/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 192 ms]
(2) BOUNDS(1, n^1)


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

(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_bb3_in(v_i.0, v_m, v_n)) :|: v_m <= 0
eval_speedpldi4_bb0_in(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_bb0_in(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]


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

(1) Koat Proof (FINISHED)
YES(?, 6*ar_1 + 8)



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

		(Comp: ?, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: ?, Cost: 1)    evalspeedpldi4bb0in(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(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(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(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(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(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)    evalspeedpldi4bb0in(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)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

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

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-0) = ar_0

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-1) = ar_1

	S("evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-2) = ar_2

	S("evalspeedpldi4bb0in(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("evalspeedpldi4bb0in(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("evalspeedpldi4bb0in(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)         evalspeedpldi4bb0in(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)         evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)         evalspeedpldi4bb0in(ar_0, ar_1, ar_2) -> Com_1(evalspeedpldi4bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]

		(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 + 8



Time: 0.211 sec (SMT: 0.190 sec)


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

(2)
BOUNDS(1, n^1)