2.22/1.41	WORST_CASE(?, O(n^2))
2.22/1.42	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.22/1.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.22/1.42	
2.22/1.42	
2.22/1.42	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.22/1.42	
2.22/1.42	(0) CpxIntTrs
2.22/1.42	(1) Koat Proof [FINISHED, 67 ms]
2.22/1.42	(2) BOUNDS(1, n^2)
2.22/1.42	
2.22/1.42	
2.22/1.42	----------------------------------------
2.22/1.42	
2.22/1.42	(0)
2.22/1.42	Obligation:
2.22/1.42	Complexity Int TRS consisting of the following rules:
2.22/1.42	eval_textbook_ex4_start(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb0_in(v_i.0, v_j.0, v_m, v_n)) :|: TRUE
2.22/1.42	eval_textbook_ex4_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb1_in(v_i.0, 1, v_m, v_n)) :|: TRUE
2.22/1.42	eval_textbook_ex4_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb2_in(1, v_j.0, v_m, v_n)) :|: v_j.0 <= v_n
2.22/1.42	eval_textbook_ex4_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb5_in(v_i.0, v_j.0, v_m, v_n)) :|: v_j.0 > v_n
2.22/1.42	eval_textbook_ex4_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 <= v_m
2.22/1.42	eval_textbook_ex4_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb4_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 > v_m
2.22/1.42	eval_textbook_ex4_bb3_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb2_in(v_i.0 + 1, v_j.0, v_m, v_n)) :|: TRUE
2.22/1.42	eval_textbook_ex4_bb4_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb1_in(v_i.0, v_j.0 + 1, v_m, v_n)) :|: TRUE
2.22/1.42	eval_textbook_ex4_bb5_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_stop(v_i.0, v_j.0, v_m, v_n)) :|: TRUE
2.22/1.42	
2.22/1.42	The start-symbols are:[eval_textbook_ex4_start_4]
2.22/1.42	
2.22/1.42	
2.22/1.42	----------------------------------------
2.22/1.42	
2.22/1.42	(1) Koat Proof (FINISHED)
2.22/1.42	YES(?, 9*ar_1 + 2*ar_1*ar_3 + 6)
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	Initial complexity problem:
2.22/1.42	
2.22/1.42	1:	T:
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.22/1.42	
2.22/1.42	2:	T:
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)    evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)    evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	A polynomial rank function with
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4start) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb0in) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb1in) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb2in) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb5in) = 1
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb3in) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb4in) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4stop) = 0
2.22/1.42	
2.22/1.42		Pol(koat_start) = 2
2.22/1.42	
2.22/1.42	orients all transitions weakly and the transitions
2.22/1.42	
2.22/1.42		evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42		evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42	strictly and produces the following problem:
2.22/1.42	
2.22/1.42	3:	T:
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)    evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)    evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)    evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)    evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	A polynomial rank function with
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4start) = V_2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb0in) = V_2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb1in) = -V_1 + V_2 + 1
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb2in) = -V_1 + V_2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb5in) = -V_1 + V_2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb3in) = -V_1 + V_2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb4in) = -V_1 + V_2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4stop) = -V_1 + V_2
2.22/1.42	
2.22/1.42		Pol(koat_start) = V_2
2.22/1.42	
2.22/1.42	orients all transitions weakly and the transition
2.22/1.42	
2.22/1.42		evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42	strictly and produces the following problem:
2.22/1.42	
2.22/1.42	4:	T:
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)       evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)       evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ar_1, Cost: 1)    evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)       evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)       evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)       evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)       evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)       evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)       evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	A polynomial rank function with
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb4in) = 1
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb1in) = 0
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb3in) = 2
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb2in) = 2
2.22/1.42	
2.22/1.42	and size complexities
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42	orients the transitions
2.22/1.42	
2.22/1.42		evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42		evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42		evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42		evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42	weakly and the transitions
2.22/1.42	
2.22/1.42		evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42		evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42	strictly and produces the following problem:
2.22/1.42	
2.22/1.42	5:	T:
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)         evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)         evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ar_1, Cost: 1)      evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)         evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)         evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: 2*ar_1, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)         evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2*ar_1, Cost: 1)    evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)         evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	A polynomial rank function with
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb3in) = -V_3 + V_4
2.22/1.42	
2.22/1.42		Pol(evaltextbookex4bb2in) = -V_3 + V_4 + 1
2.22/1.42	
2.22/1.42	and size complexities
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.22/1.42	
2.22/1.42		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 20
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 4
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = 2*ar_1 + 4
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-0) = 2*ar_1 + 4
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-0) = 2*ar_1 + 4
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 10
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = 2*ar_1 + 4
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.22/1.42	
2.22/1.42		S("evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.22/1.42	
2.22/1.42		S("evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.22/1.42	
2.22/1.42	orients the transitions
2.22/1.42	
2.22/1.42		evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42		evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42	weakly and the transition
2.22/1.42	
2.22/1.42		evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42	strictly and produces the following problem:
2.22/1.42	
2.22/1.42	6:	T:
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)                     evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)                     evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ar_1, Cost: 1)                  evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)                     evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ar_1*ar_3 + 2*ar_1, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: 2*ar_1, Cost: 1)                evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ?, Cost: 1)                     evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2*ar_1, Cost: 1)                evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)                     evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.22/1.42	
2.22/1.42	7:	T:
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)                     evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 1)                     evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: ar_1, Cost: 1)                  evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ]
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)                     evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ar_1*ar_3 + 2*ar_1, Cost: 1)    evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
2.22/1.42	
2.22/1.42			(Comp: 2*ar_1, Cost: 1)                evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
2.22/1.42	
2.22/1.42			(Comp: ar_1*ar_3 + 2*ar_1, Cost: 1)    evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2*ar_1, Cost: 1)                evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 2, Cost: 1)                     evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3))
2.22/1.42	
2.22/1.42			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.22/1.42	
2.22/1.42		start location:	koat_start
2.22/1.42	
2.22/1.42		leaf cost:	0
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	Complexity upper bound 9*ar_1 + 2*ar_1*ar_3 + 6
2.22/1.42	
2.22/1.42	
2.22/1.42	
2.22/1.42	Time: 0.107 sec (SMT: 0.091 sec)
2.22/1.42	
2.22/1.42	
2.22/1.42	----------------------------------------
2.22/1.42	
2.22/1.42	(2)
2.22/1.42	BOUNDS(1, n^2)
2.22/1.45	EOF