by AProVE
| f1_0_main_Load | 1 | f892_0_loop_LT: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ 0 = _arg7P ∧ 0 = _arg6P ∧ 0 = _arg5P ∧ 0 = _arg4P ∧ 0 = _arg3P ∧ 0 = _arg2P ∧ 0 = _arg1P ∧ 0 = _arg2 ∧ 0 ≤ _arg1 − 1 | |
| f1_0_main_Load | 2 | f892_0_loop_LT: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x1 = _x7 ∧ x2 = _x8 ∧ x3 = _x9 ∧ x4 = _x10 ∧ x5 = _x11 ∧ x6 = _x12 ∧ x7 = _x13 ∧ 1 = _x13 ∧ 1 = _x12 ∧ 0 = _x11 ∧ 0 = _x10 ∧ 0 = _x9 ∧ 0 = _x7 ∧ 1 = _x1 ∧ −1 ≤ _x8 − 1 ∧ 0 ≤ _x − 1 | |
| f1_0_main_Load | 3 | f892_0_loop_LT: | x1 = _x14 ∧ x2 = _x15 ∧ x3 = _x16 ∧ x4 = _x17 ∧ x5 = _x18 ∧ x6 = _x19 ∧ x7 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ x4 = _x24 ∧ x5 = _x25 ∧ x6 = _x26 ∧ x7 = _x27 ∧ 2 = _x27 ∧ 2 = _x26 ∧ 0 = _x25 ∧ 0 = _x24 ∧ 0 = _x21 ∧ 2 = _x15 ∧ 0 ≤ _x14 − 1 ∧ −1 ≤ _x23 − 1 ∧ −1 ≤ _x22 − 1 | |
| f1_0_main_Load | 4 | f892_0_loop_LT: | x1 = _x28 ∧ x2 = _x29 ∧ x3 = _x30 ∧ x4 = _x31 ∧ x5 = _x32 ∧ x6 = _x33 ∧ x7 = _x34 ∧ x1 = _x35 ∧ x2 = _x36 ∧ x3 = _x37 ∧ x4 = _x38 ∧ x5 = _x39 ∧ x6 = _x40 ∧ x7 = _x41 ∧ 3 = _x41 ∧ _x29 = _x40 ∧ _x35 = _x39 ∧ _x35 = _x38 ∧ 0 ≤ _x28 − 1 ∧ −1 ≤ _x37 − 1 ∧ −1 ≤ _x35 − 1 ∧ 2 ≤ _x29 − 1 ∧ −1 ≤ _x36 − 1 | |
| f892_0_loop_LT | 5 | f892_0_loop_LT: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x4 = _x45 ∧ x5 = _x46 ∧ x6 = _x47 ∧ x7 = _x48 ∧ x1 = _x49 ∧ x2 = _x50 ∧ x3 = _x51 ∧ x4 = _x52 ∧ x5 = _x53 ∧ x6 = _x54 ∧ x7 = _x55 ∧ _x48 = _x55 ∧ _x47 = _x54 ∧ _x42 = _x53 ∧ _x42 = _x52 ∧ 0 = _x51 ∧ 0 = _x50 ∧ _x42 = _x49 ∧ _x42 = _x46 ∧ _x42 = _x45 ∧ 0 ≤ 3⋅_x44 ∧ 3⋅_x44 − 2⋅_x43 ≤ −1 ∧ 0 ≤ 2⋅_x43 ∧ _x47 ≤ _x48 ∧ −1 ≤ _x47 − 1 ∧ −1 ≤ _x42 − 1 | |
| f892_0_loop_LT | 6 | f892_0_loop_LT: | x1 = _x56 ∧ x2 = _x57 ∧ x3 = _x58 ∧ x4 = _x59 ∧ x5 = _x60 ∧ x6 = _x61 ∧ x7 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ x4 = _x66 ∧ x5 = _x67 ∧ x6 = _x68 ∧ x7 = _x69 ∧ _x62 + 1 = _x69 ∧ _x61 = _x68 ∧ _x56 − 0 − 2⋅_x64 = _x67 ∧ _x56 − 0 − 2⋅_x64 = _x66 ∧ 0 = _x65 ∧ _x56 − 0 − 2⋅_x64 = _x63 ∧ _x56 = _x60 ∧ _x56 = _x59 ∧ 0 ≤ 2⋅_x64 ∧ 3⋅_x58 − 2⋅_x57 ≤ 0 − 2⋅_x64 − 1 ∧ 0 ≤ 3⋅_x58 ∧ 0 ≤ 2⋅_x57 ∧ _x61 ≤ _x62 + 1 ∧ −1 ≤ _x64 − 1 ∧ _x62 ≤ _x61 − 1 ∧ −1 ≤ _x62 − 1 ∧ −1 ≤ _x61 − 1 ∧ −1 ≤ _x56 − 1 | |
| f892_0_loop_LT | 7 | f892_0_loop_LT: | x1 = _x70 ∧ x2 = _x71 ∧ x3 = _x72 ∧ x4 = _x73 ∧ x5 = _x74 ∧ x6 = _x75 ∧ x7 = _x76 ∧ x1 = _x77 ∧ x2 = _x78 ∧ x3 = _x79 ∧ x4 = _x80 ∧ x5 = _x81 ∧ x6 = _x82 ∧ x7 = _x83 ∧ _x76 + 2 = _x83 ∧ _x75 = _x82 ∧ _x70 − 3⋅_x79 − 2⋅_x78 = _x81 ∧ _x70 − 3⋅_x79 − 2⋅_x78 = _x80 ∧ _x70 − 3⋅_x79 − 2⋅_x78 = _x77 ∧ _x70 = _x74 ∧ _x70 = _x73 ∧ 3⋅_x72 − 2⋅_x71 ≤ 3⋅_x79 − 2⋅_x78 − 1 ∧ _x76 + 2 ≤ _x75 ∧ 0 ≤ 3⋅_x79 ∧ 0 ≤ 2⋅_x78 ∧ 0 ≤ 3⋅_x72 ∧ 0 ≤ 2⋅_x71 ∧ −1 ≤ _x79 − 1 ∧ −1 ≤ _x78 − 1 ∧ −1 ≤ _x76 − 1 ∧ −1 ≤ _x70 − 1 ∧ _x76 + 1 ≤ _x75 − 1 ∧ 1 ≤ _x75 − 1 | |
| __init | 8 | f1_0_main_Load: | x1 = _x84 ∧ x2 = _x85 ∧ x3 = _x86 ∧ x4 = _x87 ∧ x5 = _x88 ∧ x6 = _x89 ∧ x7 = _x90 ∧ x1 = _x91 ∧ x2 = _x92 ∧ x3 = _x93 ∧ x4 = _x94 ∧ x5 = _x95 ∧ x6 = _x96 ∧ x7 = _x97 ∧ 0 ≤ 0 |
| f892_0_loop_LT | f892_0_loop_LT | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 |
| f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 |
| __init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 |
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.
| : | −1 + x6 − x7 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.