2.26/1.50	WORST_CASE(?, O(n^1))
2.26/1.51	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.26/1.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.26/1.51	
2.26/1.51	
2.26/1.51	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.26/1.51	
2.26/1.51	(0) CpxIntTrs
2.26/1.51	(1) Koat Proof [FINISHED, 258 ms]
2.26/1.51	(2) BOUNDS(1, n^1)
2.26/1.51	
2.26/1.51	
2.26/1.51	----------------------------------------
2.26/1.51	
2.26/1.51	(0)
2.26/1.51	Obligation:
2.26/1.51	Complexity Int TRS consisting of the following rules:
2.26/1.51	eval_speed_popl10_fig2_2_start(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb0_in(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE
2.26/1.51	eval_speed_popl10_fig2_2_bb0_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_x, v_z, v_n, v_x, v_z)) :|: TRUE
2.26/1.51	eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 < v_n
2.26/1.51	eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb3_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 >= v_n
2.26/1.51	eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0 + 1, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0
2.26/1.51	eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 && v_.01 <= v_.0
2.26/1.51	eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0 + 1, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 && v_.01 > v_.0
2.26/1.51	eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0
2.26/1.51	eval_speed_popl10_fig2_2_bb3_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_stop(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE
2.26/1.51	
2.26/1.51	The start-symbols are:[eval_speed_popl10_fig2_2_start_5]
2.26/1.51	
2.26/1.51	
2.26/1.51	----------------------------------------
2.26/1.51	
2.26/1.51	(1) Koat Proof (FINISHED)
2.26/1.51	YES(?, 2*ar_3 + 4*ar_4 + 2*ar_1 + 7)
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Initial complexity problem:
2.26/1.51	
2.26/1.51	1:	T:
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.26/1.51	
2.26/1.51		evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51		evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51	We thus obtain the following problem:
2.26/1.51	
2.26/1.51	2:	T:
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.26/1.51	
2.26/1.51	3:	T:
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)    evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)    evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	A polynomial rank function with
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb3in) = 1
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22stop) = 0
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb2in) = 2
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb1in) = 2
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb0in) = 2
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22start) = 2
2.26/1.51	
2.26/1.51		Pol(koat_start) = 2
2.26/1.51	
2.26/1.51	orients all transitions weakly and the transitions
2.26/1.51	
2.26/1.51		evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51		evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51	strictly and produces the following problem:
2.26/1.51	
2.26/1.51	4:	T:
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)    evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)    evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)    evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.26/1.51	
2.26/1.51	  For symbol evalspeedpopl10fig22bb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.26/1.51	
2.26/1.51	  For symbol evalspeedpopl10fig22bb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.26/1.51	
2.26/1.51	  For symbol evalspeedpopl10fig22bb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	This yielded the following problem:
2.26/1.51	
2.26/1.51	5:	T:
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)    evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)    evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)    evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	A polynomial rank function with
2.26/1.51	
2.26/1.51		Pol(koat_start) = -V_2 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22start) = -V_2 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb0in) = -V_2 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb1in) = -V_1 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb2in) = -V_1 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb3in) = -V_1 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22stop) = -V_1 + V_5
2.26/1.51	
2.26/1.51	orients all transitions weakly and the transition
2.26/1.51	
2.26/1.51		evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51	strictly and produces the following problem:
2.26/1.51	
2.26/1.51	6:	T:
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)              evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)              evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)              evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)              evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ar_1 + ar_4, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)              evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)              evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	A polynomial rank function with
2.26/1.51	
2.26/1.51		Pol(koat_start) = -V_4 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22start) = -V_4 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb0in) = -V_4 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb1in) = -V_3 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb2in) = -V_3 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22bb3in) = -V_3 + V_5
2.26/1.51	
2.26/1.51		Pol(evalspeedpopl10fig22stop) = -V_3 + V_5
2.26/1.51	
2.26/1.51	orients all transitions weakly and the transition
2.26/1.51	
2.26/1.51		evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51	strictly and produces the following problem:
2.26/1.51	
2.26/1.51	7:	T:
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)              evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)              evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ?, Cost: 1)              evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)              evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ar_1 + ar_4, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ar_3 + ar_4, Cost: 1)    evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)              evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.26/1.51	
2.26/1.51	8:	T:
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)                           evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: 1, Cost: 1)                           evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4))
2.26/1.51	
2.26/1.51			(Comp: ar_3 + 2*ar_4 + ar_1 + 1, Cost: 1)    evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)                           evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.26/1.51	
2.26/1.51			(Comp: ar_1 + ar_4, Cost: 1)                 evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.26/1.51	
2.26/1.51			(Comp: ar_3 + ar_4, Cost: 1)                 evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_2 ]
2.26/1.51	
2.26/1.51			(Comp: 2, Cost: 1)                           evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.26/1.51	
2.26/1.51		start location:	koat_start
2.26/1.51	
2.26/1.51		leaf cost:	0
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Complexity upper bound 2*ar_3 + 4*ar_4 + 2*ar_1 + 7
2.26/1.51	
2.26/1.51	
2.26/1.51	
2.26/1.51	Time: 0.235 sec (SMT: 0.198 sec)
2.26/1.51	
2.26/1.51	
2.26/1.51	----------------------------------------
2.26/1.51	
2.26/1.51	(2)
2.26/1.51	BOUNDS(1, n^1)
2.26/1.52	EOF