YES Termination proof succeeded Initially, performed program simplifications using lexicographic rank functions: * Removed transitions 30, 31, 32, 34, 35, 40, 41, 42, 43, 44, 46, 47, 52, 53, 54, 56, 57, 62, 63, 64, 65, 66, 67, 68, 70, 71, 76, 77, 78, 79, 80, 81, 82, 84, 85, 90, 92, 93, 98, 99, 100, 102, 103, 108, 109, 110, 111, 112, 113 using the following rank functions: - Rank function 1: RF for loc. 27: -10*m_0+10*n_0 RF for loc. 28: -10*m_0+10*n_0 RF for loc. 29: -1-10*m_0+10*n_0 RF for loc. 30: -10*m_0+10*n_0 RF for loc. 31: -7-10*m_0+10*n_0 RF for loc. 32: -6-10*m_0+10*n_0 RF for loc. 33: -6-10*m_0+10*n_0 RF for loc. 34: -6-10*m_0+10*n_0 RF for loc. 35: -6-10*m_0+10*n_0 RF for loc. 36: -6-10*m_0+10*n_0 RF for loc. 37: -6-10*m_0+10*n_0 RF for loc. 38: -6-10*m_0+10*n_0 RF for loc. 39: -6-10*m_0+10*n_0 RF for loc. 40: -6-10*m_0+10*n_0 RF for loc. 41: -3-10*m_0+10*n_0 RF for loc. 42: -2-10*m_0+10*n_0 RF for loc. 43: -2-10*m_0+10*n_0 RF for loc. 44: -2-10*m_0+10*n_0 RF for loc. 45: -2-10*m_0+10*n_0 RF for loc. 46: -10*m_0+10*n_0 RF for loc. 48: 1-10*m_0+10*n_0 RF for loc. 49: -10*m_0+10*n_0 RF for loc. 53: -6-10*m_0+10*n_0 RF for loc. 57: -6-10*m_0+10*n_0 RF for loc. 61: -6-10*m_0+10*n_0 RF for loc. 65: -2-10*m_0+10*n_0 RF for loc. 69: 2-10*m_0+10*n_0 RF for loc. 73: -2-10*m_0+10*n_0 Bound for (chained) transitions 79: 11 - Rank function 2: RF for loc. 27: 1-20*j_0+20*n_0 RF for loc. 28: -20*j_0+20*n_0 RF for loc. 29: -20*j_0+20*n_0 RF for loc. 30: 3-20*j_0+20*n_0 RF for loc. 31: -7-20*j_0+20*n_0 RF for loc. 32: -6-20*j_0+20*n_0 RF for loc. 33: -6-20*j_0+20*n_0 RF for loc. 34: -6-20*j_0+20*n_0 RF for loc. 35: -6-20*j_0+20*n_0 RF for loc. 36: -6-20*j_0+20*n_0 RF for loc. 37: -6-20*j_0+20*n_0 RF for loc. 38: -6-20*j_0+20*n_0 RF for loc. 39: -6-20*j_0+20*n_0 RF for loc. 40: -6-20*j_0+20*n_0 RF for loc. 41: -5-20*j_0+20*n_0 RF for loc. 42: -4-20*j_0+20*n_0 RF for loc. 43: -3-20*j_0+20*n_0 RF for loc. 44: -2-20*j_0+20*n_0 RF for loc. 45: -20*j_0+20*n_0 RF for loc. 46: -1-20*j_0+20*n_0 RF for loc. 48: -8-20*j_0+20*n_0 RF for loc. 49: 2-20*j_0+20*n_0 RF for loc. 53: -6-20*j_0+20*n_0 RF for loc. 57: -6-20*j_0+20*n_0 RF for loc. 61: -6-20*j_0+20*n_0 RF for loc. 65: -4-20*j_0+20*n_0 RF for loc. 69: -7-20*j_0+20*n_0 RF for loc. 73: -1-20*j_0+20*n_0 Bound for (chained) transitions 42: -6 Bound for (chained) transitions 52: -6 Bound for (chained) transitions 98: -2 - Rank function 3: RF for loc. 27: 13-16*j_0+16*n_0 RF for loc. 28: -16*j_0+16*n_0 RF for loc. 29: -16*j_0+16*n_0 RF for loc. 30: 15-16*j_0+16*n_0 RF for loc. 31: -21-16*j_0+16*n_0 RF for loc. 32: -21-16*j_0+16*n_0 RF for loc. 33: -21-16*j_0+16*n_0 RF for loc. 34: -21-16*j_0+16*n_0 RF for loc. 35: -21-16*j_0+16*n_0 RF for loc. 36: -21-16*j_0+16*n_0 RF for loc. 37: -21-16*j_0+16*n_0 RF for loc. 38: -21-16*j_0+16*n_0 RF for loc. 39: -21-16*j_0+16*n_0 RF for loc. 40: -21-16*j_0+16*n_0 RF for loc. 41: -21-16*j_0+16*n_0 RF for loc. 42: -20-16*j_0+16*n_0 RF for loc. 43: -4-16*j_0+16*n_0 RF for loc. 44: -3-16*j_0+16*n_0 RF for loc. 45: -1-16*j_0+16*n_0 RF for loc. 46: -1-16*j_0+16*n_0 RF for loc. 48: -23-16*j_0+16*n_0 RF for loc. 49: 14-16*j_0+16*n_0 RF for loc. 53: -21-16*j_0+16*n_0 RF for loc. 57: -21-16*j_0+16*n_0 RF for loc. 61: -21-16*j_0+16*n_0 RF for loc. 65: -5-16*j_0+16*n_0 RF for loc. 69: -22-16*j_0+16*n_0 RF for loc. 73: -2-16*j_0+16*n_0 Bound for (chained) transitions 30: 13 - Rank function 4: RF for loc. 27: -4 RF for loc. 28: 0 RF for loc. 29: 13-18*j_0+18*n_0 RF for loc. 30: -2 RF for loc. 31: 6-18*j_0+18*n_0 RF for loc. 32: 6-18*j_0+18*n_0 RF for loc. 33: 6-18*j_0+18*n_0 RF for loc. 34: 6-18*j_0+18*n_0 RF for loc. 35: 6-18*j_0+18*n_0 RF for loc. 36: 6-18*j_0+18*n_0 RF for loc. 37: 6-18*j_0+18*n_0 RF for loc. 38: 6-18*j_0+18*n_0 RF for loc. 39: 6-18*j_0+18*n_0 RF for loc. 40: 6-18*j_0+18*n_0 RF for loc. 41: 6-18*j_0+18*n_0 RF for loc. 42: 7-18*j_0+18*n_0 RF for loc. 43: 9-18*j_0+18*n_0 RF for loc. 44: 10-18*j_0+18*n_0 RF for loc. 45: 12-18*j_0+18*n_0 RF for loc. 46: -1 RF for loc. 48: 4-18*j_0+18*n_0 RF for loc. 49: -3 RF for loc. 53: 6-18*j_0+18*n_0 RF for loc. 57: 6-18*j_0+18*n_0 RF for loc. 61: 6-18*j_0+18*n_0 RF for loc. 65: 8-18*j_0+18*n_0 RF for loc. 69: 5-18*j_0+18*n_0 RF for loc. 73: 11-18*j_0+18*n_0 Bound for (chained) transitions 31: -4 Bound for (chained) transitions 32: -2 Bound for (chained) transitions 34: -3 Bound for (chained) transitions 80: 7 Bound for (chained) transitions 111: -1 Bound for (chained) transitions 112: 0 Bound for (chained) transitions 113: 0 - Rank function 5: RF for loc. 27: -1 RF for loc. 29: -18*i_0+18*m_0 RF for loc. 31: -10-18*i_0+18*m_0 RF for loc. 32: -25-18*i_0+18*m_0 RF for loc. 33: -8-18*i_0+18*m_0 RF for loc. 34: -24-18*i_0+18*m_0 RF for loc. 35: -23-18*i_0+18*m_0 RF for loc. 36: -22-18*i_0+18*m_0 RF for loc. 37: -20-18*i_0+18*m_0 RF for loc. 38: -19-18*i_0+18*m_0 RF for loc. 39: -18-18*i_0+18*m_0 RF for loc. 40: -10-18*i_0+18*m_0 RF for loc. 41: -7-18*i_0+18*m_0 RF for loc. 42: -6-18*i_0+18*m_0 RF for loc. 43: -4-18*i_0+18*m_0 RF for loc. 44: -3-18*i_0+18*m_0 RF for loc. 45: -1-18*i_0+18*m_0 RF for loc. 48: -30-18*i_0+18*m_0 RF for loc. 49: 0 RF for loc. 53: -23-18*i_0+18*m_0 RF for loc. 57: -21-18*i_0+18*m_0 RF for loc. 61: -9-18*i_0+18*m_0 RF for loc. 65: -5-18*i_0+18*m_0 RF for loc. 69: -29-18*i_0+18*m_0 RF for loc. 73: -2-18*i_0+18*m_0 Bound for (chained) transitions 35: 0 Bound for (chained) transitions 108: 0 Bound for (chained) transitions 110: 18 - Rank function 6: RF for loc. 29: 0 RF for loc. 31: 8-18*i_0-j_0+18*m_0+n_0 RF for loc. 32: -6-18*i_0-j_0+18*m_0+n_0 RF for loc. 33: 11-18*i_0-j_0+18*m_0+n_0 RF for loc. 34: -5-18*i_0-j_0+18*m_0+n_0 RF for loc. 35: -3-18*i_0-j_0+18*m_0+n_0 RF for loc. 36: -2-18*i_0-j_0+18*m_0+n_0 RF for loc. 37: -18*i_0-j_0+18*m_0+n_0 RF for loc. 38: 1-18*i_0-j_0+18*m_0+n_0 RF for loc. 39: 2-18*i_0-j_0+18*m_0+n_0 RF for loc. 40: 9-18*i_0-j_0+18*m_0+n_0 RF for loc. 41: 12-18*i_0-j_0+18*m_0+n_0 RF for loc. 42: 12-18*i_0+18*m_0 RF for loc. 43: 14-18*i_0+18*m_0 RF for loc. 44: 15-18*i_0+18*m_0 RF for loc. 45: 17-18*i_0+18*m_0 RF for loc. 48: -12-18*i_0-j_0+18*m_0+n_0 RF for loc. 53: -4-18*i_0-j_0+18*m_0+n_0 RF for loc. 57: -1-18*i_0-j_0+18*m_0+n_0 RF for loc. 61: 10-18*i_0-j_0+18*m_0+n_0 RF for loc. 65: 13-18*i_0+18*m_0 RF for loc. 69: -11-18*i_0-j_0+18*m_0+n_0 RF for loc. 73: 16-18*i_0+18*m_0 Bound for (chained) transitions 109: 0 - Rank function 7: RF for loc. 31: -9-19*i_0+19*n_0 RF for loc. 32: -24-19*i_0+19*n_0 RF for loc. 33: -6-19*i_0+19*n_0 RF for loc. 34: -23-19*i_0+19*n_0 RF for loc. 35: -21-19*i_0+19*n_0 RF for loc. 36: -20-19*i_0+19*n_0 RF for loc. 37: -18-19*i_0+19*n_0 RF for loc. 38: -17-19*i_0+19*n_0 RF for loc. 39: -16-19*i_0+19*n_0 RF for loc. 40: -8-19*i_0+19*n_0 RF for loc. 41: -5-19*i_0+19*n_0 RF for loc. 42: -4-19*i_0+19*n_0 RF for loc. 43: -2-19*i_0+19*n_0 RF for loc. 44: -1-19*i_0+19*n_0 RF for loc. 45: 1-19*i_0+19*n_0 RF for loc. 48: -11-19*i_0+19*n_0 RF for loc. 53: -22-19*i_0+19*n_0 RF for loc. 57: -19-19*i_0+19*n_0 RF for loc. 61: -7-19*i_0+19*n_0 RF for loc. 65: -3-19*i_0+19*n_0 RF for loc. 69: -10-19*i_0+19*n_0 RF for loc. 73: -19*i_0+19*n_0 Bound for (chained) transitions 66: -8 - Rank function 8: RF for loc. 31: -9 RF for loc. 32: -5 RF for loc. 33: -6 RF for loc. 34: -4 RF for loc. 35: -2 RF for loc. 36: -1 RF for loc. 37: 1 RF for loc. 38: 2 RF for loc. 39: 3 RF for loc. 40: -8 RF for loc. 41: -5 RF for loc. 42: -4 RF for loc. 43: -2 RF for loc. 44: -1 RF for loc. 45: 1 RF for loc. 48: -11 RF for loc. 53: -3 RF for loc. 57: 0 RF for loc. 61: -7 RF for loc. 65: -3 RF for loc. 69: -10 RF for loc. 73: 0 Bound for (chained) transitions 40, 90: -9 Bound for (chained) transitions 41: -5 Bound for (chained) transitions 43: -4 Bound for (chained) transitions 44: -2 Bound for (chained) transitions 46: -3 Bound for (chained) transitions 47: -3 Bound for (chained) transitions 53: -1 Bound for (chained) transitions 54: 1 Bound for (chained) transitions 56: 0 Bound for (chained) transitions 57: 0 Bound for (chained) transitions 62: 2 Bound for (chained) transitions 63: 3 Bound for (chained) transitions 64: 3 Bound for (chained) transitions 65: 3 Bound for (chained) transitions 67: -8 Bound for (chained) transitions 68: -6 Bound for (chained) transitions 70: -7 Bound for (chained) transitions 71: -7 Bound for (chained) transitions 76: -5 Bound for (chained) transitions 77: -5 Bound for (chained) transitions 78: -5 Bound for (chained) transitions 81: -4 Bound for (chained) transitions 82: -2 Bound for (chained) transitions 84: -3 Bound for (chained) transitions 85: -3 Bound for (chained) transitions 92: -10 Bound for (chained) transitions 93: -10 Bound for (chained) transitions 99: -1 Bound for (chained) transitions 100: 1 Bound for (chained) transitions 102: 0 Bound for (chained) transitions 103: 0 Errors: