/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 2 + max(5, 1 + 2 * Arg_1) * nat(Arg_0) + max(2 * Arg_1, 4) + max(12, 8 + 2 * Arg_1)).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 243 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 420 ms]
(4) BOUNDS(1, INF)
(5) Koat2 Proof [FINISHED, 832 ms]
(6) BOUNDS(1, 2 + max(5, 1 + 2 * Arg_1) * nat(Arg_0) + max(2 * Arg_1, 4) + max(12, 8 + 2 * Arg_1))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_speedpldi4_start(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb0_in(v_i_0, v_m, v_n)) :|: TRUE
eval_speedpldi4_bb0_in(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_0(v_i_0, v_m, v_n)) :|: TRUE
eval_speedpldi4_0(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_1(v_i_0, v_m, v_n)) :|: TRUE
eval_speedpldi4_1(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_2(v_i_0, v_m, v_n)) :|: TRUE
eval_speedpldi4_2(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb3_in(v_i_0, v_m, v_n)) :|: v_m <= 0
eval_speedpldi4_2(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb3_in(v_i_0, v_m, v_n)) :|: v_n <= v_m
eval_speedpldi4_2(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb1_in(v_n, v_m, v_n)) :|: v_m > 0 && v_n > v_m
eval_speedpldi4_bb1_in(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb2_in(v_i_0, v_m, v_n)) :|: v_i_0 > 0
eval_speedpldi4_bb1_in(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb3_in(v_i_0, v_m, v_n)) :|: v_i_0 <= 0
eval_speedpldi4_bb2_in(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb1_in(v_i_0 - 1, v_m, v_n)) :|: v_i_0 < v_m
eval_speedpldi4_bb2_in(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_bb1_in(v_i_0 - v_m, v_m, v_n)) :|: v_i_0 >= v_m
eval_speedpldi4_bb3_in(v_i_0, v_m, v_n) -> Com_1(eval_speedpldi4_stop(v_i_0, v_m, v_n)) :|: TRUE

The start-symbols are:[eval_speedpldi4_start_3]


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(1) Koat Proof (FINISHED)
YES(?, 6*ar_1 + 11)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))

		(Comp: ?, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))

		(Comp: ?, Cost: 1)    evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))

		(Comp: ?, Cost: 1)    evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))

		(Comp: ?, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_2 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 1 produces the following problem:

2:	T:

		(Comp: 1, Cost: 1)    evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_2 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalspeedpldi4start) = 2

	Pol(evalspeedpldi4bb0in) = 2

	Pol(evalspeedpldi40) = 2

	Pol(evalspeedpldi41) = 2

	Pol(evalspeedpldi42) = 2

	Pol(evalspeedpldi4bb3in) = 1

	Pol(evalspeedpldi4bb1in) = 2

	Pol(evalspeedpldi4bb2in) = 2

	Pol(evalspeedpldi4stop) = 0

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))

	evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]

strictly and produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]

		(Comp: 2, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_0 >= ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_2 >= ar_0 ]

		(Comp: 2, Cost: 1)    evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Applied AI with 'oct' on problem 3 to obtain the following invariants:

  For symbol evalspeedpldi4bb1in: X_2 - X_3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0

  For symbol evalspeedpldi4bb2in: X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0





This yielded the following problem:

4:	T:

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)    evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]

		(Comp: 2, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: 1, Cost: 1)    evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)    evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalspeedpldi4bb2in) = 2*V_3 - 1

	Pol(evalspeedpldi4bb1in) = 2*V_3

and size complexities

	S("evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0

	S("evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1

	S("evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))", 0-0) = ar_0

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))", 0-1) = ar_1

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))", 0-2) = ar_2

	S("evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))", 0-0) = ar_0

	S("evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))", 0-1) = ar_1

	S("evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))", 0-2) = ar_2

	S("evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))", 0-0) = ar_0

	S("evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))", 0-1) = ar_1

	S("evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))", 0-2) = ar_2

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_0

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-0) = ar_0

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-1) = ar_1

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-2) = ar_2

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1

	S("evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1

	S("evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0

	S("evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1

	S("evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ar_1

	S("evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0

	S("evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1

	S("evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_1

	S("evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0

	S("evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1

	S("evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-2) = ar_1

	S("evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-0) = ar_0

	S("evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-1) = ar_1

	S("evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-2) = ar_1

	S("evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))", 0-0) = ar_0

	S("evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))", 0-1) = ar_1

	S("evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))", 0-2) = ar_1 + ar_2

	S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0

	S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1

	S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2

orients the transitions

	evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]

	evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]

	evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]

weakly and the transitions

	evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]

	evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]

	evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]

strictly and produces the following problem:

5:	T:

		(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)         evalspeedpldi4bb3in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4stop(ar_0, ar_1, ar_2))

		(Comp: 2*ar_1, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - ar_0)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]

		(Comp: 2*ar_1, Cost: 1)    evalspeedpldi4bb2in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]

		(Comp: 2, Cost: 1)         evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]

		(Comp: 2*ar_1, Cost: 1)    evalspeedpldi4bb1in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]

		(Comp: 1, Cost: 1)         evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb1in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]

		(Comp: 1, Cost: 1)         evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)         evalspeedpldi42(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: 1, Cost: 1)         evalspeedpldi41(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi42(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)         evalspeedpldi40(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi41(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)         evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi40(ar_0, ar_1, ar_2))

		(Comp: 1, Cost: 1)         evalspeedpldi4start(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb0in(ar_0, ar_1, ar_2))

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 6*ar_1 + 11



Time: 0.249 sec (SMT: 0.214 sec)


----------------------------------------

(2)
BOUNDS(1, n^1)

----------------------------------------

(3) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: evalspeedpldi4start

      0: evalspeedpldi4start -> evalspeedpldi4bb0in : [], cost: 1

      1: evalspeedpldi4bb0in -> evalspeedpldi40 : [], cost: 1

      2: evalspeedpldi40 -> evalspeedpldi41 : [], cost: 1

      3: evalspeedpldi41 -> evalspeedpldi42 : [], cost: 1

      4: evalspeedpldi42 -> evalspeedpldi4bb3in : [ 0>=A ], cost: 1

      5: evalspeedpldi42 -> evalspeedpldi4bb3in : [ A>=B ], cost: 1

      6: evalspeedpldi42 -> evalspeedpldi4bb1in : C'=B, [ A>=1 && B>=1+A ], cost: 1

      7: evalspeedpldi4bb1in -> evalspeedpldi4bb2in : [ C>=1 ], cost: 1

      8: evalspeedpldi4bb1in -> evalspeedpldi4bb3in : [ 0>=C ], cost: 1

      9: evalspeedpldi4bb2in -> evalspeedpldi4bb1in : C'=-1+C, [ A>=1+C ], cost: 1

     10: evalspeedpldi4bb2in -> evalspeedpldi4bb1in : C'=C-A, [ C>=A ], cost: 1

     11: evalspeedpldi4bb3in -> evalspeedpldi4stop : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalspeedpldi4start

      0: evalspeedpldi4start -> evalspeedpldi4bb0in : [], cost: 1

      1: evalspeedpldi4bb0in -> evalspeedpldi40 : [], cost: 1

      2: evalspeedpldi40 -> evalspeedpldi41 : [], cost: 1

      3: evalspeedpldi41 -> evalspeedpldi42 : [], cost: 1

      6: evalspeedpldi42 -> evalspeedpldi4bb1in : C'=B, [ A>=1 && B>=1+A ], cost: 1

      7: evalspeedpldi4bb1in -> evalspeedpldi4bb2in : [ C>=1 ], cost: 1

      9: evalspeedpldi4bb2in -> evalspeedpldi4bb1in : C'=-1+C, [ A>=1+C ], cost: 1

     10: evalspeedpldi4bb2in -> evalspeedpldi4bb1in : C'=C-A, [ C>=A ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalspeedpldi4start

     15: evalspeedpldi4start -> evalspeedpldi4bb1in : C'=B, [ A>=1 && B>=1+A ], cost: 5

      7: evalspeedpldi4bb1in -> evalspeedpldi4bb2in : [ C>=1 ], cost: 1

      9: evalspeedpldi4bb2in -> evalspeedpldi4bb1in : C'=-1+C, [ A>=1+C ], cost: 1

     10: evalspeedpldi4bb2in -> evalspeedpldi4bb1in : C'=C-A, [ C>=A ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalspeedpldi4start

     15: evalspeedpldi4start -> evalspeedpldi4bb1in : C'=B, [ A>=1 && B>=1+A ], cost: 5

     16: evalspeedpldi4bb1in -> evalspeedpldi4bb1in : C'=-1+C, [ C>=1 && A>=1+C ], cost: 2

     17: evalspeedpldi4bb1in -> evalspeedpldi4bb1in : C'=C-A, [ C>=1 && C>=A ], cost: 2



Accelerating simple loops of location 5.

   Accelerating the following rules:

     16: evalspeedpldi4bb1in -> evalspeedpldi4bb1in : C'=-1+C, [ C>=1 && A>=1+C ], cost: 2

     17: evalspeedpldi4bb1in -> evalspeedpldi4bb1in : C'=C-A, [ C>=1 && C>=A ], cost: 2



   Accelerated rule 16 with metering function C, yielding the new rule 18.

   Found no metering function for rule 17.

   Removing the simple loops: 16.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalspeedpldi4start

     15: evalspeedpldi4start -> evalspeedpldi4bb1in : C'=B, [ A>=1 && B>=1+A ], cost: 5

     17: evalspeedpldi4bb1in -> evalspeedpldi4bb1in : C'=C-A, [ C>=1 && C>=A ], cost: 2

     18: evalspeedpldi4bb1in -> evalspeedpldi4bb1in : C'=0, [ C>=1 && A>=1+C ], cost: 2*C



Chained accelerated rules (with incoming rules):

   Start location: evalspeedpldi4start

     15: evalspeedpldi4start -> evalspeedpldi4bb1in : C'=B, [ A>=1 && B>=1+A ], cost: 5

     19: evalspeedpldi4start -> evalspeedpldi4bb1in : C'=-A+B, [ A>=1 && B>=1+A && B>=1 ], cost: 7



Removed unreachable locations (and leaf rules with constant cost):

   Start location: evalspeedpldi4start



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalspeedpldi4start



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Unknown

   Cpx degree:  ?

   Solved cost: 0

   Rule cost:   0

   Rule guard:  []



WORST_CASE(Omega(0),?)


----------------------------------------

(4)
BOUNDS(1, INF)

----------------------------------------

(5) Koat2 Proof (FINISHED)
YES( ?, 2+max([5, 1+2*Arg_1])*max([0, Arg_0])+max([4, 2*Arg_1])+max([12, 8+2*Arg_1]) {O(n^2)})



Initial Complexity Problem:

  Start:  evalspeedpldi4start  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  evalspeedpldi40, evalspeedpldi41, evalspeedpldi42, evalspeedpldi4bb0in, evalspeedpldi4bb1in, evalspeedpldi4bb2in, evalspeedpldi4bb3in, evalspeedpldi4start, evalspeedpldi4stop  

  Transitions:

  evalspeedpldi40(Arg_0,Arg_1,Arg_2) -> evalspeedpldi41(Arg_0,Arg_1,Arg_2):|:

  evalspeedpldi41(Arg_0,Arg_1,Arg_2) -> evalspeedpldi42(Arg_0,Arg_1,Arg_2):|:

  evalspeedpldi42(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb1in(Arg_0,Arg_1,Arg_1):|:1 <= Arg_0 && Arg_0+1 <= Arg_1

  evalspeedpldi42(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb3in(Arg_0,Arg_1,Arg_2):|:Arg_0 <= 0

  evalspeedpldi42(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb3in(Arg_0,Arg_1,Arg_2):|:Arg_1 <= Arg_0

  evalspeedpldi4bb0in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi40(Arg_0,Arg_1,Arg_2):|:

  evalspeedpldi4bb1in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb2in(Arg_0,Arg_1,Arg_2):|:Arg_2 <= Arg_1 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 && 1 <= Arg_2

  evalspeedpldi4bb1in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb3in(Arg_0,Arg_1,Arg_2):|:Arg_2 <= Arg_1 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_2 <= 0

  evalspeedpldi4bb2in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb1in(Arg_0,Arg_1,Arg_2-1):|:Arg_2 <= Arg_1 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_2+1 <= Arg_0

  evalspeedpldi4bb2in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb1in(Arg_0,Arg_1,Arg_2-Arg_0):|:Arg_2 <= Arg_1 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_0 <= Arg_2

  evalspeedpldi4bb3in(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4stop(Arg_0,Arg_1,Arg_2):|:

  evalspeedpldi4start(Arg_0,Arg_1,Arg_2) -> evalspeedpldi4bb0in(Arg_0,Arg_1,Arg_2):|:  



Timebounds: 

  Overall timebound: 2+max([5, 1+2*Arg_1])*max([0, Arg_0])+max([4, 2*Arg_1])+max([12, 8+2*Arg_1]) {O(n^2)}

  2: evalspeedpldi40->evalspeedpldi41: 1 {O(1)}

  3: evalspeedpldi41->evalspeedpldi42: 1 {O(1)}

  4: evalspeedpldi42->evalspeedpldi4bb3in: 1 {O(1)}

  5: evalspeedpldi42->evalspeedpldi4bb3in: 1 {O(1)}

  6: evalspeedpldi42->evalspeedpldi4bb1in: 1 {O(1)}

  1: evalspeedpldi4bb0in->evalspeedpldi40: 1 {O(1)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in: max([5, 1+2*Arg_1]) {O(n)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in: 1 {O(1)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in: max([5, 1+2*Arg_1])*max([0, Arg_0]) {O(n^2)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in: max([4, 2*Arg_1]) {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop: 1 {O(1)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in: 1 {O(1)}



Costbounds:

  Overall costbound: 2+max([5, 1+2*Arg_1])*max([0, Arg_0])+max([4, 2*Arg_1])+max([12, 8+2*Arg_1]) {O(n^2)}

  2: evalspeedpldi40->evalspeedpldi41: 1 {O(1)}

  3: evalspeedpldi41->evalspeedpldi42: 1 {O(1)}

  4: evalspeedpldi42->evalspeedpldi4bb3in: 1 {O(1)}

  5: evalspeedpldi42->evalspeedpldi4bb3in: 1 {O(1)}

  6: evalspeedpldi42->evalspeedpldi4bb1in: 1 {O(1)}

  1: evalspeedpldi4bb0in->evalspeedpldi40: 1 {O(1)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in: max([5, 1+2*Arg_1]) {O(n)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in: 1 {O(1)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in: max([5, 1+2*Arg_1])*max([0, Arg_0]) {O(n^2)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in: max([4, 2*Arg_1]) {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop: 1 {O(1)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in: 1 {O(1)}



Sizebounds:

`Lower:

  2: evalspeedpldi40->evalspeedpldi41, Arg_0: Arg_0 {O(n)}

  2: evalspeedpldi40->evalspeedpldi41, Arg_1: Arg_1 {O(n)}

  2: evalspeedpldi40->evalspeedpldi41, Arg_2: Arg_2 {O(n)}

  3: evalspeedpldi41->evalspeedpldi42, Arg_0: Arg_0 {O(n)}

  3: evalspeedpldi41->evalspeedpldi42, Arg_1: Arg_1 {O(n)}

  3: evalspeedpldi41->evalspeedpldi42, Arg_2: Arg_2 {O(n)}

  4: evalspeedpldi42->evalspeedpldi4bb3in, Arg_0: Arg_0 {O(n)}

  4: evalspeedpldi42->evalspeedpldi4bb3in, Arg_1: Arg_1 {O(n)}

  4: evalspeedpldi42->evalspeedpldi4bb3in, Arg_2: Arg_2 {O(n)}

  5: evalspeedpldi42->evalspeedpldi4bb3in, Arg_0: Arg_0 {O(n)}

  5: evalspeedpldi42->evalspeedpldi4bb3in, Arg_1: Arg_1 {O(n)}

  5: evalspeedpldi42->evalspeedpldi4bb3in, Arg_2: Arg_2 {O(n)}

  6: evalspeedpldi42->evalspeedpldi4bb1in, Arg_0: 1 {O(1)}

  6: evalspeedpldi42->evalspeedpldi4bb1in, Arg_1: 2 {O(1)}

  6: evalspeedpldi42->evalspeedpldi4bb1in, Arg_2: 2 {O(1)}

  1: evalspeedpldi4bb0in->evalspeedpldi40, Arg_0: Arg_0 {O(n)}

  1: evalspeedpldi4bb0in->evalspeedpldi40, Arg_1: Arg_1 {O(n)}

  1: evalspeedpldi4bb0in->evalspeedpldi40, Arg_2: Arg_2 {O(n)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in, Arg_0: 1 {O(1)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in, Arg_1: 2 {O(1)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in, Arg_2: 1 {O(1)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in, Arg_0: 1 {O(1)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in, Arg_1: 2 {O(1)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in, Arg_2: 0 {O(1)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_0: 1 {O(1)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_1: 2 {O(1)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_2: 0 {O(1)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_0: 1 {O(1)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_1: 2 {O(1)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_2: 0 {O(1)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop, Arg_0: min([1, Arg_0]) {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop, Arg_1: min([2, Arg_1]) {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop, Arg_2: min([0, Arg_2]) {O(n)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in, Arg_0: Arg_0 {O(n)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in, Arg_1: Arg_1 {O(n)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in, Arg_2: Arg_2 {O(n)}

`Upper:

  2: evalspeedpldi40->evalspeedpldi41, Arg_0: Arg_0 {O(n)}

  2: evalspeedpldi40->evalspeedpldi41, Arg_1: Arg_1 {O(n)}

  2: evalspeedpldi40->evalspeedpldi41, Arg_2: Arg_2 {O(n)}

  3: evalspeedpldi41->evalspeedpldi42, Arg_0: Arg_0 {O(n)}

  3: evalspeedpldi41->evalspeedpldi42, Arg_1: Arg_1 {O(n)}

  3: evalspeedpldi41->evalspeedpldi42, Arg_2: Arg_2 {O(n)}

  4: evalspeedpldi42->evalspeedpldi4bb3in, Arg_0: 0 {O(1)}

  4: evalspeedpldi42->evalspeedpldi4bb3in, Arg_1: Arg_1 {O(n)}

  4: evalspeedpldi42->evalspeedpldi4bb3in, Arg_2: Arg_2 {O(n)}

  5: evalspeedpldi42->evalspeedpldi4bb3in, Arg_0: Arg_0 {O(n)}

  5: evalspeedpldi42->evalspeedpldi4bb3in, Arg_1: Arg_1 {O(n)}

  5: evalspeedpldi42->evalspeedpldi4bb3in, Arg_2: Arg_2 {O(n)}

  6: evalspeedpldi42->evalspeedpldi4bb1in, Arg_0: Arg_0 {O(n)}

  6: evalspeedpldi42->evalspeedpldi4bb1in, Arg_1: Arg_1 {O(n)}

  6: evalspeedpldi42->evalspeedpldi4bb1in, Arg_2: Arg_1 {O(n)}

  1: evalspeedpldi4bb0in->evalspeedpldi40, Arg_0: Arg_0 {O(n)}

  1: evalspeedpldi4bb0in->evalspeedpldi40, Arg_1: Arg_1 {O(n)}

  1: evalspeedpldi4bb0in->evalspeedpldi40, Arg_2: Arg_2 {O(n)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in, Arg_0: Arg_0 {O(n)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in, Arg_1: Arg_1 {O(n)}

  7: evalspeedpldi4bb1in->evalspeedpldi4bb2in, Arg_2: Arg_1 {O(n)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in, Arg_0: Arg_0 {O(n)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in, Arg_1: Arg_1 {O(n)}

  8: evalspeedpldi4bb1in->evalspeedpldi4bb3in, Arg_2: 0 {O(1)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_0: Arg_0 {O(n)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_1: Arg_1 {O(n)}

  9: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_2: Arg_1 {O(n)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_0: Arg_0 {O(n)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_1: Arg_1 {O(n)}

  10: evalspeedpldi4bb2in->evalspeedpldi4bb1in, Arg_2: Arg_1 {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop, Arg_0: max([0, Arg_0]) {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop, Arg_1: Arg_1 {O(n)}

  11: evalspeedpldi4bb3in->evalspeedpldi4stop, Arg_2: max([0, Arg_2]) {O(n)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in, Arg_0: Arg_0 {O(n)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in, Arg_1: Arg_1 {O(n)}

  0: evalspeedpldi4start->evalspeedpldi4bb0in, Arg_2: Arg_2 {O(n)}


----------------------------------------

(6)
BOUNDS(1, 2 + max(5, 1 + 2 * Arg_1) * nat(Arg_0) + max(2 * Arg_1, 4) + max(12, 8 + 2 * Arg_1))