LTS Termination Proof

by T2Cert

Input

• Initial Location: 7
• 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 ∧ 1 − 2⋅x39 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 2⋅x39 − 2⋅x40 ≤ 0 ∧ −2⋅x39 + 2⋅x40 ≤ 0 ∧ − x39 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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
  1	1	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 ∧ 1 − 2⋅x45 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 2⋅x45 − 2⋅x46 ≤ 0 ∧ −2⋅x45 + 2⋅x46 ≤ 0 ∧ − x45 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 2⋅x45 − 2⋅x46 ≤ 0 ∧ −1 − 2⋅x45 + 2⋅x46 ≤ 0 ∧ − arg2P ≤ 0 ∧ arg2P ≤ 0 ∧ 1 − arg3P + 2⋅x45 ≤ 0 ∧ −1 + arg3P − 2⋅x45 ≤ 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 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0
  2	2	3:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ −2 + arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg3 ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 0 ∧ arg3 − arg4P ≤ 0 ∧ − arg3 + arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0
  3	3	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 3 − arg3 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg4 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ − arg3P + arg4 ≤ 0 ∧ arg3P − arg4 ≤ 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 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0
  3	4	3:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg2 − arg4 ≤ 0 ∧ −2 + arg3 ≤ 0 ∧ 1 + arg3 − x18 ≤ 0 ∧ − x18 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg4 ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0
  2	5	4:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 + x50 ≤ 0 ∧ 1 − arg3 + x51 ≤ 0 ∧ − arg1 + x52 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − x52 ≤ 0 ∧ 4 − arg1 + arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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
  4	6	5:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 + x57 ≤ 0 ∧ 1 − arg3 + x58 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg3 ≤ 0 ∧ − arg3 + 2⋅x57 ≤ 0 ∧ −1 + arg3 − 2⋅x57 ≤ 0 ∧ −1 + arg3 − 2⋅x58 ≤ 0 ∧ − arg3 + 2⋅x58 ≤ 0 ∧ − arg2P ≤ 0 ∧ arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
  5	7	6:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg3 ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 0 ∧ arg3 − arg4P ≤ 0 ∧ − arg3 + arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0
  6	8	5:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3 + arg4 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg4 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ − arg3P + arg4 ≤ 0 ∧ arg3P − arg4 ≤ 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 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0
  6	9	6:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 + arg3 − arg4 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 4 − arg1 + arg4 ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0
  7	10	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 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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)		1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0
  2		(2)		3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0
  3		(3)		3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0
  4		(4)		3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0 ∧ 3 − x52 ≤ 0
  5		(5)		3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0 ∧ 3 − x52 ≤ 0
  6		(6)		3 − arg1P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − x39 ≤ 0 ∧ 3 − x41 ≤ 0 ∧ − x45 ≤ 0 ∧ 3 − x52 ≤ 0
  7		(7)		TRUE

• initial node: 7
• cover edges:
• transition edges:

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

2 Switch to Cooperation Termination Proof

3 Transition Removal

We remove transitions 0, 1, 5, 6, 10 using the following ranking functions, which are bounded by −23.

4 Location Addition

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

2* 14 2: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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.

2 12 2_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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.

3* 21 3: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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.

3 19 3_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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.

5* 28 5: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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.

5 26 5_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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 Location Addition

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

6* 35 6: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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

11 Location Addition

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

6 33 6_var_snapshot: − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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

12 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

12.1 SCC Subproblem 1/2

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

12.1.1 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 4.

12.1.2 Transition Removal

We remove transitions 26, 28, 8 using the following ranking functions, which are bounded by −3.

12.1.3 Transition Removal

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

12.1.4 Transition Removal

We remove transitions 33, 35 using the following ranking functions, which are bounded by −1.

12.1.5 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

12.1.5.1 Cut-Point Subproblem 1/2

12.1.5.1.1 Splitting Cut-Point Transitions

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

12.1.5.2 Cut-Point Subproblem 2/2

12.1.5.2.1 Splitting Cut-Point Transitions

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

12.2 SCC Subproblem 2/2

Here we consider the SCC { 2, 3, 2_var_snapshot, 2*, 3_var_snapshot, 3* }.

12.2.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by −14.

12.2.2 Transition Removal

We remove transitions 12, 14, 3 using the following ranking functions, which are bounded by −4.

12.2.3 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by −7.

12.2.4 Transition Removal

We remove transitions 19, 21 using the following ranking functions, which are bounded by −1.

12.2.5 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

12.2.5.1 Cut-Point Subproblem 1/2

12.2.5.1.1 Splitting Cut-Point Transitions

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

12.2.5.2 Cut-Point Subproblem 2/2

12.2.5.2.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

• version: 1.0