2.26/1.37	WORST_CASE(?, O(n^1))
2.26/1.38	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.26/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.26/1.38	
2.26/1.38	
2.26/1.38	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.26/1.38	
2.26/1.38	(0) CpxIntTrs
2.26/1.38	(1) Koat Proof [FINISHED, 187 ms]
2.26/1.38	(2) BOUNDS(1, n^1)
2.26/1.38	
2.26/1.38	
2.26/1.38	----------------------------------------
2.26/1.38	
2.26/1.38	(0)
2.26/1.38	Obligation:
2.26/1.38	Complexity Int TRS consisting of the following rules:
2.26/1.38	eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.26/1.38	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
2.26/1.38	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 + v_.01 > 0
2.26/1.38	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 + v_.01 <= 0
2.26/1.38	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > v_.01
2.26/1.38	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 <= v_.01
2.26/1.38	eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_x, v_y)) :|: TRUE
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01 && v_.0 < v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01 && v_.0 > v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 >= v_.01 && v_.0 <= v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_x, v_y)) :|: v_.0 > v_.01 && v_.0 >= v_.01 && v_.0 <= v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 < v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 > v_.01
2.26/1.38	eval_foo_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 > v_.01
2.26/1.38	eval_foo_bb5_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.26/1.38	
2.26/1.38	The start-symbols are:[eval_foo_start_4]
2.26/1.38	
2.26/1.38	
2.26/1.38	----------------------------------------
2.26/1.38	
2.26/1.38	(1) Koat Proof (FINISHED)
2.26/1.38	YES(?, 6*ar_1 + 6*ar_3 + 12)
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Initial complexity problem:
2.26/1.38	
2.26/1.38	1:	T:
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.26/1.38	
2.26/1.38		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38	We thus obtain the following problem:
2.26/1.38	
2.26/1.38	2:	T:
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.26/1.38	
2.26/1.38	3:	T:
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	A polynomial rank function with
2.26/1.38	
2.26/1.38		Pol(evalfoobb4in) = 2
2.26/1.38	
2.26/1.38		Pol(evalfoobb1in) = 2
2.26/1.38	
2.26/1.38		Pol(evalfoobb3in) = 2
2.26/1.38	
2.26/1.38		Pol(evalfoobb5in) = 1
2.26/1.38	
2.26/1.38		Pol(evalfoostop) = 0
2.26/1.38	
2.26/1.38		Pol(evalfoobb2in) = 2
2.26/1.38	
2.26/1.38		Pol(evalfoobb0in) = 2
2.26/1.38	
2.26/1.38		Pol(evalfoostart) = 2
2.26/1.38	
2.26/1.38		Pol(koat_start) = 2
2.26/1.38	
2.26/1.38	orients all transitions weakly and the transitions
2.26/1.38	
2.26/1.38		evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38	strictly and produces the following problem:
2.26/1.38	
2.26/1.38	4:	T:
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	A polynomial rank function with
2.26/1.38	
2.26/1.38		Pol(evalfoobb4in) = V_1 + V_3
2.26/1.38	
2.26/1.38		Pol(evalfoobb1in) = V_1 + V_3 + 1
2.26/1.38	
2.26/1.38		Pol(evalfoobb3in) = V_1 + V_3
2.26/1.38	
2.26/1.38		Pol(evalfoobb5in) = V_1 + V_3
2.26/1.38	
2.26/1.38		Pol(evalfoostop) = V_1 + V_3
2.26/1.38	
2.26/1.38		Pol(evalfoobb2in) = V_1 + V_3
2.26/1.38	
2.26/1.38		Pol(evalfoobb0in) = V_2 + V_4 + 1
2.26/1.38	
2.26/1.38		Pol(evalfoostart) = V_2 + V_4 + 1
2.26/1.38	
2.26/1.38		Pol(koat_start) = V_2 + V_4 + 1
2.26/1.38	
2.26/1.38	orients all transitions weakly and the transition
2.26/1.38	
2.26/1.38		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38	strictly and produces the following problem:
2.26/1.38	
2.26/1.38	5:	T:
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)                  evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)                  evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)                  evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                  evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)                  evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)                  evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                  evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Repeatedly propagating knowledge in problem 5 produces the following problem:
2.26/1.38	
2.26/1.38	6:	T:
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                  evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 + ar_2 >= 1 ]
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                  evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Complexity upper bound 6*ar_1 + 6*ar_3 + 12
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Time: 0.121 sec (SMT: 0.107 sec)
2.26/1.38	
2.26/1.38	
2.26/1.38	----------------------------------------
2.26/1.38	
2.26/1.38	(2)
2.26/1.38	BOUNDS(1, n^1)
2.44/1.40	EOF