.02 < v_.01
2.09/1.39	eval_foo_bb2_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 <= 0
2.09/1.39	eval_foo_bb3_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.02 - v_.01, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE
2.09/1.39	eval_foo_bb4_in(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.02, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE
2.09/1.39	
2.09/1.39	The start-symbols are:[eval_foo_start_7]
2.09/1.39	
2.09/1.39	
2.09/1.39	----------------------------------------
2.09/1.39	
2.09/1.39	(1) Koat Proof (FINISHED)
2.09/1.39	YES(?, 4 * pow(2, ar_1 + ar_3) * (ar_1^2 + 2*ar_1*ar_3 + ar_3^2) + 5*ar_1 + 5*ar_3 + 11)
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	Initial complexity problem:
2.09/1.39	
2.09/1.39	1:	T:
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.09/1.39	
2.09/1.39	2:	T:
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	A polynomial rank function with
2.09/1.39	
2.09/1.39		Pol(evalfoostart) = 2
2.09/1.39	
2.09/1.39		Pol(evalfoobb0in) = 2
2.09/1.39	
2.09/1.39		Pol(evalfoobb1in) = 2
2.09/1.39	
2.09/1.39		Pol(evalfoobb2in) = 2
2.09/1.39	
2.09/1.39		Pol(evalfoobb4in) = 1
2.09/1.39	
2.09/1.39		Pol(evalfoobb3in) = 2
2.09/1.39	
2.09/1.39		Pol(evalfoostop) = 0
2.09/1.39	
2.09/1.39		Pol(koat_start) = 2
2.09/1.39	
2.09/1.39	orients all transitions weakly and the transitions
2.09/1.39	
2.09/1.39		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39	strictly and produces the following problem:
2.09/1.39	
2.09/1.39	3:	T:
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	A polynomial rank function with
2.09/1.39	
2.09/1.39		Pol(evalfoostart) = V_2 + V_4
2.09/1.39	
2.09/1.39		Pol(evalfoobb0in) = V_2 + V_4
2.09/1.39	
2.09/1.39		Pol(evalfoobb1in) = V_1 + V_3
2.09/1.39	
2.09/1.39		Pol(evalfoobb2in) = V_3 + V_5
2.09/1.39	
2.09/1.39		Pol(evalfoobb4in) = V_1 + V_3
2.09/1.39	
2.09/1.39		Pol(evalfoobb3in) = V_5
2.09/1.39	
2.09/1.39		Pol(evalfoostop) = V_1 + V_3
2.09/1.39	
2.09/1.39		Pol(koat_start) = V_2 + V_4
2.09/1.39	
2.09/1.39	orients all transitions weakly and the transition
2.09/1.39	
2.09/1.39		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39	strictly and produces the following problem:
2.09/1.39	
2.09/1.39	4:	T:
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)              evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)              evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.09/1.39	
2.09/1.39	5:	T:
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)              evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	A polynomial rank function with
2.09/1.39	
2.09/1.39		Pol(evalfoobb2in) = V_3 - V_5
2.09/1.39	
2.09/1.39		Pol(evalfoobb1in) = -V_1 + V_3 + 1
2.09/1.39	
2.09/1.39	and size complexities
2.09/1.39	
2.09/1.39		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
2.09/1.39	
2.09/1.39		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
2.09/1.39	
2.09/1.39		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
2.09/1.39	
2.09/1.39		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_4
2.09/1.39	
2.09/1.39		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\\ ar_2 >= 1 ]", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\\ ar_2 >= 1 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\\ ar_2 >= 1 ]", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\\ ar_2 >= 1 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\\ ar_2 >= 1 ]", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_4
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_4
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\\ ar_0 >= 1 ]", 0-0) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3) + ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\\ ar_0 >= 1 ]", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\\ ar_0 >= 1 ]", 0-2) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\\ ar_0 >= 1 ]", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\\ ar_0 >= 1 ]", 0-4) = pow(2, ar_1 + ar_3) * (ar_1 + ar_3)
2.09/1.39	
2.09/1.39		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-0) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-2) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))", 0-4) = ar_4
2.09/1.39	
2.09/1.39		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
2.09/1.39	
2.09/1.39		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.09/1.39	
2.09/1.39		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.09/1.39	
2.09/1.39		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.09/1.39	
2.09/1.39		S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.09/1.39	
2.09/1.39	orients the transitions
2.09/1.39	
2.09/1.39		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39	weakly and the transition
2.09/1.39	
2.09/1.39		evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39	strictly and produces the following problem:
2.09/1.39	
2.09/1.39	6:	T:
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)                                                                              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)                                                                              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: ?, Cost: 1)                                                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)                                                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)                                                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)                                                                    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2 * pow(2, ar_1 + ar_3) * (ar_1^2 + 2*ar_1*ar_3 + ar_3^2) + ar_1 + ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)                                                                    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)                                                                    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)                                                                              evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)                                                                              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.09/1.39	
2.09/1.39	7:	T:
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)                                                                              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 1)                                                                              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 2 * pow(2, ar_1 + ar_3) * (ar_1^2 + 2*ar_1*ar_3 + ar_3^2) + ar_1 + ar_3 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0)) [ ar_2 >= 1 /\ ar_0 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)                                                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)                                                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)                                                                    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 /\ ar_2 >= 1 ]
2.09/1.39	
2.09/1.39			(Comp: 2 * pow(2, ar_1 + ar_3) * (ar_1^2 + 2*ar_1*ar_3 + ar_3^2) + ar_1 + ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)                                                                    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_2 ]
2.09/1.39	
2.09/1.39			(Comp: ar_1 + ar_3, Cost: 1)                                                                    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_2))
2.09/1.39	
2.09/1.39			(Comp: 2, Cost: 1)                                                                              evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.09/1.39	
2.09/1.39			(Comp: 1, Cost: 0)                                                                              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.09/1.39	
2.09/1.39		start location:	koat_start
2.09/1.39	
2.09/1.39		leaf cost:	0
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	Complexity upper bound 4 * pow(2, ar_1 + ar_3) * (ar_1^2 + 2*ar_1*ar_3 + ar_3^2) + 5*ar_1 + 5*ar_3 + 11
2.09/1.39	
2.09/1.39	
2.09/1.39	
2.09/1.39	Time: 0.164 sec (SMT: 0.130 sec)
2.09/1.39	
2.09/1.39	
2.09/1.39	----------------------------------------
2.09/1.39	
2.09/1.39	(2)
2.09/1.39	BOUNDS(1, EXP)
2.32/1.41	EOF