LTS Termination Proof

by T2Cert

Input

Integer Transition System

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 ∧ 2 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 + arg2P − x5 ≤ 0 ∧ − x5 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0
0	1	1:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x10 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ arg2P ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0
1	2	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ arg2 − arg3P ≤ 0 ∧ − arg2 + arg3P ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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
2	3	3:	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 ≤ 0 ∧ 0 ≤ 0 ∧ − x39 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 + x39 − x40 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg3 + x39 ≤ 0 ∧ 1 + x39 − x41 ≤ 0 ∧ 1 − arg2 + x42 ≤ 0 ∧ 1 + x39 − x42 ≤ 0 ∧ 1 + x39 − x43 ≤ 0 ∧ − arg1 + x44 ≤ 0 ∧ arg1 − 2⋅x45 ≤ 0 ∧ − arg1 + 2⋅x45 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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
3	4	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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x52 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3P + x52 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg3 + x52 ≤ 0 ∧ 1 + x52 − x53 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 − arg2P + x52 ≤ 0 ∧ 1 + x52 − x54 ≤ 0 ∧ arg1 − 2⋅x55 ≤ 0 ∧ − arg1 + 2⋅x55 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg1 + 2⋅x55 ≤ 0 ∧ −1 + arg1 − 2⋅x55 ≤ 0 ∧ −1 − 2⋅arg1P + arg1 ≤ 0 ∧ 2⋅arg1P − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0
2	5	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 + x59 ≤ 0 ∧ 1 − arg2 + x60 ≤ 0 ∧ −1 + arg1 − 2⋅x61 ≤ 0 ∧ 1 − arg1 + 2⋅x61 ≤ 0 ∧ − arg1 + x62 ≤ 0 ∧ − x60 ≤ 0 ∧ − x60 + x63 ≤ 0 ∧ 1 − x59 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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
3	6	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg2 + x70 ≤ 0 ∧ −1 + arg1 − 2⋅x71 ≤ 0 ∧ 1 − arg1 + 2⋅x71 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − x70 ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ arg2P − x70 ≤ 0 ∧ − arg1 + 2⋅x71 ≤ 0 ∧ −1 + arg1 − 2⋅x71 ≤ 0 ∧ −1 − 2⋅arg1P + arg1 ≤ 0 ∧ 2⋅arg1P − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0
2	7	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 + x75 ≤ 0 ∧ 1 − arg2 + x75 ≤ 0 ∧ −1 + arg1 − 2⋅x76 ≤ 0 ∧ 1 − arg1 + 2⋅x76 ≤ 0 ∧ 1 − x75 ≤ 0 ∧ − arg1 + x77 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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
3	8	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 + arg2P − arg3 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ −1 + arg1 − 2⋅x83 ≤ 0 ∧ 1 − arg1 + 2⋅x83 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1 + 2⋅x83 ≤ 0 ∧ −1 + arg1 − 2⋅x83 ≤ 0 ∧ −1 − 2⋅arg1P + arg1 ≤ 0 ∧ 2⋅arg1P − arg1 ≤ 0 ∧ arg2P − arg3P ≤ 0 ∧ − arg2P + arg3P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0
0	9	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x37 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − x36 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ −1 − arg1P + x36 ≤ 0 ∧ 1 + arg1P − x36 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0
4	10	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ −1 − arg1P + arg1 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0
5	11	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 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

0:	TRUE
1:	− arg1P ≤ 0 ∧ − arg1 ≤ 0
2:	TRUE
3:	1 − arg2 ≤ 0 ∧ − arg3 ≤ 0
4:	− x37 ≤ 0 ∧ − x36 ≤ 0
5:	TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

nodes (location) invariant:

0	(0)	TRUE
1	(1)	− arg1P ≤ 0 ∧ − arg1 ≤ 0
2	(2)	TRUE
3	(3)	1 − arg2 ≤ 0 ∧ − arg3 ≤ 0
4	(4)	− x37 ≤ 0 ∧ − x36 ≤ 0
5	(5)	TRUE

initial node: 5
cover edges:
transition edges:

0 0 1

0 1 1

0 9 4

1 2 2

2 3 3

2 5 3

2 7 3

3 4 2

3 6 2

3 8 2

4 10 4

5 11 0

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

2	12	2:	− x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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	19	4:	− x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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

and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 2, 9, 11 using the following ranking functions, which are bounded by −17.

5:	0
0:	0
1:	0
2:	0
3:	0
4:	0
5:	−6
0:	−7
1:	−8
2:	−9
3:	−9
2_var_snapshot:	−9
2*:	−9
4:	−12
4_var_snapshot:	−12
4*:	−12

4 Location Addition

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

2* 15 2: − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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 13 2_var_snapshot: − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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.

4* 22 4: − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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.

4 20 4_var_snapshot: − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x77 + x77 ≤ 0 ∧ x77 − x77 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x71 + x71 ≤ 0 ∧ x71 − x71 ≤ 0 ∧ − x70 + x70 ≤ 0 ∧ x70 − x70 ≤ 0 ∧ − x63 + x63 ≤ 0 ∧ x63 − x63 ≤ 0 ∧ − x62 + x62 ≤ 0 ∧ x62 − x62 ≤ 0 ∧ − x61 + x61 ≤ 0 ∧ x61 − x61 ≤ 0 ∧ − x60 + x60 ≤ 0 ∧ x60 − x60 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x53 + x53 ≤ 0 ∧ x53 − x53 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x43 + x43 ≤ 0 ∧ x43 − x43 ≤ 0 ∧ − x42 + x42 ≤ 0 ∧ x42 − x42 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − x40 + x40 ≤ 0 ∧ x40 − x40 ≤ 0 ∧ − x4 + x4 ≤ 0 ∧ x4 − x4 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x10 + x10 ≤ 0 ∧ x10 − x10 ≤ 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 SCC Decomposition

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

8.1 SCC Subproblem 1/2

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

8.1.1 Transition Removal

We remove transitions 3, 4, 5, 6, 7, 8 using the following ranking functions, which are bounded by 3.

2:	2 + 4⋅arg2
3:	4⋅arg2
2_var_snapshot:	1 + 4⋅arg2
2*:	3 + 4⋅arg2

8.1.2 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by −1.

2:	0
3:	0
2_var_snapshot:	−1
2*:	1

8.1.3 Transition Removal

We remove transition 13 using the following ranking functions, which are bounded by −1.

2:	0
3:	0
2_var_snapshot:	−1
2*:	0

8.1.4 Splitting Cut-Point Transitions

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

8.1.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 12.

8.1.4.1.1 Splitting Cut-Point Transitions

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

8.2 SCC Subproblem 2/2

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

8.2.1 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 2.

4:	1 + 3⋅arg1
4_var_snapshot:	3⋅arg1
4*:	2 + 3⋅arg1

8.2.2 Transition Removal

We remove transition 22 using the following ranking functions, which are bounded by −2.

4:	−1
4_var_snapshot:	−2
4*:	0

8.2.3 Transition Removal

We remove transition 20 using the following ranking functions, which are bounded by −1.

4:	0
4_var_snapshot:	−1
4*:	0

8.2.4 Splitting Cut-Point Transitions

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

8.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 19.

8.2.4.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

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