LTS Termination Proof

by T2Cert

Input

• Initial Location: 5
• Transitions: (pre-variables and post-variables)

  0	0	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x4 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ −1 + arg1P − arg1 ≤ 0 ∧ −1 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 2 − arg2P ≤ 0 ∧ −2 − arg3P + x4 ≤ 0 ∧ 2 + arg3P − x4 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0
  1	1	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ −2 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  1	2	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg3 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 2 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  1	3	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg3 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  1	4	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg3 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  1	5	3:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg3 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  2	6	4:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg1 + arg3P ≤ 0 ∧ 1 − arg2 + arg4P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  4	7	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ arg2P − arg4 ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  4	8	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −3 + arg1P − arg1 ≤ 0 ∧ −2 + arg1P − arg2 ≤ 0 ∧ −2 + arg1P − arg3 ≤ 0 ∧ −3 + arg1P − arg4 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 + arg2P − arg3 ≤ 0 ∧ arg2P − arg4 ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  3	9	3:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
  3	10	4:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − x66 ≤ 0 ∧ − x65 ≤ 0 ∧ 1 − x65 + x66 ≤ 0 ∧ −2 − arg1 + arg3P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 3 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  3	11	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x73 ≤ 0 ∧ 1 − x73 + x74 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0
  5	12	0:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

The invariants are proved as follows.

IMPACT Invariant Proof

• nodes (location) invariant:

  0		(0)		TRUE
  1		(1)		− arg1P ≤ 0 ∧ 2 − arg2P ≤ 0 ∧ − arg1 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − x4 ≤ 0
  2		(2)		2 − arg1P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − x4 ≤ 0
  3		(3)		2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x4 ≤ 0
  4		(4)		− arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ − x4 ≤ 0
  5		(5)		TRUE

• initial node: 5
• cover edges:
• transition edges:

  0	0 1
  1	1 1
  1	2 2
  1	3 2
  1	4 2
  1	5 3
  2	6 4
  3	9 3
  3	10 4
  3	11 2
  4	7 2
  4	8 2
  5	12 0

2 Switch to Cooperation Termination Proof

3 Transition Removal

We remove transitions 0, 2, 3, 4, 5, 10, 11, 12 using the following ranking functions, which are bounded by −19.

4 Location Addition

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

1* 16 1: − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

5 Location Addition

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

1 14 1_var_snapshot: − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

6 Location Addition

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

2* 23 2: − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

7 Location Addition

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

2 21 2_var_snapshot: − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

8 Location Addition

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

3* 30 3: − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

9 Location Addition

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

3 28 3_var_snapshot: − x74 + x74 ≤ 0 ∧ x74 − x74 ≤ 0 ∧ − x73 + x73 ≤ 0 ∧ x73 − x73 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 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, 2_var_snapshot, 2* }.

10.1.1 Transition Removal

We remove transitions 6, 7, 8 using the following ranking functions, which are bounded by −1.

10.1.2 Transition Removal

We remove transitions 21, 23 using the following ranking functions, which are bounded by −2.

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 { 3, 3_var_snapshot, 3* }.

10.2.1 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 2.

10.2.2 Transition Removal

We remove transitions 28, 30 using the following ranking functions, which are bounded by −2.

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 { 1, 1_var_snapshot, 1* }.

10.3.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 2.

10.3.2 Transition Removal

We remove transitions 14, 16 using the following ranking functions, which are bounded by −1.

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.

Tool configuration

T2Cert

• version: 1.0