2.18/1.46	WORST_CASE(?, O(n^1))
2.18/1.47	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.18/1.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.18/1.47	
2.18/1.47	
2.18/1.47	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.18/1.47	
2.18/1.47	(0) CpxIntTrs
2.18/1.47	(1) Koat Proof [FINISHED, 169 ms]
2.18/1.47	(2) BOUNDS(1, n^1)
2.18/1.47	
2.18/1.47	
2.18/1.47	----------------------------------------
2.18/1.47	
2.18/1.47	(0)
2.18/1.47	Obligation:
2.18/1.47	Complexity Int TRS consisting of the following rules:
2.18/1.47	eval_foo_start(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y)) :|: TRUE
2.18/1.47	eval_foo_bb0_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.2, v_.24, v_c, v_x, v_y)) :|: TRUE
2.18/1.47	eval_foo_bb1_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y)) :|: v_.01 + v_.02 > 0
2.18/1.47	eval_foo_bb1_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y)) :|: v_.01 + v_.02 <= 0
2.18/1.47	eval_foo_bb2_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y)) :|: v_.01 > v_.02
2.18/1.47	eval_foo_bb2_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y)) :|: v_.01 <= v_.02
2.18/1.47	eval_foo_bb3_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01 - 1, v_.02, v_c, v_x, v_y)) :|: TRUE
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01 - 1, v_.02, v_c, v_x, v_y)) :|: v_.01 >= v_.02 && v_.01 <= v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 >= v_.02 && v_.01 <= v_.02 && v_.01 < v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 >= v_.02 && v_.01 <= v_.02 && v_.01 > v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01 - 1, v_.02 - 1, v_c, v_x, v_y)) :|: v_.01 < v_.02 && v_.01 >= v_.02 && v_.01 <= v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01 - 1, v_.02 - 1, v_c, v_x, v_y)) :|: v_.01 > v_.02 && v_.01 >= v_.02 && v_.01 <= v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02 - 1, v_c, v_x, v_y)) :|: v_.01 < v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02 - 1, v_c, v_x, v_y)) :|: v_.01 < v_.02 && v_.01 > v_.02
2.18/1.47	eval_foo_bb4_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02 - 1, v_c, v_x, v_y)) :|: v_.01 > v_.02
2.18/1.47	eval_foo_bb5_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.2, v_.24, v_.2, v_.24, v_c, v_x, v_y)) :|: TRUE
2.18/1.47	eval_foo_bb6_in(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_.2, v_.24, v_c, v_x, v_y)) :|: TRUE
2.18/1.47	
2.18/1.47	The start-symbols are:[eval_foo_start_7]
2.18/1.47	
2.18/1.47	
2.18/1.47	----------------------------------------
2.18/1.47	
2.18/1.47	(1) Koat Proof (FINISHED)
2.18/1.47	YES(?, 9*ar_1 + 9*ar_3 + 6)
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	Initial complexity problem:
2.18/1.47	
2.18/1.47	1:	T:
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2 - 1)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2 - 1)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.18/1.47	
2.18/1.47		start location:	koat_start
2.18/1.47	
2.18/1.47		leaf cost:	0
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.18/1.47	
2.18/1.47		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2 - 1)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2 - 1)) [ 0 >= 1 /\ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47		evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47	We thus obtain the following problem:
2.18/1.47	
2.18/1.47	2:	T:
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.18/1.47	
2.18/1.47		start location:	koat_start
2.18/1.47	
2.18/1.47		leaf cost:	0
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.18/1.47	
2.18/1.47	3:	T:
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.18/1.47	
2.18/1.47		start location:	koat_start
2.18/1.47	
2.18/1.47		leaf cost:	0
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	A polynomial rank function with
2.18/1.47	
2.18/1.47		Pol(evalfoobb5in) = 2
2.18/1.47	
2.18/1.47		Pol(evalfoobb1in) = 2
2.18/1.47	
2.18/1.47		Pol(evalfoobb4in) = 2
2.18/1.47	
2.18/1.47		Pol(evalfoobb3in) = 2
2.18/1.47	
2.18/1.47		Pol(evalfoobb6in) = 1
2.18/1.47	
2.18/1.47		Pol(evalfoostop) = 0
2.18/1.47	
2.18/1.47		Pol(evalfoobb2in) = 2
2.18/1.47	
2.18/1.47		Pol(evalfoobb0in) = 2
2.18/1.47	
2.18/1.47		Pol(evalfoostart) = 2
2.18/1.47	
2.18/1.47		Pol(koat_start) = 2
2.18/1.47	
2.18/1.47	orients all transitions weakly and the transitions
2.18/1.47	
2.18/1.47		evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47	strictly and produces the following problem:
2.18/1.47	
2.18/1.47	4:	T:
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.18/1.47	
2.18/1.47			(Comp: 2, Cost: 1)    evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.18/1.47	
2.18/1.47		start location:	koat_start
2.18/1.47	
2.18/1.47		leaf cost:	0
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	A polynomial rank function with
2.18/1.47	
2.18/1.47		Pol(evalfoobb5in) = V_5 + V_6
2.18/1.47	
2.18/1.47		Pol(evalfoobb1in) = V_1 + V_3
2.18/1.47	
2.18/1.47		Pol(evalfoobb4in) = V_1 + V_3 - 1
2.18/1.47	
2.18/1.47		Pol(evalfoobb3in) = V_1 + V_3 - 1
2.18/1.47	
2.18/1.47		Pol(evalfoobb6in) = V_1 + V_3
2.18/1.47	
2.18/1.47		Pol(evalfoostop) = V_1 + V_3
2.18/1.47	
2.18/1.47		Pol(evalfoobb2in) = V_1 + V_3 - 1
2.18/1.47	
2.18/1.47		Pol(evalfoobb0in) = V_2 + V_4
2.18/1.47	
2.18/1.47		Pol(evalfoostart) = V_2 + V_4
2.18/1.47	
2.18/1.47		Pol(koat_start) = V_2 + V_4
2.18/1.47	
2.18/1.47	orients all transitions weakly and the transition
2.18/1.47	
2.18/1.47		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47	strictly and produces the following problem:
2.18/1.47	
2.18/1.47	5:	T:
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)              evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)              evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)              evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)              evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.18/1.47	
2.18/1.47			(Comp: 2, Cost: 1)              evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.18/1.47	
2.18/1.47			(Comp: ?, Cost: 1)              evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: 2, Cost: 1)              evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)              evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)              evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.18/1.47	
2.18/1.47		start location:	koat_start
2.18/1.47	
2.18/1.47		leaf cost:	0
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	Repeatedly propagating knowledge in problem 5 produces the following problem:
2.18/1.47	
2.18/1.47	6:	T:
2.18/1.47	
2.18/1.47			(Comp: 3*ar_1 + 3*ar_3, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_5, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)        evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2 - 1)) [ ar_2 >= ar_0 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)        evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2)) [ ar_0 = ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)        evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_2))
2.18/1.47	
2.18/1.47			(Comp: 2, Cost: 1)                  evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)        evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ]
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)        evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]
2.18/1.47	
2.18/1.47			(Comp: 2, Cost: 1)                  evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 + ar_2 ]
2.18/1.47	
2.18/1.47			(Comp: ar_1 + ar_3, Cost: 1)        evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 + ar_2 >= 1 ]
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)                  evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 1)                  evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.18/1.47	
2.18/1.47			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.18/1.47	
2.18/1.47		start location:	koat_start
2.18/1.47	
2.18/1.47		leaf cost:	0
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	Complexity upper bound 9*ar_1 + 9*ar_3 + 6
2.18/1.47	
2.18/1.47	
2.18/1.47	
2.18/1.47	Time: 0.157 sec (SMT: 0.133 sec)
2.18/1.47	
2.18/1.47	
2.18/1.47	----------------------------------------
2.18/1.47	
2.18/1.47	(2)
2.18/1.47	BOUNDS(1, n^1)
2.18/1.48	EOF