YES Termination proof succeeded Initially, performed program simplifications using lexicographic rank functions: * Removed transitions 48, 50, 51, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 71, 72, 73, 74, 76, 77, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 98, 99, 100, 101, 102, 104, 105, 110, 111, 112, 113, 114, 116, 117, 122, 128, 130, 131 using the following rank functions: - Rank function 1: RF for loc. 42: -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: -3-4*i_0+4*n_0 RF for loc. 53: -3-4*i_0+4*n_0 RF for loc. 54: -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: -3-4*i_0+4*n_0 RF for loc. 58: -4*i_0+4*n_0 RF for loc. 59: -2-4*i_0+4*n_0 RF for loc. 60: -4*i_0+4*n_0 RF for loc. 61: -1-4*i_0+4*n_0 RF for loc. 62: -1-4*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: -3-4*i_0+4*n_0 RF for loc. 81: -4*i_0+4*n_0 RF for loc. 85: -1-4*i_0+4*n_0 RF for loc. 89: -4*i_0+4*n_0 RF for loc. 93: -4*i_0+4*n_0 Bound for (chained) transitions 100: 0 - Rank function 2: RF for loc. 42: 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: 0 RF for loc. 53: 0 RF for loc. 54: 0 RF for loc. 55: 0 RF for loc. 56: 0 RF for loc. 57: 1 RF for loc. 58: 0 RF for loc. 59: 2 RF for loc. 60: 0 RF for loc. 61: 2 RF for loc. 62: 2 RF for loc. 69: 0 RF for loc. 73: 0 RF for loc. 77: 0 RF for loc. 81: 0 RF for loc. 85: 2 RF for loc. 89: 0 RF for loc. 93: 0 Bound for (chained) transitions 87: 1 Bound for (chained) transitions 88: 2 Bound for (chained) transitions 89: 2 - Rank function 3: RF for loc. 42: 15-15*i_0-18*j_0-3*k_0 RF for loc. 43: -1-15*i_0-18*j_0-3*k_0 RF for loc. 44: -15*i_0-18*j_0-3*k_0 RF for loc. 45: 2-15*i_0-18*j_0-3*k_0 RF for loc. 46: 3-15*i_0-18*j_0-3*k_0 RF for loc. 47: 4-15*i_0-18*j_0-3*k_0 RF for loc. 48: 15-15*i_0-18*j_0-3*k_0 RF for loc. 49: 13-15*i_0-18*j_0-3*k_0 RF for loc. 50: 5-15*i_0-18*j_0-3*k_0 RF for loc. 51: 6-15*i_0-18*j_0-3*k_0 RF for loc. 52: 13-15*i_0-18*j_0-3*k_0 RF for loc. 53: 11-15*i_0-18*j_0-3*k_0 RF for loc. 54: 7-15*i_0-18*j_0-3*k_0 RF for loc. 55: 8-15*i_0-18*j_0-3*k_0 RF for loc. 56: 9-15*i_0-18*j_0-3*k_0 RF for loc. 58: 12-15*i_0-18*j_0-3*k_0 RF for loc. 59: -1+3*j_0-3*k_0 RF for loc. 60: 10-15*i_0-18*j_0-3*k_0 RF for loc. 61: 3*j_0-3*k_0 RF for loc. 62: 2+3*j_0-3*k_0 RF for loc. 69: 16-15*i_0-18*j_0-3*k_0 RF for loc. 73: 14-15*i_0-18*j_0-3*k_0 RF for loc. 77: 12-15*i_0-18*j_0-3*k_0 RF for loc. 81: 11-15*i_0-18*j_0-3*k_0 RF for loc. 85: 1+3*j_0-3*k_0 RF for loc. 89: 7-15*i_0-18*j_0-3*k_0 RF for loc. 93: 1-15*i_0-18*j_0-3*k_0 Bound for (chained) transitions 99: 3 - Rank function 4: RF for loc. 42: 15-6*i_0-18*j_0-3*k_0 RF for loc. 43: -1-6*i_0-18*j_0-3*k_0 RF for loc. 44: -6*i_0-18*j_0-3*k_0 RF for loc. 45: 1-6*i_0-18*j_0-3*k_0 RF for loc. 46: 2-6*i_0-18*j_0-3*k_0 RF for loc. 47: 4-6*i_0-18*j_0-3*k_0 RF for loc. 48: 15-6*i_0-18*j_0-3*k_0 RF for loc. 49: 13-6*i_0-18*j_0-3*k_0 RF for loc. 50: 5-6*i_0-18*j_0-3*k_0 RF for loc. 51: 6-6*i_0-18*j_0-3*k_0 RF for loc. 52: 12-6*i_0-18*j_0-3*k_0 RF for loc. 53: 10-6*i_0-18*j_0-3*k_0 RF for loc. 54: 7-6*i_0-18*j_0-3*k_0 RF for loc. 55: 9-6*i_0-18*j_0-3*k_0 RF for loc. 56: 10-6*i_0-18*j_0-3*k_0 RF for loc. 58: 13-6*i_0-18*j_0-3*k_0 RF for loc. 59: -1 RF for loc. 60: 11-6*i_0-18*j_0-3*k_0 RF for loc. 61: 0 RF for loc. 62: 1 RF for loc. 69: 16-6*i_0-18*j_0-3*k_0 RF for loc. 73: 14-6*i_0-18*j_0-3*k_0 RF for loc. 77: 11-6*i_0-18*j_0-3*k_0 RF for loc. 81: 12-6*i_0-18*j_0-3*k_0 RF for loc. 85: 0 RF for loc. 89: 8-6*i_0-18*j_0-3*k_0 RF for loc. 93: 1-6*i_0-18*j_0-3*k_0 Bound for (chained) transitions 98: 0 Bound for (chained) transitions 102: 1 - Rank function 5: RF for loc. 42: 15-24*i_0-18*j_0-3*k_0 RF for loc. 43: -1-24*i_0-18*j_0-3*k_0 RF for loc. 44: -24*i_0-18*j_0-3*k_0 RF for loc. 45: 2-24*i_0-18*j_0-3*k_0 RF for loc. 46: 3-24*i_0-18*j_0-3*k_0 RF for loc. 47: 4-24*i_0-18*j_0-3*k_0 RF for loc. 48: 15-24*i_0-18*j_0-3*k_0 RF for loc. 49: 13-24*i_0-18*j_0-3*k_0 RF for loc. 50: 5-24*i_0-18*j_0-3*k_0 RF for loc. 51: 6-24*i_0-18*j_0-3*k_0 RF for loc. 52: -6-24*i_0-18*j_0-3*k_0 RF for loc. 53: -8-24*i_0-18*j_0-3*k_0 RF for loc. 54: 7-24*i_0-18*j_0-3*k_0 RF for loc. 55: 8-24*i_0-18*j_0-3*k_0 RF for loc. 56: 9-24*i_0-18*j_0-3*k_0 RF for loc. 58: 12-24*i_0-18*j_0-3*k_0 RF for loc. 60: 10-24*i_0-18*j_0-3*k_0 RF for loc. 61: -1 RF for loc. 69: 16-24*i_0-18*j_0-3*k_0 RF for loc. 73: 14-24*i_0-18*j_0-3*k_0 RF for loc. 77: -7-24*i_0-18*j_0-3*k_0 RF for loc. 81: 11-24*i_0-18*j_0-3*k_0 RF for loc. 85: 0 RF for loc. 89: 7-24*i_0-18*j_0-3*k_0 RF for loc. 93: 1-24*i_0-18*j_0-3*k_0 Bound for (chained) transitions 104: 0 Bound for (chained) transitions 105: 0 - Rank function 6: RF for loc. 42: -i_0+n_0 RF for loc. 43: -i_0+n_0 RF for loc. 44: -i_0+n_0 RF for loc. 45: -i_0+n_0 RF for loc. 46: -i_0+n_0 RF for loc. 47: -i_0+n_0 RF for loc. 48: -i_0+n_0 RF for loc. 49: -i_0+n_0 RF for loc. 50: -i_0+n_0 RF for loc. 51: -i_0+n_0 RF for loc. 52: -i_0+n_0 RF for loc. 53: -i_0+n_0 RF for loc. 54: -i_0+n_0 RF for loc. 55: -i_0+n_0 RF for loc. 56: -i_0+n_0 RF for loc. 58: -i_0+n_0 RF for loc. 60: -i_0+n_0 RF for loc. 69: -i_0+n_0 RF for loc. 73: -i_0+n_0 RF for loc. 77: -i_0+n_0 RF for loc. 81: -i_0+n_0 RF for loc. 89: -i_0+n_0 RF for loc. 93: -i_0+n_0 Bound for (chained) transitions 57: 0 - Rank function 7: RF for loc. 42: 9+13*imax_0-13*j_0 RF for loc. 43: -2+13*imax_0-13*j_0 RF for loc. 44: -1+13*imax_0-13*j_0 RF for loc. 45: 1+13*imax_0-13*j_0 RF for loc. 46: 2+13*imax_0-13*j_0 RF for loc. 47: 3+13*imax_0-13*j_0 RF for loc. 48: 8+13*imax_0-13*j_0 RF for loc. 49: 8+13*imax_0-13*j_0 RF for loc. 50: 4+13*imax_0-13*j_0 RF for loc. 51: 4+13*imax_0-13*j_0 RF for loc. 52: 8+13*imax_0-13*j_0 RF for loc. 53: 8+13*imax_0-13*j_0 RF for loc. 54: 4+13*imax_0-13*j_0 RF for loc. 55: 4+13*imax_0-13*j_0 RF for loc. 56: 5+13*imax_0-13*j_0 RF for loc. 58: 7+13*imax_0-13*j_0 RF for loc. 60: 6+13*imax_0-13*j_0 RF for loc. 69: 10+13*imax_0-13*j_0 RF for loc. 73: 8+13*imax_0-13*j_0 RF for loc. 77: 8+13*imax_0-13*j_0 RF for loc. 81: 7+13*imax_0-13*j_0 RF for loc. 89: 4+13*imax_0-13*j_0 RF for loc. 93: 13*imax_0-13*j_0 Bound for (chained) transitions 86: 18 - Rank function 8: RF for loc. 42: 10-14*j_0+14*n_0 RF for loc. 43: -2-14*j_0+14*n_0 RF for loc. 44: -1-14*j_0+14*n_0 RF for loc. 45: -14*j_0+14*n_0 RF for loc. 46: 1-14*j_0+14*n_0 RF for loc. 47: 1-14*j_0+14*n_0 RF for loc. 48: 9-14*j_0+14*n_0 RF for loc. 49: 9-14*j_0+14*n_0 RF for loc. 50: 2-14*j_0+14*n_0 RF for loc. 51: 3-14*j_0+14*n_0 RF for loc. 52: 9-14*j_0+14*n_0 RF for loc. 53: 9-14*j_0+14*n_0 RF for loc. 54: 4-14*j_0+14*n_0 RF for loc. 55: 4-14*j_0+14*n_0 RF for loc. 56: 5-14*j_0+14*n_0 RF for loc. 58: 8-14*j_0+14*n_0 RF for loc. 60: 6-14*j_0+14*n_0 RF for loc. 69: 11-14*j_0+14*n_0 RF for loc. 73: 9-14*j_0+14*n_0 RF for loc. 77: 9-14*j_0+14*n_0 RF for loc. 81: 7-14*j_0+14*n_0 RF for loc. 89: 4-14*j_0+14*n_0 RF for loc. 93: -14*j_0+14*n_0 Bound for (chained) transitions 60: 1 Bound for (chained) transitions 122: 10 - Rank function 9: RF for loc. 42: -4-17*k_0+17*n_0 RF for loc. 43: -2-17*k_0+17*n_0 RF for loc. 44: -1-17*k_0+17*n_0 RF for loc. 45: 1-17*k_0+17*n_0 RF for loc. 46: 2-17*k_0+17*n_0 RF for loc. 47: 3-17*k_0+17*n_0 RF for loc. 48: 9-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 49: 9-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 50: 3-17*k_0+17*n_0 RF for loc. 51: 4-17*k_0+17*n_0 RF for loc. 52: 9-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 53: 9-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 54: 5-17*k_0+17*n_0 RF for loc. 55: 7-17*k_0+17*n_0 RF for loc. 56: 5-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 58: 8-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 60: 6-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 69: -3-17*k_0+17*n_0 RF for loc. 73: 9-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 77: 9-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 81: 7-3*imax_0+3*j_0-17*k_0+17*n_0 RF for loc. 89: 6-17*k_0+17*n_0 RF for loc. 93: -17*k_0+17*n_0 Bound for (chained) transitions 82: 5 - Rank function 10: RF for loc. 42: -3 RF for loc. 43: -1 RF for loc. 44: -1 RF for loc. 45: 0 RF for loc. 46: 1 RF for loc. 47: 2 RF for loc. 48: 5 RF for loc. 49: 5 RF for loc. 50: 3 RF for loc. 51: 4 RF for loc. 52: 5 RF for loc. 53: 5 RF for loc. 54: 4 RF for loc. 55: 4 RF for loc. 56: 4 RF for loc. 58: 5 RF for loc. 60: 4 RF for loc. 69: -2 RF for loc. 73: 5 RF for loc. 77: 5 RF for loc. 81: 4 RF for loc. 89: 4 RF for loc. 93: 0 Bound for (chained) transitions 48, 56: -1 Bound for (chained) transitions 50: -2 Bound for (chained) transitions 51: -2 Bound for (chained) transitions 59: 1 Bound for (chained) transitions 61: 2 Bound for (chained) transitions 62: 2 Bound for (chained) transitions 71: 3 Bound for (chained) transitions 72: 3 Bound for (chained) transitions 73: 4 Bound for (chained) transitions 90: 5 Bound for (chained) transitions 130: 0 Bound for (chained) transitions 131: 0 - Rank function 11: RF for loc. 43: -1 RF for loc. 44: 0 RF for loc. 45: 1 RF for loc. 48: 2-7*i_0+7*j_0 RF for loc. 49: -7*i_0+7*j_0 RF for loc. 51: -2 RF for loc. 52: -4-7*i_0+7*j_0 RF for loc. 53: -4-7*i_0+7*j_0 RF for loc. 54: -1 RF for loc. 55: 1 RF for loc. 56: 2 RF for loc. 58: -1-7*i_0+7*j_0 RF for loc. 60: 3 RF for loc. 73: 1-7*i_0+7*j_0 RF for loc. 77: -4-7*i_0+7*j_0 RF for loc. 81: 4 RF for loc. 89: 0 RF for loc. 93: 0 Bound for (chained) transitions 58: 0 Bound for (chained) transitions 83: -1 Bound for (chained) transitions 84: 2 Bound for (chained) transitions 85: 2 Bound for (chained) transitions 92: 4 Bound for (chained) transitions 93: 4 Bound for (chained) transitions 101: 3 Bound for (chained) transitions 113: 7 Bound for (chained) transitions 114: 1 Bound for (chained) transitions 116: 0 Bound for (chained) transitions 117: 0 Bound for (chained) transitions 128: 1 - Rank function 12: RF for loc. 48: -1 RF for loc. 49: -2 RF for loc. 52: 0 RF for loc. 53: 0 RF for loc. 58: -3 RF for loc. 73: -2 RF for loc. 77: 0 Bound for (chained) transitions 63: -1 Bound for (chained) transitions 110: 0 Bound for (chained) transitions 112: -2 - Rank function 13: RF for loc. 49: -1 RF for loc. 52: 1+2*i_0-2*k_0 RF for loc. 53: 2*i_0-2*k_0 RF for loc. 73: 0 RF for loc. 77: 2*i_0-2*k_0 Bound for (chained) transitions 66: 0 Bound for (chained) transitions 111: 2 - Rank function 14: RF for loc. 49: 0 RF for loc. 52: 1 RF for loc. 53: -1 RF for loc. 73: 1 RF for loc. 77: 0 Bound for (chained) transitions 65: 1 Bound for (chained) transitions 74: 1 Bound for (chained) transitions 76: 0 Bound for (chained) transitions 77: 0 * Removed transitions 40, 42, 43, 123, 124, 125, 126, 127, 136, 137, 138, 139, 140, 142, 144, 145 using the following rank functions: - Rank function 1: RF for loc. 35: -2-10*i_0+10*n_0 RF for loc. 36: -2-10*i_0+10*n_0 RF for loc. 37: -9-10*i_0+10*n_0 RF for loc. 38: -8-10*i_0+10*n_0 RF for loc. 39: -2-10*i_0+10*n_0 RF for loc. 40: -2-10*i_0+10*n_0 RF for loc. 64: -1-10*i_0+10*n_0 RF for loc. 65: -2-10*i_0+10*n_0 RF for loc. 97: -10*i_0+10*n_0 Bound for (chained) transitions 140: -1 - Rank function 2: RF for loc. 35: 0 RF for loc. 36: 0 RF for loc. 37: -2 RF for loc. 38: -1 RF for loc. 39: 0 RF for loc. 40: 0 RF for loc. 64: -4 RF for loc. 65: 0 RF for loc. 97: -3 Bound for (chained) transitions 123, 142: -2 Bound for (chained) transitions 124: -1 Bound for (chained) transitions 125: -1 Bound for (chained) transitions 126: -1 Bound for (chained) transitions 139: 0 Bound for (chained) transitions 144: -3 Bound for (chained) transitions 145: -3 - Rank function 3: RF for loc. 35: 2-7*j_0+7*n_0 RF for loc. 36: -7*j_0+7*n_0 RF for loc. 39: -4-7*j_0+7*n_0 RF for loc. 40: -3-7*j_0+7*n_0 RF for loc. 65: 1-7*j_0+7*n_0 Bound for (chained) transitions 138: 0 - Rank function 4: RF for loc. 35: -1 RF for loc. 36: -3 RF for loc. 39: 0 RF for loc. 40: 1 RF for loc. 65: -2 Bound for (chained) transitions 40: -1 Bound for (chained) transitions 42: -2 Bound for (chained) transitions 43: -2 Bound for (chained) transitions 127: 0 Bound for (chained) transitions 136: 1 Bound for (chained) transitions 137: 1 Errors: