YES Termination proof succeeded Initially, performed program simplifications using lexicographic rank functions: * Removed transitions 51, 52, 53, 54, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 80, 81, 82, 83, 84, 85, 88, 89, 90, 92, 93, 98, 99, 108, 110, 111, 116, 117, 118, 120, 121, 126, 127, 128, 130, 131, 136, 137, 139, 140 using the following rank functions: - Rank function 1: RF for loc. 41: -4*i_0+4*n_0 RF for loc. 43: -4*i_0+4*n_0 RF for loc. 44: -4*i_0+4*n_0 RF for loc. 45: -4*i_0+4*n_0 RF for loc. 46: -4*i_0+4*n_0 RF for loc. 47: -4*i_0+4*n_0 RF for loc. 48: -4*i_0+4*n_0 RF for loc. 49: -4*i_0+4*n_0 RF for loc. 50: -4*i_0+4*n_0 RF for loc. 51: -4*i_0+4*n_0 RF for loc. 52: -4-4*i_0+4*n_0 RF for loc. 53: -4*i_0+4*n_0 RF for loc. 54: -1-4*i_0+4*n_0 RF for loc. 55: -4*i_0+4*n_0 RF for loc. 56: -4*i_0+4*n_0 RF for loc. 57: -4*i_0+4*n_0 RF for loc. 58: -4-4*i_0+4*n_0 RF for loc. 59: -4*i_0+4*n_0 RF for loc. 60: -4-4*i_0+4*n_0 RF for loc. 61: -4*i_0+4*n_0 RF for loc. 62: -4*i_0+4*n_0 RF for loc. 69: -4*i_0+4*n_0 RF for loc. 73: -4*i_0+4*n_0 RF for loc. 77: -4*i_0+4*n_0 RF for loc. 85: -4*i_0+4*n_0 RF for loc. 89: -4-4*i_0+4*n_0 RF for loc. 93: -4*i_0+4*n_0 RF for loc. 97: -4*i_0+4*n_0 Bound for (chained) transitions 52: 0 - Rank function 2: RF for loc. 41: -6*i_0+6*n_0 RF for loc. 43: -6*i_0+6*n_0 RF for loc. 44: -6*i_0+6*n_0 RF for loc. 45: -6*i_0+6*n_0 RF for loc. 46: -6*i_0+6*n_0 RF for loc. 47: -6*i_0+6*n_0 RF for loc. 48: -6*i_0+6*n_0 RF for loc. 49: -6*i_0+6*n_0 RF for loc. 50: -6*i_0+6*n_0 RF for loc. 51: -6*i_0+6*n_0 RF for loc. 52: -4-6*i_0+6*n_0 RF for loc. 53: -6*i_0+6*n_0 RF for loc. 54: -3-6*i_0+6*n_0 RF for loc. 55: -2-6*i_0+6*n_0 RF for loc. 56: -2-6*i_0+6*n_0 RF for loc. 57: -6*i_0+6*n_0 RF for loc. 58: -5-6*i_0+6*n_0 RF for loc. 59: -6*i_0+6*n_0 RF for loc. 60: -5-6*i_0+6*n_0 RF for loc. 61: -6*i_0+6*n_0 RF for loc. 62: -6*i_0+6*n_0 RF for loc. 69: -6*i_0+6*n_0 RF for loc. 73: -6*i_0+6*n_0 RF for loc. 77: -2-6*i_0+6*n_0 RF for loc. 85: -6*i_0+6*n_0 RF for loc. 89: -5-6*i_0+6*n_0 RF for loc. 93: -6*i_0+6*n_0 RF for loc. 97: -6*i_0+6*n_0 Bound for (chained) transitions 98: 0 - Rank function 3: RF for loc. 41: 0 RF for loc. 43: 0 RF for loc. 44: 0 RF for loc. 45: 0 RF for loc. 46: 0 RF for loc. 47: 0 RF for loc. 48: 0 RF for loc. 49: 0 RF for loc. 50: 0 RF for loc. 51: 0 RF for loc. 52: 1 RF for loc. 53: 0 RF for loc. 54: 1 RF for loc. 55: 1 RF for loc. 56: 1 RF for loc. 57: 0 RF for loc. 58: 0 RF for loc. 59: 0 RF for loc. 60: 0 RF for loc. 61: 0 RF for loc. 62: 0 RF for loc. 69: 0 RF for loc. 73: 0 RF for loc. 77: 1 RF for loc. 85: 0 RF for loc. 89: 0 RF for loc. 93: 0 RF for loc. 97: 0 Bound for (chained) transitions 83: 1 - Rank function 4: RF for loc. 41: -17-5*i_0-18*j_0-3*k_0 RF for loc. 43: -16-5*i_0-18*j_0-3*k_0 RF for loc. 44: -15-5*i_0-18*j_0-3*k_0 RF for loc. 45: -14-5*i_0-18*j_0-3*k_0 RF for loc. 46: -13-5*i_0-18*j_0-3*k_0 RF for loc. 47: -12-5*i_0-18*j_0-3*k_0 RF for loc. 48: -11-5*i_0-18*j_0-3*k_0 RF for loc. 49: -10-5*i_0-18*j_0-3*k_0 RF for loc. 50: -8-5*i_0-18*j_0-3*k_0 RF for loc. 51: -7-5*i_0-18*j_0-3*k_0 RF for loc. 52: -3+3*j_0-3*k_0 RF for loc. 53: -4-5*i_0-18*j_0-3*k_0 RF for loc. 54: -2+3*j_0-3*k_0 RF for loc. 55: -1+3*j_0-3*k_0 RF for loc. 56: 1+3*j_0-3*k_0 RF for loc. 57: -6-5*i_0-18*j_0-3*k_0 RF for loc. 58: -6-5*i_0-18*j_0-3*k_0 RF for loc. 59: -2-5*i_0-18*j_0-3*k_0 RF for loc. 60: -4-5*i_0-18*j_0-3*k_0 RF for loc. 61: -3-5*i_0-18*j_0-3*k_0 RF for loc. 62: -1-5*i_0-18*j_0-3*k_0 RF for loc. 69: -16-5*i_0-18*j_0-3*k_0 RF for loc. 73: -9-5*i_0-18*j_0-3*k_0 RF for loc. 77: 3*j_0-3*k_0 RF for loc. 85: -5-5*i_0-18*j_0-3*k_0 RF for loc. 89: -5-5*i_0-18*j_0-3*k_0 RF for loc. 93: -3-5*i_0-18*j_0-3*k_0 RF for loc. 97: -5*i_0-18*j_0-3*k_0 Bound for (chained) transitions 89: 2 - Rank function 5: RF for loc. 41: -18-6*i_0-19*j_0-2*k_0 RF for loc. 43: -17-6*i_0-19*j_0-2*k_0 RF for loc. 44: -15-6*i_0-19*j_0-2*k_0 RF for loc. 45: -14-6*i_0-19*j_0-2*k_0 RF for loc. 46: -13-6*i_0-19*j_0-2*k_0 RF for loc. 47: -12-6*i_0-19*j_0-2*k_0 RF for loc. 48: -11-6*i_0-19*j_0-2*k_0 RF for loc. 49: -11-6*i_0-19*j_0-2*k_0 RF for loc. 50: -9-6*i_0-19*j_0-2*k_0 RF for loc. 51: -8-6*i_0-19*j_0-2*k_0 RF for loc. 52: -3 RF for loc. 53: -5-6*i_0-19*j_0-2*k_0 RF for loc. 54: -2 RF for loc. 55: -1 RF for loc. 56: 0 RF for loc. 57: -7-6*i_0-19*j_0-2*k_0 RF for loc. 58: -7-6*i_0-19*j_0-2*k_0 RF for loc. 59: -2-6*i_0-19*j_0-2*k_0 RF for loc. 60: -5-6*i_0-19*j_0-2*k_0 RF for loc. 61: -4-6*i_0-19*j_0-2*k_0 RF for loc. 62: -1-6*i_0-19*j_0-2*k_0 RF for loc. 69: -16-6*i_0-19*j_0-2*k_0 RF for loc. 73: -10-6*i_0-19*j_0-2*k_0 RF for loc. 77: -1 RF for loc. 85: -6-6*i_0-19*j_0-2*k_0 RF for loc. 89: -6-6*i_0-19*j_0-2*k_0 RF for loc. 93: -3-6*i_0-19*j_0-2*k_0 RF for loc. 97: -6*i_0-19*j_0-2*k_0 Bound for (chained) transitions 84: -2 Bound for (chained) transitions 85: -2 Bound for (chained) transitions 88: -1 Bound for (chained) transitions 90: 0 - Rank function 6: RF for loc. 41: -18-6*i_0-19*j_0-3*k_0 RF for loc. 43: -17-6*i_0-19*j_0-3*k_0 RF for loc. 44: -15-6*i_0-19*j_0-3*k_0 RF for loc. 45: -14-6*i_0-19*j_0-3*k_0 RF for loc. 46: -13-6*i_0-19*j_0-3*k_0 RF for loc. 47: -12-6*i_0-19*j_0-3*k_0 RF for loc. 48: -11-6*i_0-19*j_0-3*k_0 RF for loc. 49: -10-6*i_0-19*j_0-3*k_0 RF for loc. 50: -8-6*i_0-19*j_0-3*k_0 RF for loc. 51: -7-6*i_0-19*j_0-3*k_0 RF for loc. 53: -4-6*i_0-19*j_0-3*k_0 RF for loc. 55: 0 RF for loc. 57: -6-6*i_0-19*j_0-3*k_0 RF for loc. 58: -6-6*i_0-19*j_0-3*k_0 RF for loc. 59: -1-6*i_0-19*j_0-3*k_0 RF for loc. 60: -4-6*i_0-19*j_0-3*k_0 RF for loc. 61: -3-6*i_0-19*j_0-3*k_0 RF for loc. 62: -1-6*i_0-19*j_0-3*k_0 RF for loc. 69: -16-6*i_0-19*j_0-3*k_0 RF for loc. 73: -9-6*i_0-19*j_0-3*k_0 RF for loc. 77: 1 RF for loc. 85: -5-6*i_0-19*j_0-3*k_0 RF for loc. 89: -5-6*i_0-19*j_0-3*k_0 RF for loc. 93: -2-6*i_0-19*j_0-3*k_0 RF for loc. 97: -6*i_0-19*j_0-3*k_0 Bound for (chained) transitions 93: 1 - Rank function 7: RF for loc. 41: -18-6*i_0-19*j_0-3*k_0 RF for loc. 43: -17-6*i_0-19*j_0-3*k_0 RF for loc. 44: -15-6*i_0-19*j_0-3*k_0 RF for loc. 45: -14-6*i_0-19*j_0-3*k_0 RF for loc. 46: -13-6*i_0-19*j_0-3*k_0 RF for loc. 47: -12-6*i_0-19*j_0-3*k_0 RF for loc. 48: -11-6*i_0-19*j_0-3*k_0 RF for loc. 49: -10-6*i_0-19*j_0-3*k_0 RF for loc. 50: -8-6*i_0-19*j_0-3*k_0 RF for loc. 51: -7-6*i_0-19*j_0-3*k_0 RF for loc. 53: -4-6*i_0-19*j_0-3*k_0 RF for loc. 55: 0 RF for loc. 57: -6-6*i_0-19*j_0-3*k_0 RF for loc. 58: -6-6*i_0-19*j_0-3*k_0 RF for loc. 59: -1-6*i_0-19*j_0-3*k_0 RF for loc. 60: -4-6*i_0-19*j_0-3*k_0 RF for loc. 61: -3-6*i_0-19*j_0-3*k_0 RF for loc. 62: -1-6*i_0-19*j_0-3*k_0 RF for loc. 69: -16-6*i_0-19*j_0-3*k_0 RF for loc. 73: -9-6*i_0-19*j_0-3*k_0 RF for loc. 77: 1 RF for loc. 85: -5-6*i_0-19*j_0-3*k_0 RF for loc. 89: -5-6*i_0-19*j_0-3*k_0 RF for loc. 93: -2-6*i_0-19*j_0-3*k_0 RF for loc. 97: -6*i_0-19*j_0-3*k_0 Bound for (chained) transitions 92: 1 - Rank function 8: RF for loc. 41: -15+16*imax_0-16*j_0 RF for loc. 43: -14+16*imax_0-16*j_0 RF for loc. 44: -12+16*imax_0-16*j_0 RF for loc. 45: -11+16*imax_0-16*j_0 RF for loc. 46: -10+16*imax_0-16*j_0 RF for loc. 47: -9+16*imax_0-16*j_0 RF for loc. 48: -8+16*imax_0-16*j_0 RF for loc. 49: -7+16*imax_0-16*j_0 RF for loc. 50: -7+16*imax_0-16*j_0 RF for loc. 51: -6+16*imax_0-16*j_0 RF for loc. 53: -3+16*imax_0-16*j_0 RF for loc. 57: -5+16*imax_0-16*j_0 RF for loc. 58: -2+16*imax_0-16*j_0 RF for loc. 59: -2+16*imax_0-16*j_0 RF for loc. 60: -2+16*imax_0-16*j_0 RF for loc. 61: -2+16*imax_0-16*j_0 RF for loc. 62: -1+16*imax_0-16*j_0 RF for loc. 69: -13+16*imax_0-16*j_0 RF for loc. 73: -7+16*imax_0-16*j_0 RF for loc. 85: -4+16*imax_0-16*j_0 RF for loc. 89: -2+16*imax_0-16*j_0 RF for loc. 93: -2+16*imax_0-16*j_0 RF for loc. 97: 16*imax_0-16*j_0 Bound for (chained) transitions 82: 10 - Rank function 9: RF for loc. 41: -11-11*j_0+11*n_0 RF for loc. 43: -11-11*j_0+11*n_0 RF for loc. 44: -10-11*j_0+11*n_0 RF for loc. 45: -10-11*j_0+11*n_0 RF for loc. 46: -9-11*j_0+11*n_0 RF for loc. 47: -8-11*j_0+11*n_0 RF for loc. 48: -7-11*j_0+11*n_0 RF for loc. 49: -6-11*j_0+11*n_0 RF for loc. 50: -6-11*j_0+11*n_0 RF for loc. 51: -5-11*j_0+11*n_0 RF for loc. 53: -2-11*j_0+11*n_0 RF for loc. 57: -4-11*j_0+11*n_0 RF for loc. 58: -1-11*j_0+11*n_0 RF for loc. 59: -1-11*j_0+11*n_0 RF for loc. 60: -1-11*j_0+11*n_0 RF for loc. 61: -1-11*j_0+11*n_0 RF for loc. 62: -11*j_0+11*n_0 RF for loc. 69: -10-11*j_0+11*n_0 RF for loc. 73: -6-11*j_0+11*n_0 RF for loc. 85: -3-11*j_0+11*n_0 RF for loc. 89: -1-11*j_0+11*n_0 RF for loc. 93: -1-11*j_0+11*n_0 RF for loc. 97: -11*j_0+11*n_0 Bound for (chained) transitions 136: 0 - Rank function 10: RF for loc. 41: -10-19*i_0+30*imax_0-11*j_0 RF for loc. 43: -10-19*i_0+30*imax_0-11*j_0 RF for loc. 44: -8-19*i_0+30*imax_0-11*j_0 RF for loc. 45: -7-19*i_0+30*imax_0-11*j_0 RF for loc. 46: -6-19*i_0+30*imax_0-11*j_0 RF for loc. 47: -5-19*i_0+30*imax_0-11*j_0 RF for loc. 48: -4-19*i_0+30*imax_0-11*j_0 RF for loc. 49: 4-19*i_0+30*imax_0-11*j_0 RF for loc. 50: 4-19*i_0+30*imax_0-11*j_0 RF for loc. 51: -3-19*i_0+19*j_0 RF for loc. 53: -2-19*i_0+19*j_0 RF for loc. 57: -3-19*i_0+19*j_0 RF for loc. 58: -18-19*i_0+19*j_0 RF for loc. 59: -19*i_0+19*j_0 RF for loc. 60: -18-19*i_0+19*j_0 RF for loc. 61: -1-19*i_0+19*j_0 RF for loc. 62: -1-19*i_0+30*imax_0-11*j_0 RF for loc. 69: -9-19*i_0+30*imax_0-11*j_0 RF for loc. 73: 4-19*i_0+30*imax_0-11*j_0 RF for loc. 85: -3-19*i_0+19*j_0 RF for loc. 89: -18-19*i_0+19*j_0 RF for loc. 93: -19*i_0+19*j_0 RF for loc. 97: -19*i_0+30*imax_0-11*j_0 Bound for (chained) transitions 127: 18 - Rank function 11: RF for loc. 41: -15+2*i_0+i_post-3*k_0 RF for loc. 43: -14+2*i_0+i_post-3*k_0 RF for loc. 44: -12+2*i_0+i_post-3*k_0 RF for loc. 45: -11+2*i_0+i_post-3*k_0 RF for loc. 46: -10+2*i_0+i_post-3*k_0 RF for loc. 47: -10+2*i_0+i_post-3*k_0 RF for loc. 48: -9+2*i_0+i_post-3*k_0 RF for loc. 49: -8+2*i_0+i_post-3*k_0 RF for loc. 50: -6+2*i_0+i_post-3*k_0 RF for loc. 51: -5+2*i_0+i_post-3*k_0 RF for loc. 53: -2+2*i_0+i_post-3*k_0 RF for loc. 57: -4+2*i_0+i_post-3*k_0 RF for loc. 58: 5+3*i_0-3*k_0 RF for loc. 59: 1+2*i_0+i_post-3*k_0 RF for loc. 60: 7+3*i_0-3*k_0 RF for loc. 61: -1+2*i_0+i_post-3*k_0 RF for loc. 62: -17+2*i_0+i_post-3*k_0 RF for loc. 69: -13+2*i_0+i_post-3*k_0 RF for loc. 73: -7+2*i_0+i_post-3*k_0 RF for loc. 85: -3+2*i_0+i_post-3*k_0 RF for loc. 89: 6+3*i_0-3*k_0 RF for loc. 93: 2*i_0+i_post-3*k_0 RF for loc. 97: -16+2*i_0+i_post-3*k_0 Bound for (chained) transitions 117: 8 - Rank function 12: RF for loc. 41: -12-3*k_0+3*n_0 RF for loc. 43: -11-3*k_0+3*n_0 RF for loc. 44: -9-3*k_0+3*n_0 RF for loc. 45: -8-3*k_0+3*n_0 RF for loc. 46: -8-3*k_0+3*n_0 RF for loc. 47: -7-3*k_0+3*n_0 RF for loc. 48: -6-3*k_0+3*n_0 RF for loc. 49: -5-3*k_0+3*n_0 RF for loc. 50: -3-3*k_0+3*n_0 RF for loc. 51: -2-3*k_0+3*n_0 RF for loc. 53: -2+3*i_0-3*k_0 RF for loc. 57: -4+3*i_0-3*k_0 RF for loc. 58: 5 RF for loc. 59: 1+3*i_0-3*k_0 RF for loc. 60: 7 RF for loc. 61: -1+3*i_0-3*k_0 RF for loc. 62: -14-3*k_0+3*n_0 RF for loc. 69: -10-3*k_0+3*n_0 RF for loc. 73: -4-3*k_0+3*n_0 RF for loc. 85: -3+3*i_0-3*k_0 RF for loc. 89: 6 RF for loc. 93: 3*i_0-3*k_0 RF for loc. 97: -13-3*k_0+3*n_0 Bound for (chained) transitions 70: -5 Bound for (chained) transitions 116: 5 Bound for (chained) transitions 118: 7 Bound for (chained) transitions 120: 6 Bound for (chained) transitions 121: 6 - Rank function 13: RF for loc. 41: -16 RF for loc. 43: -15 RF for loc. 44: -13 RF for loc. 45: -12 RF for loc. 46: -11 RF for loc. 47: -10 RF for loc. 48: -9 RF for loc. 49: -8 RF for loc. 50: -6 RF for loc. 51: -5 RF for loc. 53: -2 RF for loc. 57: -4 RF for loc. 59: 1 RF for loc. 61: -1 RF for loc. 62: -18 RF for loc. 69: -14 RF for loc. 73: -7 RF for loc. 85: -3 RF for loc. 93: 0 RF for loc. 97: -17 Bound for (chained) transitions 51, 137: -16 Bound for (chained) transitions 53: -15 Bound for (chained) transitions 54: -13 Bound for (chained) transitions 56: -14 Bound for (chained) transitions 57: -14 Bound for (chained) transitions 62: -12 Bound for (chained) transitions 63: -11 Bound for (chained) transitions 64: -11 Bound for (chained) transitions 65: -11 Bound for (chained) transitions 66: -10 Bound for (chained) transitions 67: -10 Bound for (chained) transitions 68: -10 Bound for (chained) transitions 69: -9 Bound for (chained) transitions 71: -8 Bound for (chained) transitions 72: -6 Bound for (chained) transitions 74: -7 Bound for (chained) transitions 75: -7 Bound for (chained) transitions 80: -5 Bound for (chained) transitions 81: -5 Bound for (chained) transitions 99: -4 Bound for (chained) transitions 108: -2 Bound for (chained) transitions 110: -3 Bound for (chained) transitions 111: -3 Bound for (chained) transitions 126: -1 Bound for (chained) transitions 128: 1 Bound for (chained) transitions 130: 0 Bound for (chained) transitions 131: 0 Bound for (chained) transitions 139: -17 Bound for (chained) transitions 140: -17 * Removed transitions 41, 42, 43, 45, 46, 86, 100, 102, 103, 145, 146, 147, 148, 149, 150, 151 using the following rank functions: - Rank function 1: RF for loc. 35: 1-5*j_0+5*n_0 RF for loc. 36: -5*j_0+5*n_0 RF for loc. 37: 1-5*j_0+5*n_0 RF for loc. 38: 1-5*j_0+5*n_0 RF for loc. 39: 1-5*j_0+5*n_0 RF for loc. 40: -1-5*j_0+5*n_0 RF for loc. 63: 1-5*j_0+5*n_0 RF for loc. 65: 1-5*j_0+5*n_0 RF for loc. 81: 1-5*j_0+5*n_0 Bound for (chained) transitions 41: 1 - Rank function 2: RF for loc. 35: -4-11*i_0+11*n_0 RF for loc. 36: -11*i_0+11*n_0 RF for loc. 37: -9-11*i_0+11*n_0 RF for loc. 38: -2-11*i_0+11*n_0 RF for loc. 39: -10-11*i_0+11*n_0 RF for loc. 40: -1-11*i_0+11*n_0 RF for loc. 63: -1-11*i_0+11*n_0 RF for loc. 65: -3-11*i_0+11*n_0 RF for loc. 81: -11*i_0+11*n_0 Bound for (chained) transitions 86: -1 - Rank function 3: RF for loc. 35: -4 RF for loc. 36: 0 RF for loc. 37: -5 RF for loc. 38: -2 RF for loc. 39: -6 RF for loc. 40: -1 RF for loc. 63: -8 RF for loc. 65: -3 RF for loc. 81: -7 Bound for (chained) transitions 42: -4 Bound for (chained) transitions 43: -2 Bound for (chained) transitions 45: -3 Bound for (chained) transitions 46: -3 Bound for (chained) transitions 100, 145: -6 Bound for (chained) transitions 102: -7 Bound for (chained) transitions 103: -7 Bound for (chained) transitions 146: -5 Bound for (chained) transitions 147: -5 Bound for (chained) transitions 148: -5 Bound for (chained) transitions 149: -1 Bound for (chained) transitions 150: 0 Bound for (chained) transitions 151: 0 Errors: