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


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WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox/output/output_files/bench.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 179 ms]
(2) BOUNDS(1, n^1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_gcd_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
eval_gcd_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > 0 && v_.01 > 0
eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 <= 0
eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 <= 0
eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0 - v_.01, v_.01, v_x, v_y)) :|: v_.0 > v_.01
eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > v_.01 && v_.0 <= v_.01
eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0 - v_.01, v_.01 - v_.0, v_x, v_y)) :|: v_.0 <= v_.01 && v_.0 > v_.01
eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0, v_.01 - v_.0, v_x, v_y)) :|: v_.0 <= v_.01
eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE

The start-symbols are:[eval_gcd_start_4]


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(1) Koat Proof (FINISHED)
YES(?, 6*Ar_1 + 6*Ar_3 + 8)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalgcdstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_1, Ar_1, Ar_3, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_2 >= Ar_0 /\ Ar_0 >= Ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3))

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

	start location:	koat_start

	leaf cost:	0



Testing for reachability in the complexity graph removes the following transitions from problem 1:

	evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= Ar_0 ]

	evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_2 >= Ar_0 /\ Ar_0 >= Ar_2 + 1 ]

We thus obtain the following problem:

2:	T:

		(Comp: ?, Cost: 1)    evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_1, Ar_1, Ar_3, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3))

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

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 2 produces the following problem:

3:	T:

		(Comp: ?, Cost: 1)    evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= 1 ]

		(Comp: 1, Cost: 1)    evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_1, Ar_1, Ar_3, Ar_3))

		(Comp: 1, Cost: 1)    evalgcdstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3))

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

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalgcdbb3in) = 1

	Pol(evalgcdstop) = 0

	Pol(evalgcdbb2in) = 2

	Pol(evalgcdbb1in) = 2

	Pol(evalgcdbb0in) = 2

	Pol(evalgcdstart) = 2

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3))

	evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]

	evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

strictly and produces the following problem:

4:	T:

		(Comp: 2, Cost: 1)    evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]

		(Comp: 2, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]

		(Comp: 2, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= 1 ]

		(Comp: 1, Cost: 1)    evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_1, Ar_1, Ar_3, Ar_3))

		(Comp: 1, Cost: 1)    evalgcdstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3))

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

	start location:	koat_start

	leaf cost:	0



Applied AI with 'oct' on problem 4 to obtain the following invariants:

  For symbol evalgcdbb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0

  For symbol evalgcdbb2in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0

  For symbol evalgcdbb3in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0





This yielded the following problem:

5:	T:

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

		(Comp: 1, Cost: 1)    evalgcdstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 1)    evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_1, Ar_1, Ar_3, Ar_3))

		(Comp: ?, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_2 >= 1 ]

		(Comp: 2, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 ]

		(Comp: 2, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ]

		(Comp: 2, Cost: 1)    evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

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

	Pol(evalgcdstart) = 2*V_2 + 2*V_4

	Pol(evalgcdbb0in) = 2*V_2 + 2*V_4

	Pol(evalgcdbb1in) = 2*V_1 + 2*V_3

	Pol(evalgcdbb2in) = 2*V_1 + 2*V_3 - 1

	Pol(evalgcdbb3in) = 2*V_1 + 2*V_3

	Pol(evalgcdstop) = 2*V_1 + 2*V_3

orients all transitions weakly and the transitions

	evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ]

	evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ]

	evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_2 >= 1 ]

strictly and produces the following problem:

6:	T:

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

		(Comp: 1, Cost: 1)                  evalgcdstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 1)                  evalgcdbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_1, Ar_1, Ar_3, Ar_3))

		(Comp: 2*Ar_1 + 2*Ar_3, Cost: 1)    evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_2 >= 1 ]

		(Comp: 2, Cost: 1)                  evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 ]

		(Comp: 2, Cost: 1)                  evalgcdbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 ]

		(Comp: 2*Ar_1 + 2*Ar_3, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0 - Ar_2, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ]

		(Comp: 2*Ar_1 + 2*Ar_3, Cost: 1)    evalgcdbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdbb1in(Ar_0, Ar_1, Ar_2 - Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ]

		(Comp: 2, Cost: 1)                  evalgcdbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalgcdstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 6*Ar_1 + 6*Ar_3 + 8



Time: 0.195 sec (SMT: 0.165 sec)


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(2)
BOUNDS(1, n^1)