2.53/1.51	WORST_CASE(?, O(n^2))
2.53/1.52	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.53/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.53/1.52	
2.53/1.52	
2.53/1.52	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.53/1.52	
2.53/1.52	(0) CpxIntTrs
2.53/1.52	(1) Koat Proof [FINISHED, 276 ms]
2.53/1.52	(2) BOUNDS(1, n^2)
2.53/1.52	
2.53/1.52	
2.53/1.52	----------------------------------------
2.53/1.52	
2.53/1.52	(0)
2.53/1.52	Obligation:
2.53/1.52	Complexity Int TRS consisting of the following rules:
2.53/1.52	eval_speed_pldi09_fig1_start(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb0_in(v_n, v_x.0, v_y.0)) :|: TRUE
2.53/1.52	eval_speed_pldi09_fig1_bb0_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb1_in(v_n, 0, 0)) :|: TRUE
2.53/1.52	eval_speed_pldi09_fig1_bb1_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb2_in(v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n
2.53/1.52	eval_speed_pldi09_fig1_bb1_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb3_in(v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n
2.53/1.52	eval_speed_pldi09_fig1_bb2_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb1_in(v_n, v_x.0 + 1, v_y.0 + 1)) :|: TRUE
2.53/1.52	eval_speed_pldi09_fig1_bb3_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb4_in(v_n, v_x.0, v_y.0)) :|: v_y.0 > 0
2.53/1.52	eval_speed_pldi09_fig1_bb3_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb5_in(v_n, v_x.0, v_y.0)) :|: v_y.0 <= 0
2.53/1.52	eval_speed_pldi09_fig1_bb4_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_bb1_in(v_n, v_x.0, v_y.0 - 1)) :|: TRUE
2.53/1.52	eval_speed_pldi09_fig1_bb5_in(v_n, v_x.0, v_y.0) -> Com_1(eval_speed_pldi09_fig1_stop(v_n, v_x.0, v_y.0)) :|: TRUE
2.53/1.52	
2.53/1.52	The start-symbols are:[eval_speed_pldi09_fig1_start_3]
2.53/1.52	
2.53/1.52	
2.53/1.52	----------------------------------------
2.53/1.52	
2.53/1.52	(1) Koat Proof (FINISHED)
2.53/1.52	YES(?, 9*ar_2^2 + 8*ar_2 + 12)
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	Initial complexity problem:
2.53/1.52	
2.53/1.52	1:	T:
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.53/1.52	
2.53/1.52	2:	T:
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)    evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)    evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	A polynomial rank function with
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1start) = 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb0in) = 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb1in) = 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb2in) = 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb3in) = 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb4in) = 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb5in) = 1
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1stop) = 0
2.53/1.52	
2.53/1.52		Pol(koat_start) = 2
2.53/1.52	
2.53/1.52	orients all transitions weakly and the transitions
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52	strictly and produces the following problem:
2.53/1.52	
2.53/1.52	3:	T:
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)    evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)    evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)    evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)    evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	A polynomial rank function with
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1start) = V_3
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb0in) = V_3
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb1in) = -V_1 + V_3
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb2in) = -V_1 + V_3 - 1
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb3in) = -V_1 + V_3
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb4in) = -V_1 + V_3
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb5in) = -V_1 + V_3
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1stop) = -V_1 + V_3
2.53/1.52	
2.53/1.52		Pol(koat_start) = V_3
2.53/1.52	
2.53/1.52	orients all transitions weakly and the transition
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52	strictly and produces the following problem:
2.53/1.52	
2.53/1.52	4:	T:
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)       evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)       evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)       evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)       evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.53/1.52	
2.53/1.52	5:	T:
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)       evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)       evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)    evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)       evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)       evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	Applied AI with 'oct' on problem 5 to obtain the following invariants:
2.53/1.52	
2.53/1.52	  For symbol evalspeedpldi09fig1bb1in: X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.53/1.52	
2.53/1.52	  For symbol evalspeedpldi09fig1bb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.53/1.52	
2.53/1.52	  For symbol evalspeedpldi09fig1bb3in: X_1 - X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.53/1.52	
2.53/1.52	  For symbol evalspeedpldi09fig1bb4in: X_1 - X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.53/1.52	
2.53/1.52	  For symbol evalspeedpldi09fig1bb5in: X_1 - X_3 >= 0 /\ -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	This yielded the following problem:
2.53/1.52	
2.53/1.52	6:	T:
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)       evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ -ar_1 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)       evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)    evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.53/1.52	
2.53/1.52			(Comp: ?, Cost: 1)       evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)       evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)       evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	A polynomial rank function with
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb4in) = 3*V_2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb1in) = 3*V_2 + 2
2.53/1.52	
2.53/1.52		Pol(evalspeedpldi09fig1bb3in) = 3*V_2 + 1
2.53/1.52	
2.53/1.52	and size complexities
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))", 0-0) = 0
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))", 0-1) = 0
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-1) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-1) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_2 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-1) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 ]", 0-1) = 0
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_2
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = 0
2.53/1.52	
2.53/1.52		S("evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.53/1.52	
2.53/1.52		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.53/1.52	
2.53/1.52		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.53/1.52	
2.53/1.52	orients the transitions
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52	weakly and the transitions
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52		evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52	strictly and produces the following problem:
2.53/1.52	
2.53/1.52	7:	T:
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 0)                        koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)                        evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1stop(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ -ar_1 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.53/1.52	
2.53/1.52			(Comp: 3*ar_2^2 + 2*ar_2 + 2, Cost: 1)    evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
2.53/1.52	
2.53/1.52			(Comp: 2, Cost: 1)                        evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_1 ]
2.53/1.52	
2.53/1.52			(Comp: 3*ar_2^2 + 2*ar_2 + 2, Cost: 1)    evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb4in(ar_0, ar_1, ar_2)) [ ar_0 - ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 1 ]
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)                     evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(ar_0 + 1, ar_1 + 1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.53/1.52	
2.53/1.52			(Comp: 3*ar_2^2 + 2*ar_2 + 2, Cost: 1)    evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb3in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.53/1.52	
2.53/1.52			(Comp: ar_2, Cost: 1)                     evalspeedpldi09fig1bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)                        evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb1in(0, 0, ar_2))
2.53/1.52	
2.53/1.52			(Comp: 1, Cost: 1)                        evalspeedpldi09fig1start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi09fig1bb0in(ar_0, ar_1, ar_2))
2.53/1.52	
2.53/1.52		start location:	koat_start
2.53/1.52	
2.53/1.52		leaf cost:	0
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	Complexity upper bound 9*ar_2^2 + 8*ar_2 + 12
2.53/1.52	
2.53/1.52	
2.53/1.52	
2.53/1.52	Time: 0.263 sec (SMT: 0.233 sec)
2.53/1.52	
2.53/1.52	
2.53/1.52	----------------------------------------
2.53/1.52	
2.53/1.52	(2)
2.53/1.52	BOUNDS(1, n^2)
2.53/1.55	EOF