/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(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 336 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 871 ms]
(4) BOUNDS(n^1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_start_start(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb0_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_bb0_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_0(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_0(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_1(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_1(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_2(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_2(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_3(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_3(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_4(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_4(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_5(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_5(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb1_in(v_n, v_y, v__1, v_1, v_n, v_y)) :|: TRUE
eval_start_bb1_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb2_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: v__0 < 0
eval_start_bb1_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb5_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: v__0 >= 0
eval_start_bb2_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__01 + 1000, v__0 + 1, v_n, v_y)) :|: TRUE
eval_start_bb3_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb4_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: v__1 >= 100
eval_start_bb3_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb1_in(v_1, v__1, v__1, v_1, v_n, v_y)) :|: v__1 < 100
eval_start_bb4_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__1 - 100, v_1, v_n, v_y)) :|: TRUE
eval_start_bb5_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_stop(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE

The start-symbols are:[eval_start_start_6]


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

(1) Koat Proof (FINISHED)
YES(?, 4003*Ar_1 + 4*Ar_3 + 12)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

		(Comp: ?, Cost: 1)    evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

		(Comp: ?, Cost: 1)    evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalstartstart) = 2

	Pol(evalstartbb0in) = 2

	Pol(evalstart0) = 2

	Pol(evalstart1) = 2

	Pol(evalstart2) = 2

	Pol(evalstart3) = 2

	Pol(evalstart4) = 2

	Pol(evalstart5) = 2

	Pol(evalstartbb1in) = 2

	Pol(evalstartbb2in) = 2

	Pol(evalstartbb5in) = 1

	Pol(evalstartbb3in) = 2

	Pol(evalstartbb4in) = 2

	Pol(evalstartstop) = 0

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

	evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

strictly and produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

		(Comp: 2, Cost: 1)    evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalstartstart) = -V_2

	Pol(evalstartbb0in) = -V_2

	Pol(evalstart0) = -V_2

	Pol(evalstart1) = -V_2

	Pol(evalstart2) = -V_2

	Pol(evalstart3) = -V_2

	Pol(evalstart4) = -V_2

	Pol(evalstart5) = -V_2

	Pol(evalstartbb1in) = -V_1

	Pol(evalstartbb2in) = -V_1 - 1

	Pol(evalstartbb5in) = -V_1

	Pol(evalstartbb3in) = -V_6

	Pol(evalstartbb4in) = -V_6

	Pol(evalstartstop) = -V_1

	Pol(koat_start) = -V_2

orients all transitions weakly and the transition

	evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

strictly and produces the following problem:

4:	T:

		(Comp: 1, Cost: 1)       evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: Ar_1, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)       evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)       evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))

		(Comp: ?, Cost: 1)       evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

		(Comp: ?, Cost: 1)       evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)       evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

		(Comp: 2, Cost: 1)       evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 4 produces the following problem:

5:	T:

		(Comp: 1, Cost: 1)       evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: Ar_1, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)       evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

		(Comp: Ar_1, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))

		(Comp: ?, Cost: 1)       evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

		(Comp: ?, Cost: 1)       evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)       evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

		(Comp: 2, Cost: 1)       evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalstartbb4in) = 1

	Pol(evalstartbb3in) = 1

	Pol(evalstartbb1in) = 0

and size complexities

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5

	S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = 2*Ar_1

	S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ?

	S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ?

	S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = 2*Ar_1 + 2*Ar_5

	S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-0) = 2*Ar_1

	S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-1) = Ar_1

	S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-2) = ?

	S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-3) = Ar_3

	S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-4) = ?

	S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-5) = 2*Ar_1

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-0) = 2*Ar_1

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-1) = Ar_1

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-2) = ?

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-3) = Ar_3

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-4) = ?

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-5) = 2*Ar_1

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-0) = 2*Ar_1

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-1) = Ar_1

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-2) = ?

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-3) = Ar_3

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-4) = ?

	S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-5) = 2*Ar_1

	S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-0) = 2*Ar_1

	S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-1) = Ar_1

	S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-2) = ?

	S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-3) = Ar_3

	S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-4) = ?

	S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-5) = 2*Ar_1

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-0) = 2*Ar_1

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-1) = Ar_1

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-2) = ?

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-3) = Ar_3

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-4) = ?

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-5) = 2*Ar_1 + 2*Ar_5

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-2) = ?

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-4) = ?

	S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-5) = 2*Ar_1 + 2*Ar_5

	S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1

	S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3

	S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

	S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0

	S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1

	S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2

	S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3

	S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4

	S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5

orients the transitions

	evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

	evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

	evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

weakly and the transition

	evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

strictly and produces the following problem:

6:	T:

		(Comp: 1, Cost: 1)       evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: Ar_1, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)       evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]

		(Comp: Ar_1, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))

		(Comp: ?, Cost: 1)       evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]

		(Comp: Ar_1, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)       evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))

		(Comp: 2, Cost: 1)       evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Applied AI with 'oct' on problem 6 to obtain the following invariants:

  For symbol evalstartbb1in: X_1 - X_2 >= 0

  For symbol evalstartbb2in: -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0

  For symbol evalstartbb3in: -X_6 >= 0 /\ -X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 + 1 >= 0 /\ -X_1 - X_6 - 1 >= 0 /\ -X_2 + X_6 - 1 >= 0 /\ -X_1 + X_6 - 1 >= 0 /\ X_3 - X_5 + 1000 >= 0 /\ -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0

  For symbol evalstartbb4in: -X_6 >= 0 /\ X_5 - X_6 - 100 >= 0 /\ X_3 - X_6 + 900 >= 0 /\ -X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 + 1 >= 0 /\ -X_1 - X_6 - 1 >= 0 /\ -X_2 + X_6 - 1 >= 0 /\ -X_1 + X_6 - 1 >= 0 /\ X_3 - X_5 + 1000 >= 0 /\ X_5 - 100 >= 0 /\ X_3 + X_5 + 800 >= 0 /\ -X_2 + X_5 - 101 >= 0 /\ -X_1 + X_5 - 101 >= 0 /\ X_3 + 900 >= 0 /\ -X_2 + X_3 + 899 >= 0 /\ -X_1 + X_3 + 899 >= 0 /\ -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0

  For symbol evalstartbb5in: X_1 - X_2 >= 0 /\ X_1 >= 0





This yielded the following problem:

7:	T:

		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)       evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)       evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) [ -Ar_5 >= 0 /\ Ar_4 - Ar_5 - 100 >= 0 /\ Ar_2 - Ar_5 + 900 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ Ar_4 - 100 >= 0 /\ Ar_2 + Ar_4 + 800 >= 0 /\ -Ar_1 + Ar_4 - 101 >= 0 /\ -Ar_0 + Ar_4 - 101 >= 0 /\ Ar_2 + 900 >= 0 /\ -Ar_1 + Ar_2 + 899 >= 0 /\ -Ar_0 + Ar_2 + 899 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ]

		(Comp: Ar_1, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ 99 >= Ar_4 ]

		(Comp: ?, Cost: 1)       evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ Ar_4 >= 100 ]

		(Comp: Ar_1, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) [ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ]

		(Comp: 2, Cost: 1)       evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: Ar_1, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)       evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)       evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = -2000*V_2 + 2*V_4

	Pol(evalstartstart) = -2000*V_2 + 2*V_4

	Pol(evalstartbb5in) = -2000*V_1 + 2*V_3

	Pol(evalstartstop) = -2000*V_1 + 2*V_3

	Pol(evalstartbb4in) = 2*V_5 - 2000*V_6 - 100

	Pol(evalstartbb3in) = 2*V_5 - 2000*V_6

	Pol(evalstartbb1in) = -2000*V_1 + 2*V_3

	Pol(evalstartbb2in) = -2000*V_1 + 2*V_3

	Pol(evalstart5) = -2000*V_2 + 2*V_4

	Pol(evalstart4) = -2000*V_2 + 2*V_4

	Pol(evalstart3) = -2000*V_2 + 2*V_4

	Pol(evalstart2) = -2000*V_2 + 2*V_4

	Pol(evalstart1) = -2000*V_2 + 2*V_4

	Pol(evalstart0) = -2000*V_2 + 2*V_4

	Pol(evalstartbb0in) = -2000*V_2 + 2*V_4

orients all transitions weakly and the transitions

	evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) [ -Ar_5 >= 0 /\ Ar_4 - Ar_5 - 100 >= 0 /\ Ar_2 - Ar_5 + 900 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ Ar_4 - 100 >= 0 /\ Ar_2 + Ar_4 + 800 >= 0 /\ -Ar_1 + Ar_4 - 101 >= 0 /\ -Ar_0 + Ar_4 - 101 >= 0 /\ Ar_2 + 900 >= 0 /\ -Ar_1 + Ar_2 + 899 >= 0 /\ -Ar_0 + Ar_2 + 899 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ]

	evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ Ar_4 >= 100 ]

strictly and produces the following problem:

8:	T:

		(Comp: 1, Cost: 0)                     koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)                     evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: 2000*Ar_1 + 2*Ar_3, Cost: 1)    evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) [ -Ar_5 >= 0 /\ Ar_4 - Ar_5 - 100 >= 0 /\ Ar_2 - Ar_5 + 900 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ Ar_4 - 100 >= 0 /\ Ar_2 + Ar_4 + 800 >= 0 /\ -Ar_1 + Ar_4 - 101 >= 0 /\ -Ar_0 + Ar_4 - 101 >= 0 /\ Ar_2 + 900 >= 0 /\ -Ar_1 + Ar_2 + 899 >= 0 /\ -Ar_0 + Ar_2 + 899 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ]

		(Comp: Ar_1, Cost: 1)                  evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ 99 >= Ar_4 ]

		(Comp: 2000*Ar_1 + 2*Ar_3, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ Ar_4 >= 100 ]

		(Comp: Ar_1, Cost: 1)                  evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) [ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ]

		(Comp: 2, Cost: 1)                     evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: Ar_1, Cost: 1)                  evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)                     evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

		(Comp: 1, Cost: 1)                     evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 4003*Ar_1 + 4*Ar_3 + 12



Time: 0.403 sec (SMT: 0.281 sec)


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

(2)
BOUNDS(1, n^1)

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstart4 : [], cost: 1

      6: evalstart4 -> evalstart5 : [], cost: 1

      7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1

      8: evalstartbb1in -> evalstartbb2in : [ 0>=1+A ], cost: 1

      9: evalstartbb1in -> evalstartbb5in : [ A>=0 ], cost: 1

     10: evalstartbb2in -> evalstartbb3in : E'=1000+C, F'=1+A, [], cost: 1

     11: evalstartbb3in -> evalstartbb4in : [ E>=100 ], cost: 1

     12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1

     13: evalstartbb4in -> evalstartbb3in : E'=-100+E, [], cost: 1

     14: evalstartbb5in -> evalstartstop : [], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

      0: evalstartstart -> evalstartbb0in : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstart4 : [], cost: 1

      6: evalstart4 -> evalstart5 : [], cost: 1

      7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1

      8: evalstartbb1in -> evalstartbb2in : [ 0>=1+A ], cost: 1

     10: evalstartbb2in -> evalstartbb3in : E'=1000+C, F'=1+A, [], cost: 1

     11: evalstartbb3in -> evalstartbb4in : [ E>=100 ], cost: 1

     12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1

     13: evalstartbb4in -> evalstartbb3in : E'=-100+E, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     22: evalstartbb1in -> evalstartbb3in : E'=1000+C, F'=1+A, [ 0>=1+A ], cost: 2

     12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1

     23: evalstartbb3in -> evalstartbb3in : E'=-100+E, [ E>=100 ], cost: 2



Accelerating simple loops of location 10.

   Accelerating the following rules:

     23: evalstartbb3in -> evalstartbb3in : E'=-100+E, [ E>=100 ], cost: 2



   Accelerated rule 23 with metering function meter (where 100*meter==-99+E), yielding the new rule 24.

   Removing the simple loops: 23.



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

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     22: evalstartbb1in -> evalstartbb3in : E'=1000+C, F'=1+A, [ 0>=1+A ], cost: 2

     12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1

     24: evalstartbb3in -> evalstartbb3in : E'=-100*meter+E, [ E>=100 && 100*meter==-99+E && meter>=1 ], cost: 2*meter



Chained accelerated rules (with incoming rules):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     22: evalstartbb1in -> evalstartbb3in : E'=1000+C, F'=1+A, [ 0>=1+A ], cost: 2

     25: evalstartbb1in -> evalstartbb3in : E'=1000+C-100*meter, F'=1+A, [ 0>=1+A && 1000+C>=100 && 100*meter==901+C && meter>=1 ], cost: 2+2*meter

     12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     26: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C, E'=1000+C, F'=1+A, [ 0>=1+A && 99>=1000+C ], cost: 3

     27: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C-100*meter, E'=1000+C-100*meter, F'=1+A, [ 0>=1+A && 1000+C>=100 && 100*meter==901+C && meter>=1 ], cost: 3+2*meter



Accelerating simple loops of location 8.

   Accelerating the following rules:

     26: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C, E'=1000+C, F'=1+A, [ 0>=1+A && 99>=1000+C ], cost: 3

     27: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C-100*meter, E'=1000+C-100*meter, F'=1+A, [ 0>=1+A && 1000+C>=100 && 100*meter==901+C && meter>=1 ], cost: 3+2*meter



   Accelerated rule 26 with metering function meter_1 (where 1000*meter_1==-900-C) (after adding A<=C), yielding the new rule 28.

      During metering: Instantiating temporary variables by {meter==1}

   Accelerated rule 27 with metering function meter_2 (where 900*meter_2==-801-C), yielding the new rule 29.

   Removing the simple loops: 27.



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

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     26: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C, E'=1000+C, F'=1+A, [ 0>=1+A && 99>=1000+C ], cost: 3

     28: evalstartbb1in -> evalstartbb1in : A'=A+meter_1, C'=C+1000*meter_1, E'=C+1000*meter_1, F'=A+meter_1, [ 0>=1+A && 99>=1000+C && A<=C && 1000*meter_1==-900-C && meter_1>=1 ], cost: 3*meter_1

     29: evalstartbb1in -> evalstartbb1in : A'=A+meter_2, C'=C+900*meter_2, E'=C+900*meter_2, F'=A+meter_2, [ 0>=1+A && 100==901+C && 900*meter_2==-801-C && meter_2>=1 ], cost: 5*meter_2



Chained accelerated rules (with incoming rules):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     30: evalstartstart -> evalstartbb1in : A'=1+B, C'=1000+D, E'=1000+D, F'=1+B, [ 0>=1+B && 99>=1000+D ], cost: 11

     31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 0>=1+B && 99>=1000+D && B<=D && 1000*meter_1==-900-D && meter_1>=1 ], cost: 8+3*meter_1



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

   Start location: evalstartstart

     31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 0>=1+B && 99>=1000+D && B<=D && 1000*meter_1==-900-D && meter_1>=1 ], cost: 8+3*meter_1



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalstartstart

     31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 0>=1+B && 99>=1000+D && B<=D && 1000*meter_1==-900-D && meter_1>=1 ], cost: 8+3*meter_1



Computing asymptotic complexity for rule 31

   Simplified the guard:

     31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 99>=1000+D && B<=D && 1000*meter_1==-900-D ], cost: 8+3*meter_1

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      8+3*meter_1 (+), -899-D-1000*meter_1 (+/+!), 1+D-B (+/+!), 901+D+1000*meter_1 (+/+!), -900-D (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {D==100-1000*n,meter_1==-1+n,B==100-1000*n}

      resulting limit problem:

      [solved]



   Solution:

      D / 100-1000*n

      meter_1 / -1+n

      B / 100-1000*n

   Resulting cost 5+3*n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



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

   Complexity:  Poly(n^1)

   Cpx degree:  1

   Solved cost: 5+3*n

   Rule cost:   8+3*meter_1

   Rule guard:  [ 99>=1000+D && B<=D && 1000*meter_1==-900-D ]



WORST_CASE(Omega(n^1),?)


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

(4)
BOUNDS(n^1, INF)