2.26/1.47	WORST_CASE(?, O(n^1))
2.52/1.48	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.52/1.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.52/1.48	
2.52/1.48	
2.52/1.48	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.52/1.48	
2.52/1.48	(0) CpxIntTrs
2.52/1.48	(1) Koat Proof [FINISHED, 185 ms]
2.52/1.48	(2) BOUNDS(1, n^1)
2.52/1.48	
2.52/1.48	
2.52/1.48	----------------------------------------
2.52/1.48	
2.52/1.48	(0)
2.52/1.48	Obligation:
2.52/1.48	Complexity Int TRS consisting of the following rules:
2.52/1.48	eval_speed_popl10_simple_multiple_start(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb0_in(v_m, v_n, v_x.0, v_y.0)) :|: TRUE
2.52/1.48	eval_speed_popl10_simple_multiple_bb0_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, 0, 0)) :|: TRUE
2.52/1.48	eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n
2.52/1.48	eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb3_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n
2.52/1.48	eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0 + 1)) :|: v_y.0 < v_m
2.52/1.48	eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0 + 1)) :|: v_y.0 < v_m && v_y.0 >= v_m
2.52/1.48	eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 >= v_m && v_y.0 < v_m
2.52/1.48	eval_speed_popl10_simple_multiple_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0)) :|: v_y.0 >= v_m
2.52/1.48	eval_speed_popl10_simple_multiple_bb3_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_multiple_stop(v_m, v_n, v_x.0, v_y.0)) :|: TRUE
2.52/1.48	
2.52/1.48	The start-symbols are:[eval_speed_popl10_simple_multiple_start_4]
2.52/1.48	
2.52/1.48	
2.52/1.48	----------------------------------------
2.52/1.48	
2.52/1.48	(1) Koat Proof (FINISHED)
2.52/1.48	YES(?, 2*ar_2 + 2*ar_3 + 7)
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Initial complexity problem:
2.52/1.48	
2.52/1.48	1:	T:
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.52/1.48	
2.52/1.48		evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48		evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48	We thus obtain the following problem:
2.52/1.48	
2.52/1.48	2:	T:
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.52/1.48	
2.52/1.48	3:	T:
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)    evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)    evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	A polynomial rank function with
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb3in) = 1
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplestop) = 0
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb2in) = 2
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb1in) = 2
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb0in) = 2
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplestart) = 2
2.52/1.48	
2.52/1.48		Pol(koat_start) = 2
2.52/1.48	
2.52/1.48	orients all transitions weakly and the transitions
2.52/1.48	
2.52/1.48		evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48		evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48	strictly and produces the following problem:
2.52/1.48	
2.52/1.48	4:	T:
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)    evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)    evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)    evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	A polynomial rank function with
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb3in) = -V_2 + V_4
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplestop) = -V_2 + V_4
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb2in) = -V_2 + V_4
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb1in) = -V_2 + V_4
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb0in) = V_4
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplestart) = V_4
2.52/1.48	
2.52/1.48		Pol(koat_start) = V_4
2.52/1.48	
2.52/1.48	orients all transitions weakly and the transition
2.52/1.48	
2.52/1.48		evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48	strictly and produces the following problem:
2.52/1.48	
2.52/1.48	5:	T:
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)       evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)       evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: ar_3, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)       evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)       evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)       evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)       evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Applied AI with 'oct' on problem 5 to obtain the following invariants:
2.52/1.48	
2.52/1.48	  For symbol evalspeedpopl10simplemultiplebb1in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.52/1.48	
2.52/1.48	  For symbol evalspeedpopl10simplemultiplebb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.52/1.48	
2.52/1.48	  For symbol evalspeedpopl10simplemultiplebb3in: X_1 - X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	This yielded the following problem:
2.52/1.48	
2.52/1.48	6:	T:
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)       evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)       evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)       evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)       evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ar_3, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)       evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)       evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	A polynomial rank function with
2.52/1.48	
2.52/1.48		Pol(koat_start) = V_3
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplestart) = V_3
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb0in) = V_3
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb1in) = -V_1 + V_3
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb2in) = -V_1 + V_3
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplebb3in) = -V_1 + V_3
2.52/1.48	
2.52/1.48		Pol(evalspeedpopl10simplemultiplestop) = -V_1 + V_3
2.52/1.48	
2.52/1.48	orients all transitions weakly and the transition
2.52/1.48	
2.52/1.48		evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48	strictly and produces the following problem:
2.52/1.48	
2.52/1.48	7:	T:
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)       evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)       evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ?, Cost: 1)       evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)       evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ar_3, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ar_2, Cost: 1)    evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)       evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.52/1.48	
2.52/1.48	8:	T:
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)                  evalspeedpopl10simplemultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: 1, Cost: 1)                  evalspeedpopl10simplemultiplebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(0, 0, ar_2, ar_3))
2.52/1.48	
2.52/1.48			(Comp: ar_2 + ar_3 + 1, Cost: 1)    evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_0 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)                  evalspeedpopl10simplemultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_2 ]
2.52/1.48	
2.52/1.48			(Comp: ar_3, Cost: 1)               evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 + 1 ]
2.52/1.48	
2.52/1.48			(Comp: ar_2, Cost: 1)               evalspeedpopl10simplemultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplebb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 ]
2.52/1.48	
2.52/1.48			(Comp: 2, Cost: 1)                  evalspeedpopl10simplemultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplemultiplestop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
2.52/1.48	
2.52/1.48		start location:	koat_start
2.52/1.48	
2.52/1.48		leaf cost:	0
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Complexity upper bound 2*ar_2 + 2*ar_3 + 7
2.52/1.48	
2.52/1.48	
2.52/1.48	
2.52/1.48	Time: 0.210 sec (SMT: 0.186 sec)
2.52/1.48	
2.52/1.48	
2.52/1.48	----------------------------------------
2.52/1.48	
2.52/1.48	(2)
2.52/1.48	BOUNDS(1, n^1)
2.52/1.50	EOF