2.12/1.32	WORST_CASE(?, O(n^1))
2.26/1.33	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.26/1.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.26/1.33	
2.26/1.33	
2.26/1.33	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.26/1.33	
2.26/1.33	(0) CpxIntTrs
2.26/1.33	(1) Koat Proof [FINISHED, 77 ms]
2.26/1.33	(2) BOUNDS(1, n^1)
2.26/1.33	
2.26/1.33	
2.26/1.33	----------------------------------------
2.26/1.33	
2.26/1.33	(0)
2.26/1.33	Obligation:
2.26/1.33	Complexity Int TRS consisting of the following rules:
2.26/1.33	eval_speed_popl10_simple_single_2_start(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb0_in(v_m, v_n, v_x.0, v_y.0)) :|: TRUE
2.26/1.33	eval_speed_popl10_simple_single_2_bb0_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb1_in(v_m, v_n, 0, 0)) :|: TRUE
2.26/1.33	eval_speed_popl10_simple_single_2_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb2_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n
2.26/1.33	eval_speed_popl10_simple_single_2_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb3_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n
2.26/1.33	eval_speed_popl10_simple_single_2_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0 + 1)) :|: TRUE
2.26/1.33	eval_speed_popl10_simple_single_2_bb3_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb4_in(v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 < v_m
2.26/1.33	eval_speed_popl10_simple_single_2_bb3_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb5_in(v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 >= v_m
2.26/1.33	eval_speed_popl10_simple_single_2_bb4_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0 + 1)) :|: TRUE
2.26/1.33	eval_speed_popl10_simple_single_2_bb5_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speed_popl10_simple_single_2_stop(v_m, v_n, v_x.0, v_y.0)) :|: TRUE
2.26/1.33	
2.26/1.33	The start-symbols are:[eval_speed_popl10_simple_single_2_start_4]
2.26/1.33	
2.26/1.33	
2.26/1.33	----------------------------------------
2.26/1.33	
2.26/1.33	(1) Koat Proof (FINISHED)
2.26/1.33	YES(?, 3*ar_2 + 3*ar_3 + 10)
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	Initial complexity problem:
2.26/1.33	
2.26/1.33	1:	T:
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.26/1.33	
2.26/1.33	2:	T:
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)    evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)    evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	A polynomial rank function with
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2start) = 2
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb0in) = 2
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb1in) = 2
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb2in) = 2
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb3in) = 2
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb4in) = 2
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb5in) = 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2stop) = 0
2.26/1.33	
2.26/1.33		Pol(koat_start) = 2
2.26/1.33	
2.26/1.33	orients all transitions weakly and the transitions
2.26/1.33	
2.26/1.33		evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33		evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33	strictly and produces the following problem:
2.26/1.33	
2.26/1.33	3:	T:
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)    evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)    evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)    evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)    evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	A polynomial rank function with
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2start) = V_3
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb0in) = V_3
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb1in) = -V_1 + V_3
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb2in) = -V_1 + V_3 - 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb3in) = -V_1 + V_3
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb4in) = -V_1 + V_3 - 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb5in) = -V_1 + V_3
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2stop) = -V_1 + V_3
2.26/1.33	
2.26/1.33		Pol(koat_start) = V_3
2.26/1.33	
2.26/1.33	orients all transitions weakly and the transition
2.26/1.33	
2.26/1.33		evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33	strictly and produces the following problem:
2.26/1.33	
2.26/1.33	4:	T:
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)       evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)       evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)       evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)       evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.26/1.33	
2.26/1.33	5:	T:
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)       evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)       evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)    evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)       evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)       evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)       evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	A polynomial rank function with
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2start) = V_4 + 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb0in) = V_4 + 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb1in) = -V_2 + V_4 + 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb2in) = -V_2 + V_4
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb3in) = -V_2 + V_4 + 1
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb4in) = -V_2 + V_4
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2bb5in) = -V_2 + V_4
2.26/1.33	
2.26/1.33		Pol(evalspeedpopl10simplesingle2stop) = -V_2 + V_4
2.26/1.33	
2.26/1.33		Pol(koat_start) = V_4 + 1
2.26/1.33	
2.26/1.33	orients all transitions weakly and the transition
2.26/1.33	
2.26/1.33		evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33	strictly and produces the following problem:
2.26/1.33	
2.26/1.33	6:	T:
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)           evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)           evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)        evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)           evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)        evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ar_3 + 1, Cost: 1)    evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)           evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ?, Cost: 1)           evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)           evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.26/1.33	
2.26/1.33	7:	T:
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)                  evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 1)                  evalspeedpopl10simplesingle2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(0, 0, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)               evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: ar_3 + ar_2 + 2, Cost: 1)    evalspeedpopl10simplesingle2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ]
2.26/1.33	
2.26/1.33			(Comp: ar_2, Cost: 1)               evalspeedpopl10simplesingle2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: ar_3 + 1, Cost: 1)           evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)                  evalspeedpopl10simplesingle2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.26/1.33	
2.26/1.33			(Comp: ar_3 + 1, Cost: 1)           evalspeedpopl10simplesingle2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2bb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 2, Cost: 1)                  evalspeedpopl10simplesingle2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2stop(ar_0, ar_1, ar_2, ar_3))
2.26/1.33	
2.26/1.33			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpopl10simplesingle2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.26/1.33	
2.26/1.33		start location:	koat_start
2.26/1.33	
2.26/1.33		leaf cost:	0
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	Complexity upper bound 3*ar_2 + 3*ar_3 + 10
2.26/1.33	
2.26/1.33	
2.26/1.33	
2.26/1.33	Time: 0.112 sec (SMT: 0.097 sec)
2.26/1.33	
2.26/1.33	
2.26/1.33	----------------------------------------
2.26/1.33	
2.26/1.33	(2)
2.26/1.33	BOUNDS(1, n^1)
2.29/1.36	EOF