NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l14 0: l0 -> l1 : Result_4^0'=Result_4^post_1, tmp_8^0'=tmp_8^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, z_7^0'=z_7^post_1, [ Result_4^0==Result_4^post_1 && tmp_8^0==tmp_8^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 && z_7^0==z_7^post_1 ], cost: 1 8: l1 -> l7 : Result_4^0'=Result_4^post_9, tmp_8^0'=tmp_8^post_9, x_5^0'=x_5^post_9, y_6^0'=y_6^post_9, z_7^0'=z_7^post_9, [ 0<=-1-x_5^0+y_6^0 && Result_4^0==Result_4^post_9 && tmp_8^0==tmp_8^post_9 && x_5^0==x_5^post_9 && y_6^0==y_6^post_9 && z_7^0==z_7^post_9 ], cost: 1 9: l1 -> l8 : Result_4^0'=Result_4^post_10, tmp_8^0'=tmp_8^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, z_7^0'=z_7^post_10, [ -x_5^0+y_6^0<=0 && Result_4^post_10==Result_4^post_10 && tmp_8^0==tmp_8^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 && z_7^0==z_7^post_10 ], cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post_2, tmp_8^0'=tmp_8^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, z_7^0'=z_7^post_2, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_2==tmp_8^post_2 && tmp_8^post_2<=0 && 0<=tmp_8^post_2 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 && z_7^0==z_7^post_2 ], cost: 1 2: l2 -> l5 : Result_4^0'=Result_4^post_3, tmp_8^0'=tmp_8^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, z_7^0'=z_7^post_3, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_3==tmp_8^post_3 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 && z_7^0==z_7^post_3 ], cost: 1 7: l2 -> l1 : Result_4^0'=Result_4^post_8, tmp_8^0'=tmp_8^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, z_7^0'=z_7^post_8, [ z_7^0-y_6^0<=0 && x_5^post_8==1+x_5^0 && Result_4^0==Result_4^post_8 && tmp_8^0==tmp_8^post_8 && y_6^0==y_6^post_8 && z_7^0==z_7^post_8 ], cost: 1 16: l3 -> l11 : Result_4^0'=Result_4^post_17, tmp_8^0'=tmp_8^post_17, x_5^0'=x_5^post_17, y_6^0'=y_6^post_17, z_7^0'=z_7^post_17, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_17==tmp_8^post_17 && tmp_8^post_17<=0 && 0<=tmp_8^post_17 && Result_4^0==Result_4^post_17 && x_5^0==x_5^post_17 && y_6^0==y_6^post_17 && z_7^0==z_7^post_17 ], cost: 1 18: l3 -> l12 : Result_4^0'=Result_4^post_19, tmp_8^0'=tmp_8^post_19, x_5^0'=x_5^post_19, y_6^0'=y_6^post_19, z_7^0'=z_7^post_19, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_19==tmp_8^post_19 && Result_4^0==Result_4^post_19 && x_5^0==x_5^post_19 && y_6^0==y_6^post_19 && z_7^0==z_7^post_19 ], cost: 1 3: l5 -> l6 : Result_4^0'=Result_4^post_4, tmp_8^0'=tmp_8^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, z_7^0'=z_7^post_4, [ 1+tmp_8^0<=0 && Result_4^0==Result_4^post_4 && tmp_8^0==tmp_8^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 && z_7^0==z_7^post_4 ], cost: 1 4: l5 -> l6 : Result_4^0'=Result_4^post_5, tmp_8^0'=tmp_8^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, z_7^0'=z_7^post_5, [ 1<=tmp_8^0 && Result_4^0==Result_4^post_5 && tmp_8^0==tmp_8^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 && z_7^0==z_7^post_5 ], cost: 1 5: l6 -> l4 : Result_4^0'=Result_4^post_6, tmp_8^0'=tmp_8^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, z_7^0'=z_7^post_6, [ y_6^post_6==1+y_6^0 && Result_4^0==Result_4^post_6 && tmp_8^0==tmp_8^post_6 && x_5^0==x_5^post_6 && z_7^0==z_7^post_6 ], cost: 1 6: l4 -> l2 : Result_4^0'=Result_4^post_7, tmp_8^0'=tmp_8^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, z_7^0'=z_7^post_7, [ Result_4^0==Result_4^post_7 && tmp_8^0==tmp_8^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 && z_7^0==z_7^post_7 ], cost: 1 10: l7 -> l3 : Result_4^0'=Result_4^post_11, tmp_8^0'=tmp_8^post_11, x_5^0'=x_5^post_11, y_6^0'=y_6^post_11, z_7^0'=z_7^post_11, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_11==tmp_8^post_11 && tmp_8^post_11<=0 && 0<=tmp_8^post_11 && Result_4^0==Result_4^post_11 && x_5^0==x_5^post_11 && y_6^0==y_6^post_11 && z_7^0==z_7^post_11 ], cost: 1 11: l7 -> l9 : Result_4^0'=Result_4^post_12, tmp_8^0'=tmp_8^post_12, x_5^0'=x_5^post_12, y_6^0'=y_6^post_12, z_7^0'=z_7^post_12, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_12==tmp_8^post_12 && Result_4^0==Result_4^post_12 && x_5^0==x_5^post_12 && y_6^0==y_6^post_12 && z_7^0==z_7^post_12 ], cost: 1 15: l7 -> l1 : Result_4^0'=Result_4^post_16, tmp_8^0'=tmp_8^post_16, x_5^0'=x_5^post_16, y_6^0'=y_6^post_16, z_7^0'=z_7^post_16, [ z_7^0-y_6^0<=0 && x_5^post_16==1+x_5^0 && Result_4^0==Result_4^post_16 && tmp_8^0==tmp_8^post_16 && y_6^0==y_6^post_16 && z_7^0==z_7^post_16 ], cost: 1 12: l9 -> l10 : Result_4^0'=Result_4^post_13, tmp_8^0'=tmp_8^post_13, x_5^0'=x_5^post_13, y_6^0'=y_6^post_13, z_7^0'=z_7^post_13, [ 1+tmp_8^0<=0 && Result_4^0==Result_4^post_13 && tmp_8^0==tmp_8^post_13 && x_5^0==x_5^post_13 && y_6^0==y_6^post_13 && z_7^0==z_7^post_13 ], cost: 1 13: l9 -> l10 : Result_4^0'=Result_4^post_14, tmp_8^0'=tmp_8^post_14, x_5^0'=x_5^post_14, y_6^0'=y_6^post_14, z_7^0'=z_7^post_14, [ 1<=tmp_8^0 && Result_4^0==Result_4^post_14 && tmp_8^0==tmp_8^post_14 && x_5^0==x_5^post_14 && y_6^0==y_6^post_14 && z_7^0==z_7^post_14 ], cost: 1 14: l10 -> l2 : Result_4^0'=Result_4^post_15, tmp_8^0'=tmp_8^post_15, x_5^0'=x_5^post_15, y_6^0'=y_6^post_15, z_7^0'=z_7^post_15, [ y_6^post_15==1+y_6^0 && Result_4^0==Result_4^post_15 && tmp_8^0==tmp_8^post_15 && x_5^0==x_5^post_15 && z_7^0==z_7^post_15 ], cost: 1 17: l11 -> l3 : Result_4^0'=Result_4^post_18, tmp_8^0'=tmp_8^post_18, x_5^0'=x_5^post_18, y_6^0'=y_6^post_18, z_7^0'=z_7^post_18, [ Result_4^0==Result_4^post_18 && tmp_8^0==tmp_8^post_18 && x_5^0==x_5^post_18 && y_6^0==y_6^post_18 && z_7^0==z_7^post_18 ], cost: 1 19: l12 -> l13 : Result_4^0'=Result_4^post_20, tmp_8^0'=tmp_8^post_20, x_5^0'=x_5^post_20, y_6^0'=y_6^post_20, z_7^0'=z_7^post_20, [ 1+tmp_8^0<=0 && Result_4^0==Result_4^post_20 && tmp_8^0==tmp_8^post_20 && x_5^0==x_5^post_20 && y_6^0==y_6^post_20 && z_7^0==z_7^post_20 ], cost: 1 20: l12 -> l13 : Result_4^0'=Result_4^post_21, tmp_8^0'=tmp_8^post_21, x_5^0'=x_5^post_21, y_6^0'=y_6^post_21, z_7^0'=z_7^post_21, [ 1<=tmp_8^0 && Result_4^0==Result_4^post_21 && tmp_8^0==tmp_8^post_21 && x_5^0==x_5^post_21 && y_6^0==y_6^post_21 && z_7^0==z_7^post_21 ], cost: 1 21: l13 -> l2 : Result_4^0'=Result_4^post_22, tmp_8^0'=tmp_8^post_22, x_5^0'=x_5^post_22, y_6^0'=y_6^post_22, z_7^0'=z_7^post_22, [ y_6^post_22==1+y_6^0 && Result_4^0==Result_4^post_22 && tmp_8^0==tmp_8^post_22 && x_5^0==x_5^post_22 && z_7^0==z_7^post_22 ], cost: 1 22: l14 -> l0 : Result_4^0'=Result_4^post_23, tmp_8^0'=tmp_8^post_23, x_5^0'=x_5^post_23, y_6^0'=y_6^post_23, z_7^0'=z_7^post_23, [ Result_4^0==Result_4^post_23 && tmp_8^0==tmp_8^post_23 && x_5^0==x_5^post_23 && y_6^0==y_6^post_23 && z_7^0==z_7^post_23 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 22: l14 -> l0 : Result_4^0'=Result_4^post_23, tmp_8^0'=tmp_8^post_23, x_5^0'=x_5^post_23, y_6^0'=y_6^post_23, z_7^0'=z_7^post_23, [ Result_4^0==Result_4^post_23 && tmp_8^0==tmp_8^post_23 && x_5^0==x_5^post_23 && y_6^0==y_6^post_23 && z_7^0==z_7^post_23 ], cost: 1 Removed unreachable and leaf rules: Start location: l14 0: l0 -> l1 : Result_4^0'=Result_4^post_1, tmp_8^0'=tmp_8^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, z_7^0'=z_7^post_1, [ Result_4^0==Result_4^post_1 && tmp_8^0==tmp_8^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 && z_7^0==z_7^post_1 ], cost: 1 8: l1 -> l7 : Result_4^0'=Result_4^post_9, tmp_8^0'=tmp_8^post_9, x_5^0'=x_5^post_9, y_6^0'=y_6^post_9, z_7^0'=z_7^post_9, [ 0<=-1-x_5^0+y_6^0 && Result_4^0==Result_4^post_9 && tmp_8^0==tmp_8^post_9 && x_5^0==x_5^post_9 && y_6^0==y_6^post_9 && z_7^0==z_7^post_9 ], cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post_2, tmp_8^0'=tmp_8^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, z_7^0'=z_7^post_2, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_2==tmp_8^post_2 && tmp_8^post_2<=0 && 0<=tmp_8^post_2 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 && z_7^0==z_7^post_2 ], cost: 1 2: l2 -> l5 : Result_4^0'=Result_4^post_3, tmp_8^0'=tmp_8^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, z_7^0'=z_7^post_3, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_3==tmp_8^post_3 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 && z_7^0==z_7^post_3 ], cost: 1 7: l2 -> l1 : Result_4^0'=Result_4^post_8, tmp_8^0'=tmp_8^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, z_7^0'=z_7^post_8, [ z_7^0-y_6^0<=0 && x_5^post_8==1+x_5^0 && Result_4^0==Result_4^post_8 && tmp_8^0==tmp_8^post_8 && y_6^0==y_6^post_8 && z_7^0==z_7^post_8 ], cost: 1 16: l3 -> l11 : Result_4^0'=Result_4^post_17, tmp_8^0'=tmp_8^post_17, x_5^0'=x_5^post_17, y_6^0'=y_6^post_17, z_7^0'=z_7^post_17, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_17==tmp_8^post_17 && tmp_8^post_17<=0 && 0<=tmp_8^post_17 && Result_4^0==Result_4^post_17 && x_5^0==x_5^post_17 && y_6^0==y_6^post_17 && z_7^0==z_7^post_17 ], cost: 1 18: l3 -> l12 : Result_4^0'=Result_4^post_19, tmp_8^0'=tmp_8^post_19, x_5^0'=x_5^post_19, y_6^0'=y_6^post_19, z_7^0'=z_7^post_19, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_19==tmp_8^post_19 && Result_4^0==Result_4^post_19 && x_5^0==x_5^post_19 && y_6^0==y_6^post_19 && z_7^0==z_7^post_19 ], cost: 1 3: l5 -> l6 : Result_4^0'=Result_4^post_4, tmp_8^0'=tmp_8^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, z_7^0'=z_7^post_4, [ 1+tmp_8^0<=0 && Result_4^0==Result_4^post_4 && tmp_8^0==tmp_8^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 && z_7^0==z_7^post_4 ], cost: 1 4: l5 -> l6 : Result_4^0'=Result_4^post_5, tmp_8^0'=tmp_8^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, z_7^0'=z_7^post_5, [ 1<=tmp_8^0 && Result_4^0==Result_4^post_5 && tmp_8^0==tmp_8^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 && z_7^0==z_7^post_5 ], cost: 1 5: l6 -> l4 : Result_4^0'=Result_4^post_6, tmp_8^0'=tmp_8^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, z_7^0'=z_7^post_6, [ y_6^post_6==1+y_6^0 && Result_4^0==Result_4^post_6 && tmp_8^0==tmp_8^post_6 && x_5^0==x_5^post_6 && z_7^0==z_7^post_6 ], cost: 1 6: l4 -> l2 : Result_4^0'=Result_4^post_7, tmp_8^0'=tmp_8^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, z_7^0'=z_7^post_7, [ Result_4^0==Result_4^post_7 && tmp_8^0==tmp_8^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 && z_7^0==z_7^post_7 ], cost: 1 10: l7 -> l3 : Result_4^0'=Result_4^post_11, tmp_8^0'=tmp_8^post_11, x_5^0'=x_5^post_11, y_6^0'=y_6^post_11, z_7^0'=z_7^post_11, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_11==tmp_8^post_11 && tmp_8^post_11<=0 && 0<=tmp_8^post_11 && Result_4^0==Result_4^post_11 && x_5^0==x_5^post_11 && y_6^0==y_6^post_11 && z_7^0==z_7^post_11 ], cost: 1 11: l7 -> l9 : Result_4^0'=Result_4^post_12, tmp_8^0'=tmp_8^post_12, x_5^0'=x_5^post_12, y_6^0'=y_6^post_12, z_7^0'=z_7^post_12, [ 0<=-1+z_7^0-y_6^0 && tmp_8^post_12==tmp_8^post_12 && Result_4^0==Result_4^post_12 && x_5^0==x_5^post_12 && y_6^0==y_6^post_12 && z_7^0==z_7^post_12 ], cost: 1 15: l7 -> l1 : Result_4^0'=Result_4^post_16, tmp_8^0'=tmp_8^post_16, x_5^0'=x_5^post_16, y_6^0'=y_6^post_16, z_7^0'=z_7^post_16, [ z_7^0-y_6^0<=0 && x_5^post_16==1+x_5^0 && Result_4^0==Result_4^post_16 && tmp_8^0==tmp_8^post_16 && y_6^0==y_6^post_16 && z_7^0==z_7^post_16 ], cost: 1 12: l9 -> l10 : Result_4^0'=Result_4^post_13, tmp_8^0'=tmp_8^post_13, x_5^0'=x_5^post_13, y_6^0'=y_6^post_13, z_7^0'=z_7^post_13, [ 1+tmp_8^0<=0 && Result_4^0==Result_4^post_13 && tmp_8^0==tmp_8^post_13 && x_5^0==x_5^post_13 && y_6^0==y_6^post_13 && z_7^0==z_7^post_13 ], cost: 1 13: l9 -> l10 : Result_4^0'=Result_4^post_14, tmp_8^0'=tmp_8^post_14, x_5^0'=x_5^post_14, y_6^0'=y_6^post_14, z_7^0'=z_7^post_14, [ 1<=tmp_8^0 && Result_4^0==Result_4^post_14 && tmp_8^0==tmp_8^post_14 && x_5^0==x_5^post_14 && y_6^0==y_6^post_14 && z_7^0==z_7^post_14 ], cost: 1 14: l10 -> l2 : Result_4^0'=Result_4^post_15, tmp_8^0'=tmp_8^post_15, x_5^0'=x_5^post_15, y_6^0'=y_6^post_15, z_7^0'=z_7^post_15, [ y_6^post_15==1+y_6^0 && Result_4^0==Result_4^post_15 && tmp_8^0==tmp_8^post_15 && x_5^0==x_5^post_15 && z_7^0==z_7^post_15 ], cost: 1 17: l11 -> l3 : Result_4^0'=Result_4^post_18, tmp_8^0'=tmp_8^post_18, x_5^0'=x_5^post_18, y_6^0'=y_6^post_18, z_7^0'=z_7^post_18, [ Result_4^0==Result_4^post_18 && tmp_8^0==tmp_8^post_18 && x_5^0==x_5^post_18 && y_6^0==y_6^post_18 && z_7^0==z_7^post_18 ], cost: 1 19: l12 -> l13 : Result_4^0'=Result_4^post_20, tmp_8^0'=tmp_8^post_20, x_5^0'=x_5^post_20, y_6^0'=y_6^post_20, z_7^0'=z_7^post_20, [ 1+tmp_8^0<=0 && Result_4^0==Result_4^post_20 && tmp_8^0==tmp_8^post_20 && x_5^0==x_5^post_20 && y_6^0==y_6^post_20 && z_7^0==z_7^post_20 ], cost: 1 20: l12 -> l13 : Result_4^0'=Result_4^post_21, tmp_8^0'=tmp_8^post_21, x_5^0'=x_5^post_21, y_6^0'=y_6^post_21, z_7^0'=z_7^post_21, [ 1<=tmp_8^0 && Result_4^0==Result_4^post_21 && tmp_8^0==tmp_8^post_21 && x_5^0==x_5^post_21 && y_6^0==y_6^post_21 && z_7^0==z_7^post_21 ], cost: 1 21: l13 -> l2 : Result_4^0'=Result_4^post_22, tmp_8^0'=tmp_8^post_22, x_5^0'=x_5^post_22, y_6^0'=y_6^post_22, z_7^0'=z_7^post_22, [ y_6^post_22==1+y_6^0 && Result_4^0==Result_4^post_22 && tmp_8^0==tmp_8^post_22 && x_5^0==x_5^post_22 && z_7^0==z_7^post_22 ], cost: 1 22: l14 -> l0 : Result_4^0'=Result_4^post_23, tmp_8^0'=tmp_8^post_23, x_5^0'=x_5^post_23, y_6^0'=y_6^post_23, z_7^0'=z_7^post_23, [ Result_4^0==Result_4^post_23 && tmp_8^0==tmp_8^post_23 && x_5^0==x_5^post_23 && y_6^0==y_6^post_23 && z_7^0==z_7^post_23 ], cost: 1 Simplified all rules, resulting in: Start location: l14 0: l0 -> l1 : [], cost: 1 8: l1 -> l7 : [ 0<=-1-x_5^0+y_6^0 ], cost: 1 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 2: l2 -> l5 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 16: l3 -> l11 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 18: l3 -> l12 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 3: l5 -> l6 : [ 1+tmp_8^0<=0 ], cost: 1 4: l5 -> l6 : [ 1<=tmp_8^0 ], cost: 1 5: l6 -> l4 : y_6^0'=1+y_6^0, [], cost: 1 6: l4 -> l2 : [], cost: 1 10: l7 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 11: l7 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 15: l7 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 12: l9 -> l10 : [ 1+tmp_8^0<=0 ], cost: 1 13: l9 -> l10 : [ 1<=tmp_8^0 ], cost: 1 14: l10 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 17: l11 -> l3 : [], cost: 1 19: l12 -> l13 : [ 1+tmp_8^0<=0 ], cost: 1 20: l12 -> l13 : [ 1<=tmp_8^0 ], cost: 1 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 22: l14 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l14 8: l1 -> l7 : [ 0<=-1-x_5^0+y_6^0 ], cost: 1 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 2: l2 -> l5 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 18: l3 -> l12 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 24: l3 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 2 3: l5 -> l6 : [ 1+tmp_8^0<=0 ], cost: 1 4: l5 -> l6 : [ 1<=tmp_8^0 ], cost: 1 25: l6 -> l2 : y_6^0'=1+y_6^0, [], cost: 2 10: l7 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 11: l7 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 15: l7 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 12: l9 -> l10 : [ 1+tmp_8^0<=0 ], cost: 1 13: l9 -> l10 : [ 1<=tmp_8^0 ], cost: 1 14: l10 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 19: l12 -> l13 : [ 1+tmp_8^0<=0 ], cost: 1 20: l12 -> l13 : [ 1<=tmp_8^0 ], cost: 1 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 23: l14 -> l1 : [], cost: 2 Accelerating simple loops of location 3. Accelerating the following rules: 24: l3 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 2 Accelerated rule 24 with non-termination, yielding the new rule 26. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 24. Accelerated all simple loops using metering functions (where possible): Start location: l14 8: l1 -> l7 : [ 0<=-1-x_5^0+y_6^0 ], cost: 1 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 2: l2 -> l5 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 18: l3 -> l12 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 26: l3 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 3: l5 -> l6 : [ 1+tmp_8^0<=0 ], cost: 1 4: l5 -> l6 : [ 1<=tmp_8^0 ], cost: 1 25: l6 -> l2 : y_6^0'=1+y_6^0, [], cost: 2 10: l7 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 11: l7 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 15: l7 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 12: l9 -> l10 : [ 1+tmp_8^0<=0 ], cost: 1 13: l9 -> l10 : [ 1<=tmp_8^0 ], cost: 1 14: l10 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 19: l12 -> l13 : [ 1+tmp_8^0<=0 ], cost: 1 20: l12 -> l13 : [ 1<=tmp_8^0 ], cost: 1 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 23: l14 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l14 8: l1 -> l7 : [ 0<=-1-x_5^0+y_6^0 ], cost: 1 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 2: l2 -> l5 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 18: l3 -> l12 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 3: l5 -> l6 : [ 1+tmp_8^0<=0 ], cost: 1 4: l5 -> l6 : [ 1<=tmp_8^0 ], cost: 1 25: l6 -> l2 : y_6^0'=1+y_6^0, [], cost: 2 10: l7 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 11: l7 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 15: l7 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 28: l7 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 12: l9 -> l10 : [ 1+tmp_8^0<=0 ], cost: 1 13: l9 -> l10 : [ 1<=tmp_8^0 ], cost: 1 14: l10 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 19: l12 -> l13 : [ 1+tmp_8^0<=0 ], cost: 1 20: l12 -> l13 : [ 1<=tmp_8^0 ], cost: 1 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 23: l14 -> l1 : [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l14 29: l1 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 30: l1 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 31: l1 -> l1 : x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && z_7^0-y_6^0<=0 ], cost: 2 32: l1 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 35: l2 -> l6 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_3<=0 ], cost: 2 36: l2 -> l6 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_3 ], cost: 2 33: l3 -> l13 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 2 34: l3 -> l13 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 2 25: l6 -> l2 : y_6^0'=1+y_6^0, [], cost: 2 37: l9 -> l2 : y_6^0'=1+y_6^0, [ 1+tmp_8^0<=0 ], cost: 2 38: l9 -> l2 : y_6^0'=1+y_6^0, [ 1<=tmp_8^0 ], cost: 2 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 23: l14 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 31: l1 -> l1 : x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && z_7^0-y_6^0<=0 ], cost: 2 Accelerated rule 31 with backward acceleration, yielding the new rule 39. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 31. Accelerated all simple loops using metering functions (where possible): Start location: l14 29: l1 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 30: l1 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 32: l1 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 39: l1 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: -2*x_5^0+2*y_6^0 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 35: l2 -> l6 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_3<=0 ], cost: 2 36: l2 -> l6 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_3 ], cost: 2 33: l3 -> l13 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 2 34: l3 -> l13 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 2 25: l6 -> l2 : y_6^0'=1+y_6^0, [], cost: 2 37: l9 -> l2 : y_6^0'=1+y_6^0, [ 1+tmp_8^0<=0 ], cost: 2 38: l9 -> l2 : y_6^0'=1+y_6^0, [ 1<=tmp_8^0 ], cost: 2 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 23: l14 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l14 29: l1 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 30: l1 -> l9 : tmp_8^0'=tmp_8^post_12, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 32: l1 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 35: l2 -> l6 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_3<=0 ], cost: 2 36: l2 -> l6 : tmp_8^0'=tmp_8^post_3, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_3 ], cost: 2 40: l2 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -1-x_5^0+y_6^0>=0 ], cost: -1-2*x_5^0+2*y_6^0 33: l3 -> l13 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 2 34: l3 -> l13 : tmp_8^0'=tmp_8^post_19, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 2 25: l6 -> l2 : y_6^0'=1+y_6^0, [], cost: 2 37: l9 -> l2 : y_6^0'=1+y_6^0, [ 1+tmp_8^0<=0 ], cost: 2 38: l9 -> l2 : y_6^0'=1+y_6^0, [ 1<=tmp_8^0 ], cost: 2 21: l13 -> l2 : y_6^0'=1+y_6^0, [], cost: 1 23: l14 -> l1 : [], cost: 2 41: l14 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 Eliminated locations (on tree-shaped paths): Start location: l14 29: l1 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 32: l1 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 42: l1 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 ], cost: 4 43: l1 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 ], cost: 4 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 40: l2 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -1-x_5^0+y_6^0>=0 ], cost: -1-2*x_5^0+2*y_6^0 44: l2 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_3<=0 ], cost: 4 45: l2 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_3 ], cost: 4 46: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 3 47: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 3 23: l14 -> l1 : [], cost: 2 41: l14 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 Accelerating simple loops of location 2. Accelerating the following rules: 44: l2 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_3<=0 ], cost: 4 45: l2 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_3 ], cost: 4 Accelerated rule 44 with backward acceleration, yielding the new rule 48. Accelerated rule 45 with backward acceleration, yielding the new rule 49. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 44 45. Accelerated all simple loops using metering functions (where possible): Start location: l14 29: l1 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 32: l1 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 42: l1 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 ], cost: 4 43: l1 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 ], cost: 4 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 40: l2 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -1-x_5^0+y_6^0>=0 ], cost: -1-2*x_5^0+2*y_6^0 48: l2 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 49: l2 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 46: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 3 47: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 3 23: l14 -> l1 : [], cost: 2 41: l14 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 Chained accelerated rules (with incoming rules): Start location: l14 29: l1 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 2 32: l1 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 42: l1 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 ], cost: 4 43: l1 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 ], cost: 4 50: l1 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 51: l1 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 54: l1 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 55: l1 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 7: l2 -> l1 : x_5^0'=1+x_5^0, [ z_7^0-y_6^0<=0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 40: l2 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -1-x_5^0+y_6^0>=0 ], cost: -1-2*x_5^0+2*y_6^0 46: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 3 47: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 3 52: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 53: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 56: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 57: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 23: l14 -> l1 : [], cost: 2 41: l14 -> l1 : x_5^0'=y_6^0, [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 Eliminated location l1 (as a last resort): Start location: l14 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 66: l2 -> [18] : [ z_7^0-y_6^0<=0 && -1-x_5^0+y_6^0>=0 ], cost: -1-2*x_5^0+2*y_6^0 46: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 3 47: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 3 52: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 53: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 56: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 57: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 58: l14 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 4 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 60: l14 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 ], cost: 6 61: l14 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 ], cost: 6 62: l14 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 63: l14 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 64: l14 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 65: l14 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 Merged rules: Start location: l14 1: l2 -> l3 : tmp_8^0'=0, [ 0<=-1+z_7^0-y_6^0 ], cost: 1 27: l2 -> [15] : [ 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 66: l2 -> [18] : [ z_7^0-y_6^0<=0 && -1-x_5^0+y_6^0>=0 ], cost: -1-2*x_5^0+2*y_6^0 46: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 ], cost: 3 47: l3 -> l2 : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 ], cost: 3 68: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 69: l3 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 58: l14 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 4 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 60: l14 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 ], cost: 6 61: l14 -> l2 : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 ], cost: 6 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 70: l14 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 71: l14 -> l2 : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 Eliminated location l2 (as a last resort): Start location: l14 72: l3 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 1+tmp_8^post_19<=0 && 0<=-2+z_7^0-y_6^0 ], cost: 4 73: l3 -> [15] : [ 1+tmp_8^post_19<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 74: l3 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -1+z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 4-2*x_5^0+2*y_6^0 75: l3 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 1<=tmp_8^post_19 && 0<=-2+z_7^0-y_6^0 ], cost: 4 76: l3 -> [15] : [ 1<=tmp_8^post_19 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 77: l3 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -1+z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 4-2*x_5^0+2*y_6^0 84: l3 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: -2+6*z_7^0-2*x_5^0-4*y_6^0 85: l3 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: -2+6*z_7^0-2*x_5^0-4*y_6^0 88: l3 -> [19] : [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 89: l3 -> [19] : [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 58: l14 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 4 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 78: l14 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: 7 79: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 80: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 81: l14 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: 7 82: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 83: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 86: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 87: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 90: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 91: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 Accelerating simple loops of location 3. [accelerate] Removed some duplicate simple loops Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 75: l3 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-2+z_7^0-y_6^0 ], cost: 4 Accelerated rule 75 with backward acceleration, yielding the new rule 92. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 75. Accelerated all simple loops using metering functions (where possible): Start location: l14 73: l3 -> [15] : [ 1+tmp_8^post_19<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 74: l3 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -1+z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 4-2*x_5^0+2*y_6^0 76: l3 -> [15] : [ 1<=tmp_8^post_19 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 77: l3 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -1+z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 4-2*x_5^0+2*y_6^0 84: l3 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: -2+6*z_7^0-2*x_5^0-4*y_6^0 85: l3 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: -2+6*z_7^0-2*x_5^0-4*y_6^0 88: l3 -> [19] : [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 89: l3 -> [19] : [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 92: l3 -> l3 : tmp_8^0'=0, y_6^0'=-1+z_7^0, [ -1+z_7^0-y_6^0>=1 ], cost: -4+4*z_7^0-4*y_6^0 58: l14 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 4 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 78: l14 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: 7 79: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 80: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 81: l14 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: 7 82: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 83: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 86: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 87: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 90: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 91: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 Chained accelerated rules (with incoming rules): Start location: l14 73: l3 -> [15] : [ 1+tmp_8^post_19<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 74: l3 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -1+z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 4-2*x_5^0+2*y_6^0 76: l3 -> [15] : [ 1<=tmp_8^post_19 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 77: l3 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -1+z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 4-2*x_5^0+2*y_6^0 84: l3 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: -2+6*z_7^0-2*x_5^0-4*y_6^0 85: l3 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: -2+6*z_7^0-2*x_5^0-4*y_6^0 88: l3 -> [19] : [ 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 89: l3 -> [19] : [ 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 58: l14 -> l3 : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: 4 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 78: l14 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: 7 79: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 80: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 81: l14 -> l3 : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: 7 82: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 83: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 86: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 87: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 90: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 91: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 93: l14 -> l3 : tmp_8^0'=0, y_6^0'=-1+z_7^0, [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 94: l14 -> l3 : tmp_8^0'=0, y_6^0'=-1+z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 95: l14 -> l3 : tmp_8^0'=0, y_6^0'=-1+z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 Eliminated locations (on tree-shaped paths): Start location: l14 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 79: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 80: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 82: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 83: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 86: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 87: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 90: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 91: l14 -> [19] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 96: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_19<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 97: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -1+z_7^0-y_6^0<=0 ], cost: 8-2*x_5^0+2*y_6^0 98: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_19 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 99: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -1+z_7^0-y_6^0<=0 ], cost: 8-2*x_5^0+2*y_6^0 100: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 101: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 102: l14 -> [19] : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 3+4*z_7^0-4*y_6^0 103: l14 -> [19] : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 3+4*z_7^0-4*y_6^0 104: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1+tmp_8^post_19<=0 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 105: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 106: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1<=tmp_8^post_19 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 107: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 108: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 109: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 110: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 111: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 112: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1+tmp_8^post_19<=0 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 113: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 114: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1<=tmp_8^post_19 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 115: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 116: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 117: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 118: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 119: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 120: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 && 1+tmp_8^post_19<=0 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 121: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 && 1<=tmp_8^post_19 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 122: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 && 1+tmp_8^post_19<=0 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 123: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 && 1<=tmp_8^post_19 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 124: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 && 1+tmp_8^post_19<=0 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 125: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 && 1<=tmp_8^post_19 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 126: l14 -> [21] : [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 127: l14 -> [21] : [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 128: l14 -> [21] : [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l14 59: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ], cost: NONTERM 67: l14 -> [18] : [ z_7^0-y_6^0<=0 && -x_5^0+y_6^0>=0 ], cost: 2-2*x_5^0+2*y_6^0 79: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 80: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_12<=0 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 82: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 83: l14 -> [18] : tmp_8^0'=tmp_8^post_12, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_12 && -1+z_7^0-y_6^0<=0 ], cost: 7-2*x_5^0+2*y_6^0 96: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_19<=0 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 97: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -1+z_7^0-y_6^0<=0 ], cost: 8-2*x_5^0+2*y_6^0 98: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_19 && 0<=-2+z_7^0-y_6^0 ], cost: NONTERM 99: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -1+z_7^0-y_6^0<=0 ], cost: 8-2*x_5^0+2*y_6^0 100: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 101: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 102: l14 -> [19] : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_3<=0 && -1+z_7^0-y_6^0>=1 ], cost: 3+4*z_7^0-4*y_6^0 103: l14 -> [19] : tmp_8^0'=0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_3 && -1+z_7^0-y_6^0>=1 ], cost: 3+4*z_7^0-4*y_6^0 104: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1+tmp_8^post_19<=0 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 105: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 106: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1<=tmp_8^post_19 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 107: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 0<=-2+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 108: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 109: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 110: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 111: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_8^post_12<=0 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 112: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1+tmp_8^post_19<=0 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 113: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 && 1+tmp_8^post_19<=0 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 114: l14 -> [15] : [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1<=tmp_8^post_19 && 0<=-3+z_7^0-y_6^0 ], cost: NONTERM 115: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=2+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 0<=-2+z_7^0-y_6^0 && 1<=tmp_8^post_19 && -2+z_7^0-y_6^0<=0 ], cost: 13-2*x_5^0+2*y_6^0 116: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 117: l14 -> [18] : tmp_8^0'=tmp_8^post_3, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 118: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1+tmp_8^post_3<=0 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 119: l14 -> [19] : tmp_8^0'=0, y_6^0'=1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_8^post_12 && 1<=tmp_8^post_3 && -2+z_7^0-y_6^0>=1 ], cost: 2+4*z_7^0-4*y_6^0 120: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 && 1+tmp_8^post_19<=0 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 121: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 && 1<=tmp_8^post_19 && -1+z_7^0-x_5^0>=0 ], cost: 2+6*z_7^0-2*x_5^0-4*y_6^0 124: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 && 1+tmp_8^post_19<=0 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 125: l14 -> [18] : tmp_8^0'=tmp_8^post_19, y_6^0'=z_7^0, [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 && 1<=tmp_8^post_19 && -1+z_7^0-x_5^0>=0 ], cost: 1+6*z_7^0-2*x_5^0-4*y_6^0 126: l14 -> [21] : [ 0<=-1-x_5^0+y_6^0 && -1+z_7^0-y_6^0>=1 ], cost: 4*z_7^0-4*y_6^0 128: l14 -> [21] : [ 0<=-1-x_5^0+y_6^0 && -2+z_7^0-y_6^0>=1 ], cost: -1+4*z_7^0-4*y_6^0 Computing asymptotic complexity for rule 59 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ 0<=-1-x_5^0+y_6^0 && 0<=-1+z_7^0-y_6^0 ] NO