YES Termination proof succeeded Initially, performed program simplifications using lexicographic rank functions: * Removed transitions 34, 35, 36, 38, 39, 44, 45, 46, 48, 49, 54, 55, 56, 58, 59, 64, 65, 66, 68, 69, 74, 75, 76, 77, 78, 80, 81, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 101, 102, 103, 105, 106, 111, 112, 113, 114, 115, 116, 117 using the following rank functions: - Rank function 1: RF for loc. 30: -24*i_0+24*n_0 RF for loc. 31: -24*i_0+24*n_0 RF for loc. 32: -24*i_0+24*n_0 RF for loc. 33: -24*i_0+24*n_0 RF for loc. 34: -24*i_0+24*n_0 RF for loc. 35: -24*i_0+24*n_0 RF for loc. 36: -24*i_0+24*n_0 RF for loc. 37: -24*i_0+24*n_0 RF for loc. 38: -24*i_0+24*n_0 RF for loc. 39: -24*i_0+24*n_0 RF for loc. 40: -24*i_0+24*n_0 RF for loc. 41: -24*i_0+24*n_0 RF for loc. 42: -24*i_0+24*n_0 RF for loc. 43: -1-24*i_0+24*n_0 RF for loc. 44: -1-24*i_0+24*n_0 RF for loc. 45: -24*i_0+24*n_0 RF for loc. 46: -24*i_0+24*n_0 RF for loc. 47: -24*i_0+24*n_0 RF for loc. 48: -24*i_0+24*n_0 RF for loc. 49: -24*i_0+24*n_0 RF for loc. 50: -1-24*i_0+24*n_0 RF for loc. 51: -24*i_0+24*n_0 RF for loc. 53: -24*i_0+24*n_0 RF for loc. 57: -24*i_0+24*n_0 RF for loc. 61: -24*i_0+24*n_0 RF for loc. 65: -24*i_0+24*n_0 RF for loc. 69: -24*i_0+24*n_0 RF for loc. 73: -24*i_0+24*n_0 RF for loc. 77: -24*i_0+24*n_0 Bound for (chained) transitions 55: 0 - Rank function 2: RF for loc. 30: 1-30*i_0+30*n_0 RF for loc. 31: -30*i_0+30*n_0 RF for loc. 32: 1-30*i_0+30*n_0 RF for loc. 33: 1-30*i_0+30*n_0 RF for loc. 34: 1-30*i_0+30*n_0 RF for loc. 35: 1-30*i_0+30*n_0 RF for loc. 36: 1-30*i_0+30*n_0 RF for loc. 37: 1-30*i_0+30*n_0 RF for loc. 38: 1-30*i_0+30*n_0 RF for loc. 39: 1-30*i_0+30*n_0 RF for loc. 40: 1-30*i_0+30*n_0 RF for loc. 41: 1-30*i_0+30*n_0 RF for loc. 42: 1-30*i_0+30*n_0 RF for loc. 43: -27-30*i_0+30*n_0 RF for loc. 44: -28-30*i_0+30*n_0 RF for loc. 45: 1-30*i_0+30*n_0 RF for loc. 46: -26-30*i_0+30*n_0 RF for loc. 47: 1-30*i_0+30*n_0 RF for loc. 48: 1-30*i_0+30*n_0 RF for loc. 49: 1-30*i_0+30*n_0 RF for loc. 50: -1-30*i_0+30*n_0 RF for loc. 51: 1-30*i_0+30*n_0 RF for loc. 53: 1-30*i_0+30*n_0 RF for loc. 57: 1-30*i_0+30*n_0 RF for loc. 61: 1-30*i_0+30*n_0 RF for loc. 65: 1-30*i_0+30*n_0 RF for loc. 69: 1-30*i_0+30*n_0 RF for loc. 73: 1-30*i_0+30*n_0 RF for loc. 77: 1-30*i_0+30*n_0 Bound for (chained) transitions 34: 1 - Rank function 3: RF for loc. 30: 18-20*i_0+20*n_0 RF for loc. 31: -20*i_0+20*n_0 RF for loc. 32: 18-20*i_0+20*n_0 RF for loc. 33: 18-20*i_0+20*n_0 RF for loc. 34: 18-20*i_0+20*n_0 RF for loc. 35: 18-20*i_0+20*n_0 RF for loc. 36: 18-20*i_0+20*n_0 RF for loc. 37: 18-20*i_0+20*n_0 RF for loc. 38: 18-20*i_0+20*n_0 RF for loc. 39: 18-20*i_0+20*n_0 RF for loc. 40: 18-20*i_0+20*n_0 RF for loc. 41: 18-20*i_0+20*n_0 RF for loc. 42: 18-20*i_0+20*n_0 RF for loc. 43: -20*i_0+20*n_0 RF for loc. 44: -1-20*i_0+20*n_0 RF for loc. 45: 18-20*i_0+20*n_0 RF for loc. 46: -20*i_0+20*n_0 RF for loc. 47: 18-20*i_0+20*n_0 RF for loc. 48: 18-20*i_0+20*n_0 RF for loc. 49: 18-20*i_0+20*n_0 RF for loc. 50: -1-20*i_0+20*n_0 RF for loc. 51: 18-20*i_0+20*n_0 RF for loc. 53: 18-20*i_0+20*n_0 RF for loc. 57: 18-20*i_0+20*n_0 RF for loc. 61: 18-20*i_0+20*n_0 RF for loc. 65: 18-20*i_0+20*n_0 RF for loc. 69: 18-20*i_0+20*n_0 RF for loc. 73: 18-20*i_0+20*n_0 RF for loc. 77: 18-20*i_0+20*n_0 Bound for (chained) transitions 91: 18 - Rank function 4: RF for loc. 30: -4-13*k_0+13*n_0 RF for loc. 31: -13*k_0+13*n_0 RF for loc. 32: -5-13*k_0+13*n_0 RF for loc. 33: -2-13*k_0+13*n_0 RF for loc. 34: -11-13*k_0+13*n_0 RF for loc. 35: -11-13*k_0+13*n_0 RF for loc. 36: -11-13*k_0+13*n_0 RF for loc. 37: -11-13*k_0+13*n_0 RF for loc. 38: -11-13*k_0+13*n_0 RF for loc. 39: -11-13*k_0+13*n_0 RF for loc. 40: -12-13*k_0+13*n_0 RF for loc. 41: -10-13*k_0+13*n_0 RF for loc. 42: -9-13*k_0+13*n_0 RF for loc. 43: -5-13*k_0+13*n_0 RF for loc. 44: -6-13*k_0+13*n_0 RF for loc. 45: -6-13*k_0+13*n_0 RF for loc. 46: -4-13*k_0+13*n_0 RF for loc. 47: -8-13*k_0+13*n_0 RF for loc. 48: -6-13*k_0+13*n_0 RF for loc. 49: -6-13*k_0+13*n_0 RF for loc. 50: -1-13*k_0+13*n_0 RF for loc. 51: -1-13*k_0+13*n_0 RF for loc. 53: -3-13*k_0+13*n_0 RF for loc. 57: -11-13*k_0+13*n_0 RF for loc. 61: -11-13*k_0+13*n_0 RF for loc. 65: -11-13*k_0+13*n_0 RF for loc. 69: -13*k_0+13*n_0 RF for loc. 73: -7-13*k_0+13*n_0 RF for loc. 77: -6-13*k_0+13*n_0 Bound for (chained) transitions 74: 12 - Rank function 5: RF for loc. 30: 7 RF for loc. 31: 8 RF for loc. 32: 29-22*i_0+22*n_0 RF for loc. 33: 8 RF for loc. 34: -22*i_0+22*n_0 RF for loc. 35: -22*i_0+22*n_0 RF for loc. 36: -22*i_0+22*n_0 RF for loc. 37: -22*i_0+22*n_0 RF for loc. 38: -22*i_0+22*n_0 RF for loc. 39: -22*i_0+22*n_0 RF for loc. 40: -1-22*i_0+22*n_0 RF for loc. 41: 1-22*i_0+22*n_0 RF for loc. 42: 2-22*i_0+22*n_0 RF for loc. 43: -15-22*i_0+22*n_0 RF for loc. 44: -16-22*i_0+22*n_0 RF for loc. 45: 5-22*i_0+22*n_0 RF for loc. 46: -14-22*i_0+22*n_0 RF for loc. 47: 3-22*i_0+22*n_0 RF for loc. 48: 6-22*i_0+22*n_0 RF for loc. 49: 28-22*i_0+22*n_0 RF for loc. 50: 8 RF for loc. 51: -3-22*i_0+22*n_0 RF for loc. 53: 8 RF for loc. 57: -22*i_0+22*n_0 RF for loc. 61: -22*i_0+22*n_0 RF for loc. 65: -22*i_0+22*n_0 RF for loc. 69: -2-22*i_0+22*n_0 RF for loc. 73: 4-22*i_0+22*n_0 RF for loc. 77: 7-22*i_0+22*n_0 Bound for (chained) transitions 39: 8 Bound for (chained) transitions 45: 0 - Rank function 6: RF for loc. 30: -22 RF for loc. 31: -18 RF for loc. 32: -23*i_0+23*n_0 RF for loc. 33: -20 RF for loc. 34: -9-23*i_0+23*n_0 RF for loc. 35: -9-23*i_0+23*n_0 RF for loc. 36: -9-23*i_0+23*n_0 RF for loc. 37: -9-23*i_0+23*n_0 RF for loc. 38: -9-23*i_0+23*n_0 RF for loc. 39: -9-23*i_0+23*n_0 RF for loc. 40: -10-23*i_0+23*n_0 RF for loc. 41: -8-23*i_0+23*n_0 RF for loc. 42: -7-23*i_0+23*n_0 RF for loc. 43: -1-23*i_0+23*n_0 RF for loc. 44: -2-23*i_0+23*n_0 RF for loc. 45: -4-23*i_0+23*n_0 RF for loc. 46: -23*i_0+23*n_0 RF for loc. 47: -6-23*i_0+23*n_0 RF for loc. 48: -3-23*i_0+23*n_0 RF for loc. 49: -1-23*i_0+23*n_0 RF for loc. 50: -19 RF for loc. 51: -12-23*i_0+23*n_0 RF for loc. 53: -21 RF for loc. 57: -9-23*i_0+23*n_0 RF for loc. 61: -9-23*i_0+23*n_0 RF for loc. 65: -9-23*i_0+23*n_0 RF for loc. 69: -11-23*i_0+23*n_0 RF for loc. 73: -5-23*i_0+23*n_0 RF for loc. 77: -2-23*i_0+23*n_0 Bound for (chained) transitions 35: -22 Bound for (chained) transitions 36: -20 Bound for (chained) transitions 101: -3 Bound for (chained) transitions 115: -19 Bound for (chained) transitions 116: -18 Bound for (chained) transitions 117: -18 - Rank function 7: RF for loc. 30: 0 RF for loc. 32: -23*j_0+23*n_0 RF for loc. 34: -31-23*j_0+23*n_0 RF for loc. 35: -9-23*j_0+23*n_0 RF for loc. 36: -30-23*j_0+23*n_0 RF for loc. 37: -29-23*j_0+23*n_0 RF for loc. 38: -27-23*j_0+23*n_0 RF for loc. 39: -11-23*j_0+23*n_0 RF for loc. 40: -12-23*j_0+23*n_0 RF for loc. 41: -8-23*j_0+23*n_0 RF for loc. 42: -7-23*j_0+23*n_0 RF for loc. 43: -1-23*j_0+23*n_0 RF for loc. 44: -4-23*j_0+23*n_0 RF for loc. 45: -4-23*j_0+23*n_0 RF for loc. 46: -23*j_0+23*n_0 RF for loc. 47: -6-23*j_0+23*n_0 RF for loc. 48: -3-23*j_0+23*n_0 RF for loc. 49: -1-23*j_0+23*n_0 RF for loc. 51: -14-23*j_0+23*n_0 RF for loc. 53: 1 RF for loc. 57: -31-23*j_0+23*n_0 RF for loc. 61: -28-23*j_0+23*n_0 RF for loc. 65: -10-23*j_0+23*n_0 RF for loc. 69: -13-23*j_0+23*n_0 RF for loc. 73: -5-23*j_0+23*n_0 RF for loc. 77: -2-23*j_0+23*n_0 Bound for (chained) transitions 38: 1 Bound for (chained) transitions 65: -11 - Rank function 8: RF for loc. 32: 0 RF for loc. 34: -4 RF for loc. 35: -9 RF for loc. 36: -2 RF for loc. 37: -1 RF for loc. 38: 1 RF for loc. 39: -11 RF for loc. 40: -12 RF for loc. 41: -8 RF for loc. 42: -7 RF for loc. 43: -1 RF for loc. 44: -2 RF for loc. 45: -4 RF for loc. 46: 0 RF for loc. 47: -6 RF for loc. 48: -3 RF for loc. 49: -1 RF for loc. 51: -14 RF for loc. 57: -3 RF for loc. 61: 0 RF for loc. 65: -10 RF for loc. 69: -13 RF for loc. 73: -5 RF for loc. 77: -2 Bound for (chained) transitions 44: -4 Bound for (chained) transitions 46: -2 Bound for (chained) transitions 48: -3 Bound for (chained) transitions 49: -3 Bound for (chained) transitions 54: -1 Bound for (chained) transitions 56: 1 Bound for (chained) transitions 58: 0 Bound for (chained) transitions 59: 0 Bound for (chained) transitions 64: -11 Bound for (chained) transitions 66: -9 Bound for (chained) transitions 68: -10 Bound for (chained) transitions 69: -10 Bound for (chained) transitions 75: -8 Bound for (chained) transitions 76: -7 Bound for (chained) transitions 77: -7 Bound for (chained) transitions 78, 111: -12 Bound for (chained) transitions 80: -13 Bound for (chained) transitions 81: -13 Bound for (chained) transitions 86: -1 Bound for (chained) transitions 87: -2 Bound for (chained) transitions 88: 0 Bound for (chained) transitions 89: 0 Bound for (chained) transitions 90: 0 Bound for (chained) transitions 92: -6 Bound for (chained) transitions 93: -4 Bound for (chained) transitions 95: -5 Bound for (chained) transitions 96: -5 Bound for (chained) transitions 102: -3 Bound for (chained) transitions 103: -1 Bound for (chained) transitions 105: -2 Bound for (chained) transitions 106: -2 Bound for (chained) transitions 112: 0 Bound for (chained) transitions 113: 0 Bound for (chained) transitions 114: 0 Errors: