by AProVE
f1_0_main_Load | 1 | f480_0_main_InvokeMethod: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 = _arg2 ∧ 2 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 | |
f1_0_main_Load | 2 | f480_0_main_InvokeMethod: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ 0 = _x1 ∧ 1 ≤ _x3 − 1 ∧ 0 ≤ _x − 1 ∧ _x3 − 1 ≤ _x | |
f1_0_main_Load | 3 | f481_0_main_InvokeMethod: | x1 = _x7 ∧ x2 = _x8 ∧ x3 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ 0 ≤ _x7 − 1 ∧ −1 ≤ _x13 − 1 ∧ 2 ≤ _x10 − 1 ∧ 1 = _x8 | |
f1_0_main_Load | 4 | f481_0_main_InvokeMethod: | x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ x1 = _x19 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x19 − 1 ≤ _x16 ∧ −1 ≤ _x24 − 1 ∧ 0 ≤ _x16 − 1 ∧ 1 ≤ _x19 − 1 ∧ 1 = _x17 | |
f1_0_main_Load | 5 | f482_0_main_InvokeMethod: | x1 = _x25 ∧ x2 = _x26 ∧ x3 = _x29 ∧ x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ 0 ≤ _x33⋅_x34 ∧ 1 ≤ _x26 − 1 ∧ −1 ≤ _x34 − 1 ∧ −1 ≤ _x33 − 1 ∧ _x30 ≤ _x25 ∧ 0 ≤ _x25 − 1 ∧ 0 ≤ _x30 − 1 ∧ 2 ≤ _x31 − 1 | |
f1_0_main_Load | 6 | f482_0_main_InvokeMethod: | x1 = _x35 ∧ x2 = _x36 ∧ x3 = _x37 ∧ x1 = _x38 ∧ x2 = _x39 ∧ x3 = _x40 ∧ 0 ≤ _x41⋅_x42 ∧ 1 ≤ _x36 − 1 ∧ −1 ≤ _x42 − 1 ∧ −1 ≤ _x41 − 1 ∧ _x38 ≤ _x35 ∧ _x39 − 1 ≤ _x35 ∧ 0 ≤ _x35 − 1 ∧ 0 ≤ _x38 − 1 ∧ 1 ≤ _x39 − 1 | |
f1_0_main_Load | 7 | f193_0__init__LE: | x1 = _x43 ∧ x2 = _x44 ∧ x3 = _x45 ∧ x1 = _x47 ∧ x2 = _x48 ∧ x3 = _x49 ∧ 10 = _x47 ∧ 0 = _x44 ∧ 0 ≤ _x43 − 1 | |
f1_0_main_Load | 8 | f193_0__init__LE: | x1 = _x50 ∧ x2 = _x51 ∧ x3 = _x52 ∧ x1 = _x53 ∧ x2 = _x54 ∧ x3 = _x55 ∧ 0 ≤ _x50 − 1 ∧ −1 ≤ _x56 − 1 ∧ 1 = _x51 ∧ 10 = _x53 | |
f1_0_main_Load | 9 | f193_0__init__LE: | x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ 0 ≤ _x63⋅_x65 ∧ 1 ≤ _x58 − 1 ∧ −1 ≤ _x65 − 1 ∧ −1 ≤ _x63 − 1 ∧ 0 ≤ _x57 − 1 ∧ _x63⋅_x65 + 10 = _x60 | |
f193_0__init__LE | 10 | f193_0__init__LE: | x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x1 = _x70 ∧ x2 = _x71 ∧ x3 = _x72 ∧ _x66 − 1 = _x70 ∧ _x66 − 1 ≤ _x66 − 1 ∧ 1 ≤ _x66 − 1 | |
f193_0__init__LE | 11 | f518_0__init__InvokeMethod: | x1 = _x73 ∧ x2 = _x74 ∧ x3 = _x75 ∧ x1 = _x76 ∧ x2 = _x77 ∧ x3 = _x78 ∧ _x73 − 1 = _x77 ∧ 1 ≤ _x73 − 1 ∧ 4 ≤ _x76 − 1 ∧ _x73 − 1 ≤ _x73 − 1 | |
f193_0__init__LE | 12 | f518_0__init__InvokeMethod: | x1 = _x79 ∧ x2 = _x80 ∧ x3 = _x81 ∧ x1 = _x82 ∧ x2 = _x83 ∧ x3 = _x84 ∧ _x79 − 1 = _x83 ∧ 1 ≤ _x79 − 1 ∧ 3 ≤ _x82 − 1 ∧ _x79 − 1 ≤ _x79 − 1 | |
f518_0__init__InvokeMethod | 13 | f193_0__init__LE: | x1 = _x85 ∧ x2 = _x86 ∧ x3 = _x87 ∧ x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ _x86 = _x88 ∧ 0 ≤ _x86 − 1 ∧ 2 ≤ _x85 − 1 | |
f480_0_main_InvokeMethod | 14 | f388_0_height_NONNULL: | x1 = _x91 ∧ x2 = _x92 ∧ x3 = _x93 ∧ x1 = _x94 ∧ x2 = _x95 ∧ x3 = _x96 ∧ −1 ≤ _x95 − 1 ∧ 0 ≤ _x94 − 1 ∧ 0 ≤ _x91 − 1 ∧ _x95 + 1 ≤ _x91 ∧ _x94 ≤ _x91 | |
f481_0_main_InvokeMethod | 15 | f388_0_height_NONNULL: | x1 = _x97 ∧ x2 = _x98 ∧ x3 = _x99 ∧ x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ −1 ≤ _x101 − 1 ∧ 0 ≤ _x100 − 1 ∧ 0 ≤ _x97 − 1 ∧ _x101 + 1 ≤ _x97 ∧ _x100 ≤ _x97 | |
f482_0_main_InvokeMethod | 16 | f388_0_height_NONNULL: | x1 = _x103 ∧ x2 = _x104 ∧ x3 = _x105 ∧ x1 = _x106 ∧ x2 = _x107 ∧ x3 = _x108 ∧ _x106 ≤ _x104 ∧ 1 ≤ _x109 − 1 ∧ _x107 + 1 ≤ _x104 ∧ 0 ≤ _x103 − 1 ∧ 0 ≤ _x104 − 1 ∧ 0 ≤ _x106 − 1 ∧ −1 ≤ _x107 − 1 | |
f388_0_height_NONNULL | 17 | f388_0_height_NONNULL: | x1 = _x110 ∧ x2 = _x111 ∧ x3 = _x112 ∧ x1 = _x113 ∧ x2 = _x114 ∧ x3 = _x115 ∧ −1 ≤ _x114 − 1 ∧ 0 ≤ _x113 − 1 ∧ 0 ≤ _x111 − 1 ∧ 2 ≤ _x110 − 1 ∧ _x114 + 1 ≤ _x111 ∧ _x114 + 3 ≤ _x110 ∧ _x113 ≤ _x111 ∧ _x113 + 2 ≤ _x110 | |
f388_0_height_NONNULL | 18 | f388_0_height_NONNULL: | x1 = _x116 ∧ x2 = _x117 ∧ x3 = _x118 ∧ x1 = _x119 ∧ x2 = _x120 ∧ x3 = _x121 ∧ −1 ≤ _x120 − 1 ∧ 0 ≤ _x119 − 1 ∧ −1 ≤ _x117 − 1 ∧ 2 ≤ _x116 − 1 ∧ _x120 + 3 ≤ _x116 ∧ _x119 + 2 ≤ _x116 | |
__init | 19 | f1_0_main_Load: | x1 = _x122 ∧ x2 = _x123 ∧ x3 = _x124 ∧ x1 = _x125 ∧ x2 = _x126 ∧ x3 = _x127 ∧ 0 ≤ 0 |
f193_0__init__LE | f193_0__init__LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f518_0__init__InvokeMethod | f518_0__init__InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f480_0_main_InvokeMethod | f480_0_main_InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f481_0_main_InvokeMethod | f481_0_main_InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f482_0_main_InvokeMethod | f482_0_main_InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f388_0_height_NONNULL | f388_0_height_NONNULL | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
__init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
We consider subproblems for each of the 2 SCC(s) of the program graph.
Here we consider the SCC {
, }.We remove transitions
, , , using the following ranking functions, which are bounded by 0.: | 2⋅x1 |
: | 1 + 2⋅x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.
Here we consider the SCC {
}.We remove transitions
, using the following ranking functions, which are bounded by 0.: | x1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.