by AProVE
f1_0_main_Load | 1 | f162_0_power_GT: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ 0 = _arg2P ∧ 0 = _arg1P ∧ 0 = _arg2 ∧ 0 ≤ _arg1 − 1 | |
f1_0_main_Load | 2 | f97_0_random_GT: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x1 = _x4 ∧ x2 = _x5 ∧ x3 = _x6 ∧ x4 = _x7 ∧ 0 = _x5 ∧ 0 ≤ _x4 − 1 ∧ 0 ≤ _x − 1 ∧ 0 ≤ _x1 − 1 ∧ _x4 ≤ _x | |
f1_0_main_Load | 3 | f97_0_random_GT: | x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x11 ∧ x4 = _x12 ∧ x1 = _x13 ∧ x2 = _x15 ∧ x3 = _x16 ∧ x4 = _x17 ∧ 0 ≤ _x13 − 1 ∧ 0 ≤ _x8 − 1 ∧ _x13 ≤ _x8 ∧ 0 ≤ _x9 − 1 ∧ −1 ≤ _x15 − 1 | |
f97_0_random_GT | 4 | f162_0_power_GT: | x1 = _x18 ∧ x2 = _x20 ∧ x3 = _x21 ∧ x4 = _x22 ∧ x1 = _x23 ∧ x2 = _x24 ∧ x3 = _x25 ∧ x4 = _x26 ∧ 0 = _x24 ∧ _x20 = _x23 ∧ 0 ≤ _x18 − 1 | |
f97_0_random_GT | 5 | f155_0_main_InvokeMethod: | x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x1 = _x31 ∧ x2 = _x32 ∧ x3 = _x33 ∧ x4 = _x34 ∧ _x31 ≤ _x27 ∧ 1 ≤ _x35 − 1 ∧ 0 ≤ _x27 − 1 ∧ 0 ≤ _x31 − 1 ∧ _x28 = _x32 ∧ 0 = _x33 | |
f97_0_random_GT | 6 | f155_0_main_InvokeMethod: | x1 = _x36 ∧ x2 = _x38 ∧ x3 = _x39 ∧ x4 = _x40 ∧ x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x4 = _x45 ∧ 1 ≤ _x46 − 1 ∧ −1 ≤ _x44 − 1 ∧ _x42 ≤ _x36 ∧ 0 ≤ _x36 − 1 ∧ 0 ≤ _x42 − 1 ∧ _x38 = _x43 | |
f155_0_main_InvokeMethod | 7 | f162_0_power_GT: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x4 = _x51 ∧ x1 = _x52 ∧ x2 = _x53 ∧ x3 = _x54 ∧ x4 = _x55 ∧ 0 ≤ _x48 − 1 ∧ 1 ≤ _x56 − 1 ∧ _x49 = _x52 ∧ _x50 = _x53 | |
f162_0_power_GT | 8 | f162_0_power_GT': | x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ x4 = _x60 ∧ x1 = _x61 ∧ x2 = _x62 ∧ x3 = _x63 ∧ x4 = _x64 ∧ _x58 = _x62 ∧ _x57 = _x61 ∧ 1 ≤ _x58 − 1 ∧ _x57 ≤ 1 | |
f162_0_power_GT' | 9 | f213_0_power_NE: | x1 = _x65 ∧ x2 = _x66 ∧ x3 = _x67 ∧ x4 = _x68 ∧ x1 = _x69 ∧ x2 = _x70 ∧ x3 = _x71 ∧ x4 = _x72 ∧ 1 ≤ _x66 − 1 ∧ _x65 ≤ 1 ∧ _x66 − 2⋅_x73 ≤ 1 ∧ 0 ≤ _x66 − 2⋅_x73 ∧ _x65 = _x69 ∧ _x66 = _x70 ∧ _x66 − 2⋅_x73 = _x71 | |
f162_0_power_GT | 10 | f162_0_power_GT': | x1 = _x74 ∧ x2 = _x75 ∧ x3 = _x76 ∧ x4 = _x77 ∧ x1 = _x78 ∧ x2 = _x79 ∧ x3 = _x80 ∧ x4 = _x81 ∧ _x75 = _x79 ∧ _x74 = _x78 ∧ 1 ≤ _x75 − 1 ∧ 2 ≤ _x74 − 1 | |
f162_0_power_GT' | 11 | f213_0_power_NE: | x1 = _x82 ∧ x2 = _x83 ∧ x3 = _x84 ∧ x4 = _x85 ∧ x1 = _x86 ∧ x2 = _x87 ∧ x3 = _x88 ∧ x4 = _x89 ∧ 1 ≤ _x83 − 1 ∧ 2 ≤ _x82 − 1 ∧ _x83 − 2⋅_x90 ≤ 1 ∧ 0 ≤ _x83 − 2⋅_x90 ∧ _x82 = _x86 ∧ _x83 = _x87 ∧ _x83 − 2⋅_x90 = _x88 | |
f213_0_power_NE | 12 | f213_0_power_NE': | x1 = _x91 ∧ x2 = _x92 ∧ x3 = _x93 ∧ x4 = _x94 ∧ x1 = _x95 ∧ x2 = _x96 ∧ x3 = _x97 ∧ x4 = _x98 ∧ 1 ≤ _x92 − 1 ∧ 0 ≤ _x99 − 1 ∧ _x99 ≤ _x92 − 1 ∧ 0 = _x93 ∧ _x91 = _x95 ∧ _x92 = _x96 ∧ 0 = _x97 ∧ _x94 = _x98 | |
f213_0_power_NE' | 13 | f162_0_power_GT: | x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ x4 = _x103 ∧ x1 = _x104 ∧ x2 = _x105 ∧ x3 = _x106 ∧ x4 = _x107 ∧ _x100 = _x104 ∧ 0 = _x102 ∧ 0 ≤ _x101 − 2⋅_x105 ∧ _x101 − 2⋅_x105 ≤ 1 ∧ 0 ≤ _x105 − 1 ∧ _x105 ≤ _x101 − 1 ∧ 1 ≤ _x101 − 1 | |
f213_0_power_NE | 14 | f162_0_power_GT: | x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x4 = _x111 ∧ x1 = _x112 ∧ x2 = _x113 ∧ x3 = _x114 ∧ x4 = _x115 ∧ _x109 − 1 = _x113 ∧ _x108 = _x112 ∧ 1 = _x110 ∧ _x109 − 1 ≤ _x109 − 1 ∧ 1 ≤ _x109 − 1 | |
__init | 15 | f1_0_main_Load: | x1 = _x116 ∧ x2 = _x117 ∧ x3 = _x118 ∧ x4 = _x119 ∧ x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x4 = _x123 ∧ 0 ≤ 0 |
f97_0_random_GT | f97_0_random_GT | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
f162_0_power_GT' | f162_0_power_GT' | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
f155_0_main_InvokeMethod | f155_0_main_InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
f213_0_power_NE | f213_0_power_NE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
f213_0_power_NE' | f213_0_power_NE' | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
f162_0_power_GT | f162_0_power_GT | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
__init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
We consider subproblems for each of the 1 SCC(s) of the program graph.
Here we consider the SCC {
, , , }.We remove transitions
, , , , , , using the following ranking functions, which are bounded by 0.: | 4⋅x2 + 2 |
: | 4⋅x2 + 1 |
: | 2⋅x2 + 3 |
: | 4⋅x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.