LTS Termination Proof

by T2Cert

Input

• Initial Location: 8
• Transitions: (pre-variables and post-variables)

  0	0	1:		− tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  2	1	3:		− i2_0 + size1_0 ≤ 0 ∧ − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  2	2	4:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i2_0 − size1_0 ≤ 0 ∧ −1 − i2_0 + i2_post ≤ 0 ∧ 1 + i2_0 − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0
  5	3	6:		− tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  6	4	4:		0 ≤ 0 ∧ 0 ≤ 0 ∧ − i2_0 + size1_0 ≤ 0 ∧ i2_post ≤ 0 ∧ − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0
  6	5	5:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i2_0 − size1_0 ≤ 0 ∧ −1 − i2_0 + i2_post ≤ 0 ∧ 1 + i2_0 − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0
  4	6	2:		− tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  1	7	5:		0 ≤ 0 ∧ 0 ≤ 0 ∧ − i2_0 + size1_0 ≤ 0 ∧ i2_post ≤ 0 ∧ − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0
  1	8	0:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i2_0 − size1_0 ≤ 0 ∧ −1 − i2_0 + i2_post ≤ 0 ∧ 1 + i2_0 − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0
  7	9	0:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ − size1_post + size77_post ≤ 0 ∧ size1_post − size77_post ≤ 0 ∧ size1010_post − size1_post ≤ 0 ∧ − size1010_post + size1_post ≤ 0 ∧ i2_post ≤ 0 ∧ − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ size1010_0 − size1010_post ≤ 0 ∧ − size1010_0 + size1010_post ≤ 0 ∧ size1_0 − size1_post ≤ 0 ∧ − size1_0 + size1_post ≤ 0 ∧ size77_0 − size77_post ≤ 0 ∧ − size77_0 + size77_post ≤ 0 ∧ tmp1111_0 − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_post ≤ 0 ∧ tmp88_0 − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_post ≤ 0
  8	10	7:		− tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

The invariants are proved as follows.

IMPACT Invariant Proof

• nodes (location) invariant:

  0		(0)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ −10 + size1_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  1		(1)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ −10 + size1_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  2		(2)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  3		(3)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  4		(4)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  5		(5)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  6		(6)		−10 + size1010_post ≤ 0 ∧ −10 + size1_post ≤ 0 ∧ 10 − size1_post ≤ 0 ∧ −10 + size77_post ≤ 0 ∧ −10 + size1010_0 ≤ 0 ∧ 10 − size1_0 ≤ 0 ∧ −10 + size77_0 ≤ 0
  7		(7)		TRUE
  8		(8)		TRUE

• initial node: 8
• cover edges:
• transition edges:

  0	0 1
  1	7 5
  1	8 0
  2	1 3
  2	2 4
  4	6 2
  5	3 6
  6	4 4
  6	5 5
  7	9 0
  8	10 7

2 Switch to Cooperation Termination Proof

3 Transition Removal

We remove transitions 1, 4, 7, 9, 10 using the following ranking functions, which are bounded by −21.

4 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

0* 14 0: − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

5 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

0 12 0_var_snapshot: − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

6 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

4* 21 4: − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

7 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

4 19 4_var_snapshot: − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

8 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

5* 28 5: − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

9 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

5 26 5_var_snapshot: − tmp88_post + tmp88_post ≤ 0 ∧ tmp88_post − tmp88_post ≤ 0 ∧ − tmp88_0 + tmp88_0 ≤ 0 ∧ tmp88_0 − tmp88_0 ≤ 0 ∧ − tmp1111_post + tmp1111_post ≤ 0 ∧ tmp1111_post − tmp1111_post ≤ 0 ∧ − tmp1111_0 + tmp1111_0 ≤ 0 ∧ tmp1111_0 − tmp1111_0 ≤ 0 ∧ − size77_post + size77_post ≤ 0 ∧ size77_post − size77_post ≤ 0 ∧ − size77_0 + size77_0 ≤ 0 ∧ size77_0 − size77_0 ≤ 0 ∧ − size1_post + size1_post ≤ 0 ∧ size1_post − size1_post ≤ 0 ∧ − size1_0 + size1_0 ≤ 0 ∧ size1_0 − size1_0 ≤ 0 ∧ − size1010_post + size1010_post ≤ 0 ∧ size1010_post − size1010_post ≤ 0 ∧ − size1010_0 + size1010_0 ≤ 0 ∧ size1010_0 − size1010_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

10 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

10.1 SCC Subproblem 1/3

Here we consider the SCC { 2, 4, 4_var_snapshot, 4* }.

10.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 2.

10.1.2 Transition Removal

We remove transitions 19, 21, 6 using the following ranking functions, which are bounded by −11.

10.1.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

10.1.3.1 Cut-Point Subproblem 1/1

10.1.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

10.2 SCC Subproblem 2/3

Here we consider the SCC { 5, 6, 5_var_snapshot, 5* }.

10.2.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by 0.

10.2.2 Transition Removal

We remove transitions 26, 28, 3 using the following ranking functions, which are bounded by −1.

10.2.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

10.2.3.1 Cut-Point Subproblem 1/1

10.2.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

10.3 SCC Subproblem 3/3

Here we consider the SCC { 0, 1, 0_var_snapshot, 0* }.

10.3.1 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by −280.

10.3.2 Transition Removal

We remove transitions 12, 14, 0 using the following ranking functions, which are bounded by −11.

10.3.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

10.3.3.1 Cut-Point Subproblem 1/1

10.3.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

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