WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l23 0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, m^0'=m^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, x^0'=x^post_1, y^0'=y^post_1, [ 1+n^0<=j^0 && i^0==i^post_1 && j^0==j^post_1 && m^0==m^post_1 && n^0==n^post_1 && tmp^0==tmp^post_1 && tmp___0^0==tmp___0^post_1 && x^0==x^post_1 && y^0==y^post_1 ], cost: 1 1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, m^0'=m^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_2, y^0'=y^post_2, [ j^0<=n^0 && tmp^post_2==tmp^post_2 && tmp___0^post_2==tmp___0^post_2 && i^0==i^post_2 && j^0==j^post_2 && m^0==m^post_2 && n^0==n^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1 30: l1 -> l15 : i^0'=i^post_31, j^0'=j^post_31, m^0'=m^post_31, n^0'=n^post_31, tmp^0'=tmp^post_31, tmp___0^0'=tmp___0^post_31, x^0'=x^post_31, y^0'=y^post_31, [ i^0<=m^0 && m^0<=i^0 && i^0==i^post_31 && j^0==j^post_31 && m^0==m^post_31 && n^0==n^post_31 && tmp^0==tmp^post_31 && tmp___0^0==tmp___0^post_31 && x^0==x^post_31 && y^0==y^post_31 ], cost: 1 31: l1 -> l21 : i^0'=i^post_32, j^0'=j^post_32, m^0'=m^post_32, n^0'=n^post_32, tmp^0'=tmp^post_32, tmp___0^0'=tmp___0^post_32, x^0'=x^post_32, y^0'=y^post_32, [ 1+m^0<=i^0 && i^0==i^post_32 && j^0==j^post_32 && m^0==m^post_32 && n^0==n^post_32 && tmp^0==tmp^post_32 && tmp___0^0==tmp___0^post_32 && x^0==x^post_32 && y^0==y^post_32 ], cost: 1 32: l1 -> l21 : i^0'=i^post_33, j^0'=j^post_33, m^0'=m^post_33, n^0'=n^post_33, tmp^0'=tmp^post_33, tmp___0^0'=tmp___0^post_33, x^0'=x^post_33, y^0'=y^post_33, [ 1+i^0<=m^0 && i^0==i^post_33 && j^0==j^post_33 && m^0==m^post_33 && n^0==n^post_33 && tmp^0==tmp^post_33 && tmp___0^0==tmp___0^post_33 && x^0==x^post_33 && y^0==y^post_33 ], cost: 1 34: l2 -> l22 : i^0'=i^post_35, j^0'=j^post_35, m^0'=m^post_35, n^0'=n^post_35, tmp^0'=tmp^post_35, tmp___0^0'=tmp___0^post_35, x^0'=x^post_35, y^0'=y^post_35, [ tmp^0<=tmp___0^0 && i^0==i^post_35 && j^0==j^post_35 && m^0==m^post_35 && n^0==n^post_35 && tmp^0==tmp^post_35 && tmp___0^0==tmp___0^post_35 && x^0==x^post_35 && y^0==y^post_35 ], cost: 1 35: l2 -> l22 : i^0'=i^post_36, j^0'=j^post_36, m^0'=m^post_36, n^0'=n^post_36, tmp^0'=tmp^post_36, tmp___0^0'=tmp___0^post_36, x^0'=x^post_36, y^0'=y^post_36, [ 1+tmp___0^0<=tmp^0 && x^post_36==x^post_36 && i^post_36==j^0 && j^0==j^post_36 && m^0==m^post_36 && n^0==n^post_36 && tmp^0==tmp^post_36 && tmp___0^0==tmp___0^post_36 && y^0==y^post_36 ], cost: 1 2: l3 -> l0 : i^0'=i^post_3, j^0'=j^post_3, m^0'=m^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, x^0'=x^post_3, y^0'=y^post_3, [ i^0==i^post_3 && j^0==j^post_3 && m^0==m^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1 3: l4 -> l5 : i^0'=i^post_4, j^0'=j^post_4, m^0'=m^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, x^0'=x^post_4, y^0'=y^post_4, [ m^post_4==1+m^0 && i^0==i^post_4 && j^0==j^post_4 && n^0==n^post_4 && tmp^0==tmp^post_4 && tmp___0^0==tmp___0^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1 26: l5 -> l16 : i^0'=i^post_27, j^0'=j^post_27, m^0'=m^post_27, n^0'=n^post_27, tmp^0'=tmp^post_27, tmp___0^0'=tmp___0^post_27, x^0'=x^post_27, y^0'=y^post_27, [ i^0==i^post_27 && j^0==j^post_27 && m^0==m^post_27 && n^0==n^post_27 && tmp^0==tmp^post_27 && tmp___0^0==tmp___0^post_27 && x^0==x^post_27 && y^0==y^post_27 ], cost: 1 4: l6 -> l7 : i^0'=i^post_5, j^0'=j^post_5, m^0'=m^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, x^0'=x^post_5, y^0'=y^post_5, [ i^post_5==1+i^0 && j^0==j^post_5 && m^0==m^post_5 && n^0==n^post_5 && tmp^0==tmp^post_5 && tmp___0^0==tmp___0^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1 17: l7 -> l14 : i^0'=i^post_18, j^0'=j^post_18, m^0'=m^post_18, n^0'=n^post_18, tmp^0'=tmp^post_18, tmp___0^0'=tmp___0^post_18, x^0'=x^post_18, y^0'=y^post_18, [ i^0==i^post_18 && j^0==j^post_18 && m^0==m^post_18 && n^0==n^post_18 && tmp^0==tmp^post_18 && tmp___0^0==tmp___0^post_18 && x^0==x^post_18 && y^0==y^post_18 ], cost: 1 5: l8 -> l6 : i^0'=i^post_6, j^0'=j^post_6, m^0'=m^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, x^0'=x^post_6, y^0'=y^post_6, [ 1+n^0<=j^0 && i^0==i^post_6 && j^0==j^post_6 && m^0==m^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 && tmp___0^0==tmp___0^post_6 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1 6: l8 -> l9 : i^0'=i^post_7, j^0'=j^post_7, m^0'=m^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, x^0'=x^post_7, y^0'=y^post_7, [ j^0<=n^0 && j^post_7==1+j^0 && i^0==i^post_7 && m^0==m^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 && tmp___0^0==tmp___0^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1 7: l9 -> l8 : i^0'=i^post_8, j^0'=j^post_8, m^0'=m^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, x^0'=x^post_8, y^0'=y^post_8, [ i^0==i^post_8 && j^0==j^post_8 && m^0==m^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1 8: l10 -> l9 : i^0'=i^post_9, j^0'=j^post_9, m^0'=m^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, tmp___0^0'=tmp___0^post_9, x^0'=x^post_9, y^0'=y^post_9, [ 1+n^0<=j^0 && i^0==i^post_9 && j^0==j^post_9 && m^0==m^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 && tmp___0^0==tmp___0^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1 9: l10 -> l11 : i^0'=i^post_10, j^0'=j^post_10, m^0'=m^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, tmp___0^0'=tmp___0^post_10, x^0'=x^post_10, y^0'=y^post_10, [ j^0<=n^0 && j^post_10==1+j^0 && i^0==i^post_10 && m^0==m^post_10 && n^0==n^post_10 && tmp^0==tmp^post_10 && tmp___0^0==tmp___0^post_10 && x^0==x^post_10 && y^0==y^post_10 ], cost: 1 10: l11 -> l10 : i^0'=i^post_11, j^0'=j^post_11, m^0'=m^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, tmp___0^0'=tmp___0^post_11, x^0'=x^post_11, y^0'=y^post_11, [ i^0==i^post_11 && j^0==j^post_11 && m^0==m^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 && tmp___0^0==tmp___0^post_11 && x^0==x^post_11 && y^0==y^post_11 ], cost: 1 11: l12 -> l11 : i^0'=i^post_12, j^0'=j^post_12, m^0'=m^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, tmp___0^0'=tmp___0^post_12, x^0'=x^post_12, y^0'=y^post_12, [ y^post_12==y^post_12 && i^0==i^post_12 && j^0==j^post_12 && m^0==m^post_12 && n^0==n^post_12 && tmp^0==tmp^post_12 && tmp___0^0==tmp___0^post_12 && x^0==x^post_12 ], cost: 1 12: l13 -> l6 : i^0'=i^post_13, j^0'=j^post_13, m^0'=m^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, tmp___0^0'=tmp___0^post_13, x^0'=x^post_13, y^0'=y^post_13, [ y^0<=0 && 0<=y^0 && i^0==i^post_13 && j^0==j^post_13 && m^0==m^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 && tmp___0^0==tmp___0^post_13 && x^0==x^post_13 && y^0==y^post_13 ], cost: 1 13: l13 -> l12 : i^0'=i^post_14, j^0'=j^post_14, m^0'=m^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, tmp___0^0'=tmp___0^post_14, x^0'=x^post_14, y^0'=y^post_14, [ 1<=y^0 && i^0==i^post_14 && j^0==j^post_14 && m^0==m^post_14 && n^0==n^post_14 && tmp^0==tmp^post_14 && tmp___0^0==tmp___0^post_14 && x^0==x^post_14 && y^0==y^post_14 ], cost: 1 14: l13 -> l12 : i^0'=i^post_15, j^0'=j^post_15, m^0'=m^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, tmp___0^0'=tmp___0^post_15, x^0'=x^post_15, y^0'=y^post_15, [ 1+y^0<=0 && i^0==i^post_15 && j^0==j^post_15 && m^0==m^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 && tmp___0^0==tmp___0^post_15 && x^0==x^post_15 && y^0==y^post_15 ], cost: 1 15: l14 -> l4 : i^0'=i^post_16, j^0'=j^post_16, m^0'=m^post_16, n^0'=n^post_16, tmp^0'=tmp^post_16, tmp___0^0'=tmp___0^post_16, x^0'=x^post_16, y^0'=y^post_16, [ 1+n^0<=i^0 && i^0==i^post_16 && j^0==j^post_16 && m^0==m^post_16 && n^0==n^post_16 && tmp^0==tmp^post_16 && tmp___0^0==tmp___0^post_16 && x^0==x^post_16 && y^0==y^post_16 ], cost: 1 16: l14 -> l13 : i^0'=i^post_17, j^0'=j^post_17, m^0'=m^post_17, n^0'=n^post_17, tmp^0'=tmp^post_17, tmp___0^0'=tmp___0^post_17, x^0'=x^post_17, y^0'=y^post_17, [ i^0<=n^0 && y^post_17==y^post_17 && i^0==i^post_17 && j^0==j^post_17 && m^0==m^post_17 && n^0==n^post_17 && tmp^0==tmp^post_17 && tmp___0^0==tmp___0^post_17 && x^0==x^post_17 ], cost: 1 18: l15 -> l4 : i^0'=i^post_19, j^0'=j^post_19, m^0'=m^post_19, n^0'=n^post_19, tmp^0'=tmp^post_19, tmp___0^0'=tmp___0^post_19, x^0'=x^post_19, y^0'=y^post_19, [ x^0<=0 && 0<=x^0 && i^0==i^post_19 && j^0==j^post_19 && m^0==m^post_19 && n^0==n^post_19 && tmp^0==tmp^post_19 && tmp___0^0==tmp___0^post_19 && x^0==x^post_19 && y^0==y^post_19 ], cost: 1 19: l15 -> l7 : i^0'=i^post_20, j^0'=j^post_20, m^0'=m^post_20, n^0'=n^post_20, tmp^0'=tmp^post_20, tmp___0^0'=tmp___0^post_20, x^0'=x^post_20, y^0'=y^post_20, [ 1<=x^0 && i^0==i^post_20 && j^0==j^post_20 && m^0==m^post_20 && n^0==n^post_20 && tmp^0==tmp^post_20 && tmp___0^0==tmp___0^post_20 && x^0==x^post_20 && y^0==y^post_20 ], cost: 1 20: l15 -> l7 : i^0'=i^post_21, j^0'=j^post_21, m^0'=m^post_21, n^0'=n^post_21, tmp^0'=tmp^post_21, tmp___0^0'=tmp___0^post_21, x^0'=x^post_21, y^0'=y^post_21, [ 1+x^0<=0 && i^0==i^post_21 && j^0==j^post_21 && m^0==m^post_21 && n^0==n^post_21 && tmp^0==tmp^post_21 && tmp___0^0==tmp___0^post_21 && x^0==x^post_21 && y^0==y^post_21 ], cost: 1 21: l16 -> l17 : i^0'=i^post_22, j^0'=j^post_22, m^0'=m^post_22, n^0'=n^post_22, tmp^0'=tmp^post_22, tmp___0^0'=tmp___0^post_22, x^0'=x^post_22, y^0'=y^post_22, [ n^0<=m^0 && i^0==i^post_22 && j^0==j^post_22 && m^0==m^post_22 && n^0==n^post_22 && tmp^0==tmp^post_22 && tmp___0^0==tmp___0^post_22 && x^0==x^post_22 && y^0==y^post_22 ], cost: 1 22: l16 -> l3 : i^0'=i^post_23, j^0'=j^post_23, m^0'=m^post_23, n^0'=n^post_23, tmp^0'=tmp^post_23, tmp___0^0'=tmp___0^post_23, x^0'=x^post_23, y^0'=y^post_23, [ 1+m^0<=n^0 && x^post_23==0 && i^post_23==m^0 && j^0==j^post_23 && m^0==m^post_23 && n^0==n^post_23 && tmp^0==tmp^post_23 && tmp___0^0==tmp___0^post_23 && y^0==y^post_23 ], cost: 1 23: l18 -> l15 : i^0'=i^post_24, j^0'=j^post_24, m^0'=m^post_24, n^0'=n^post_24, tmp^0'=tmp^post_24, tmp___0^0'=tmp___0^post_24, x^0'=x^post_24, y^0'=y^post_24, [ 1+n^0<=j^0 && i^0==i^post_24 && j^0==j^post_24 && m^0==m^post_24 && n^0==n^post_24 && tmp^0==tmp^post_24 && tmp___0^0==tmp___0^post_24 && x^0==x^post_24 && y^0==y^post_24 ], cost: 1 24: l18 -> l19 : i^0'=i^post_25, j^0'=j^post_25, m^0'=m^post_25, n^0'=n^post_25, tmp^0'=tmp^post_25, tmp___0^0'=tmp___0^post_25, x^0'=x^post_25, y^0'=y^post_25, [ j^0<=n^0 && y^post_25==y^post_25 && j^post_25==1+j^0 && i^0==i^post_25 && m^0==m^post_25 && n^0==n^post_25 && tmp^0==tmp^post_25 && tmp___0^0==tmp___0^post_25 && x^0==x^post_25 ], cost: 1 25: l19 -> l18 : i^0'=i^post_26, j^0'=j^post_26, m^0'=m^post_26, n^0'=n^post_26, tmp^0'=tmp^post_26, tmp___0^0'=tmp___0^post_26, x^0'=x^post_26, y^0'=y^post_26, [ i^0==i^post_26 && j^0==j^post_26 && m^0==m^post_26 && n^0==n^post_26 && tmp^0==tmp^post_26 && tmp___0^0==tmp___0^post_26 && x^0==x^post_26 && y^0==y^post_26 ], cost: 1 27: l20 -> l19 : i^0'=i^post_28, j^0'=j^post_28, m^0'=m^post_28, n^0'=n^post_28, tmp^0'=tmp^post_28, tmp___0^0'=tmp___0^post_28, x^0'=x^post_28, y^0'=y^post_28, [ 1+n^0<=j^0 && i^0==i^post_28 && j^0==j^post_28 && m^0==m^post_28 && n^0==n^post_28 && tmp^0==tmp^post_28 && tmp___0^0==tmp___0^post_28 && x^0==x^post_28 && y^0==y^post_28 ], cost: 1 28: l20 -> l21 : i^0'=i^post_29, j^0'=j^post_29, m^0'=m^post_29, n^0'=n^post_29, tmp^0'=tmp^post_29, tmp___0^0'=tmp___0^post_29, x^0'=x^post_29, y^0'=y^post_29, [ j^0<=n^0 && y^post_29==y^post_29 && j^post_29==1+j^0 && i^0==i^post_29 && m^0==m^post_29 && n^0==n^post_29 && tmp^0==tmp^post_29 && tmp___0^0==tmp___0^post_29 && x^0==x^post_29 ], cost: 1 29: l21 -> l20 : i^0'=i^post_30, j^0'=j^post_30, m^0'=m^post_30, n^0'=n^post_30, tmp^0'=tmp^post_30, tmp___0^0'=tmp___0^post_30, x^0'=x^post_30, y^0'=y^post_30, [ i^0==i^post_30 && j^0==j^post_30 && m^0==m^post_30 && n^0==n^post_30 && tmp^0==tmp^post_30 && tmp___0^0==tmp___0^post_30 && x^0==x^post_30 && y^0==y^post_30 ], cost: 1 33: l22 -> l3 : i^0'=i^post_34, j^0'=j^post_34, m^0'=m^post_34, n^0'=n^post_34, tmp^0'=tmp^post_34, tmp___0^0'=tmp___0^post_34, x^0'=x^post_34, y^0'=y^post_34, [ j^post_34==1+j^0 && i^0==i^post_34 && m^0==m^post_34 && n^0==n^post_34 && tmp^0==tmp^post_34 && tmp___0^0==tmp___0^post_34 && x^0==x^post_34 && y^0==y^post_34 ], cost: 1 36: l23 -> l5 : i^0'=i^post_37, j^0'=j^post_37, m^0'=m^post_37, n^0'=n^post_37, tmp^0'=tmp^post_37, tmp___0^0'=tmp___0^post_37, x^0'=x^post_37, y^0'=y^post_37, [ i^0==i^post_37 && j^0==j^post_37 && m^0==m^post_37 && n^0==n^post_37 && tmp^0==tmp^post_37 && tmp___0^0==tmp___0^post_37 && x^0==x^post_37 && y^0==y^post_37 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 36: l23 -> l5 : i^0'=i^post_37, j^0'=j^post_37, m^0'=m^post_37, n^0'=n^post_37, tmp^0'=tmp^post_37, tmp___0^0'=tmp___0^post_37, x^0'=x^post_37, y^0'=y^post_37, [ i^0==i^post_37 && j^0==j^post_37 && m^0==m^post_37 && n^0==n^post_37 && tmp^0==tmp^post_37 && tmp___0^0==tmp___0^post_37 && x^0==x^post_37 && y^0==y^post_37 ], cost: 1 Removed unreachable and leaf rules: Start location: l23 0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, m^0'=m^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, x^0'=x^post_1, y^0'=y^post_1, [ 1+n^0<=j^0 && i^0==i^post_1 && j^0==j^post_1 && m^0==m^post_1 && n^0==n^post_1 && tmp^0==tmp^post_1 && tmp___0^0==tmp___0^post_1 && x^0==x^post_1 && y^0==y^post_1 ], cost: 1 1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, m^0'=m^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_2, y^0'=y^post_2, [ j^0<=n^0 && tmp^post_2==tmp^post_2 && tmp___0^post_2==tmp___0^post_2 && i^0==i^post_2 && j^0==j^post_2 && m^0==m^post_2 && n^0==n^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1 30: l1 -> l15 : i^0'=i^post_31, j^0'=j^post_31, m^0'=m^post_31, n^0'=n^post_31, tmp^0'=tmp^post_31, tmp___0^0'=tmp___0^post_31, x^0'=x^post_31, y^0'=y^post_31, [ i^0<=m^0 && m^0<=i^0 && i^0==i^post_31 && j^0==j^post_31 && m^0==m^post_31 && n^0==n^post_31 && tmp^0==tmp^post_31 && tmp___0^0==tmp___0^post_31 && x^0==x^post_31 && y^0==y^post_31 ], cost: 1 31: l1 -> l21 : i^0'=i^post_32, j^0'=j^post_32, m^0'=m^post_32, n^0'=n^post_32, tmp^0'=tmp^post_32, tmp___0^0'=tmp___0^post_32, x^0'=x^post_32, y^0'=y^post_32, [ 1+m^0<=i^0 && i^0==i^post_32 && j^0==j^post_32 && m^0==m^post_32 && n^0==n^post_32 && tmp^0==tmp^post_32 && tmp___0^0==tmp___0^post_32 && x^0==x^post_32 && y^0==y^post_32 ], cost: 1 32: l1 -> l21 : i^0'=i^post_33, j^0'=j^post_33, m^0'=m^post_33, n^0'=n^post_33, tmp^0'=tmp^post_33, tmp___0^0'=tmp___0^post_33, x^0'=x^post_33, y^0'=y^post_33, [ 1+i^0<=m^0 && i^0==i^post_33 && j^0==j^post_33 && m^0==m^post_33 && n^0==n^post_33 && tmp^0==tmp^post_33 && tmp___0^0==tmp___0^post_33 && x^0==x^post_33 && y^0==y^post_33 ], cost: 1 34: l2 -> l22 : i^0'=i^post_35, j^0'=j^post_35, m^0'=m^post_35, n^0'=n^post_35, tmp^0'=tmp^post_35, tmp___0^0'=tmp___0^post_35, x^0'=x^post_35, y^0'=y^post_35, [ tmp^0<=tmp___0^0 && i^0==i^post_35 && j^0==j^post_35 && m^0==m^post_35 && n^0==n^post_35 && tmp^0==tmp^post_35 && tmp___0^0==tmp___0^post_35 && x^0==x^post_35 && y^0==y^post_35 ], cost: 1 35: l2 -> l22 : i^0'=i^post_36, j^0'=j^post_36, m^0'=m^post_36, n^0'=n^post_36, tmp^0'=tmp^post_36, tmp___0^0'=tmp___0^post_36, x^0'=x^post_36, y^0'=y^post_36, [ 1+tmp___0^0<=tmp^0 && x^post_36==x^post_36 && i^post_36==j^0 && j^0==j^post_36 && m^0==m^post_36 && n^0==n^post_36 && tmp^0==tmp^post_36 && tmp___0^0==tmp___0^post_36 && y^0==y^post_36 ], cost: 1 2: l3 -> l0 : i^0'=i^post_3, j^0'=j^post_3, m^0'=m^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, x^0'=x^post_3, y^0'=y^post_3, [ i^0==i^post_3 && j^0==j^post_3 && m^0==m^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1 3: l4 -> l5 : i^0'=i^post_4, j^0'=j^post_4, m^0'=m^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, x^0'=x^post_4, y^0'=y^post_4, [ m^post_4==1+m^0 && i^0==i^post_4 && j^0==j^post_4 && n^0==n^post_4 && tmp^0==tmp^post_4 && tmp___0^0==tmp___0^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1 26: l5 -> l16 : i^0'=i^post_27, j^0'=j^post_27, m^0'=m^post_27, n^0'=n^post_27, tmp^0'=tmp^post_27, tmp___0^0'=tmp___0^post_27, x^0'=x^post_27, y^0'=y^post_27, [ i^0==i^post_27 && j^0==j^post_27 && m^0==m^post_27 && n^0==n^post_27 && tmp^0==tmp^post_27 && tmp___0^0==tmp___0^post_27 && x^0==x^post_27 && y^0==y^post_27 ], cost: 1 4: l6 -> l7 : i^0'=i^post_5, j^0'=j^post_5, m^0'=m^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, x^0'=x^post_5, y^0'=y^post_5, [ i^post_5==1+i^0 && j^0==j^post_5 && m^0==m^post_5 && n^0==n^post_5 && tmp^0==tmp^post_5 && tmp___0^0==tmp___0^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1 17: l7 -> l14 : i^0'=i^post_18, j^0'=j^post_18, m^0'=m^post_18, n^0'=n^post_18, tmp^0'=tmp^post_18, tmp___0^0'=tmp___0^post_18, x^0'=x^post_18, y^0'=y^post_18, [ i^0==i^post_18 && j^0==j^post_18 && m^0==m^post_18 && n^0==n^post_18 && tmp^0==tmp^post_18 && tmp___0^0==tmp___0^post_18 && x^0==x^post_18 && y^0==y^post_18 ], cost: 1 5: l8 -> l6 : i^0'=i^post_6, j^0'=j^post_6, m^0'=m^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, x^0'=x^post_6, y^0'=y^post_6, [ 1+n^0<=j^0 && i^0==i^post_6 && j^0==j^post_6 && m^0==m^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 && tmp___0^0==tmp___0^post_6 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1 6: l8 -> l9 : i^0'=i^post_7, j^0'=j^post_7, m^0'=m^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, x^0'=x^post_7, y^0'=y^post_7, [ j^0<=n^0 && j^post_7==1+j^0 && i^0==i^post_7 && m^0==m^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 && tmp___0^0==tmp___0^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1 7: l9 -> l8 : i^0'=i^post_8, j^0'=j^post_8, m^0'=m^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, x^0'=x^post_8, y^0'=y^post_8, [ i^0==i^post_8 && j^0==j^post_8 && m^0==m^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1 8: l10 -> l9 : i^0'=i^post_9, j^0'=j^post_9, m^0'=m^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, tmp___0^0'=tmp___0^post_9, x^0'=x^post_9, y^0'=y^post_9, [ 1+n^0<=j^0 && i^0==i^post_9 && j^0==j^post_9 && m^0==m^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 && tmp___0^0==tmp___0^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1 9: l10 -> l11 : i^0'=i^post_10, j^0'=j^post_10, m^0'=m^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, tmp___0^0'=tmp___0^post_10, x^0'=x^post_10, y^0'=y^post_10, [ j^0<=n^0 && j^post_10==1+j^0 && i^0==i^post_10 && m^0==m^post_10 && n^0==n^post_10 && tmp^0==tmp^post_10 && tmp___0^0==tmp___0^post_10 && x^0==x^post_10 && y^0==y^post_10 ], cost: 1 10: l11 -> l10 : i^0'=i^post_11, j^0'=j^post_11, m^0'=m^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, tmp___0^0'=tmp___0^post_11, x^0'=x^post_11, y^0'=y^post_11, [ i^0==i^post_11 && j^0==j^post_11 && m^0==m^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 && tmp___0^0==tmp___0^post_11 && x^0==x^post_11 && y^0==y^post_11 ], cost: 1 11: l12 -> l11 : i^0'=i^post_12, j^0'=j^post_12, m^0'=m^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, tmp___0^0'=tmp___0^post_12, x^0'=x^post_12, y^0'=y^post_12, [ y^post_12==y^post_12 && i^0==i^post_12 && j^0==j^post_12 && m^0==m^post_12 && n^0==n^post_12 && tmp^0==tmp^post_12 && tmp___0^0==tmp___0^post_12 && x^0==x^post_12 ], cost: 1 12: l13 -> l6 : i^0'=i^post_13, j^0'=j^post_13, m^0'=m^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, tmp___0^0'=tmp___0^post_13, x^0'=x^post_13, y^0'=y^post_13, [ y^0<=0 && 0<=y^0 && i^0==i^post_13 && j^0==j^post_13 && m^0==m^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 && tmp___0^0==tmp___0^post_13 && x^0==x^post_13 && y^0==y^post_13 ], cost: 1 13: l13 -> l12 : i^0'=i^post_14, j^0'=j^post_14, m^0'=m^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, tmp___0^0'=tmp___0^post_14, x^0'=x^post_14, y^0'=y^post_14, [ 1<=y^0 && i^0==i^post_14 && j^0==j^post_14 && m^0==m^post_14 && n^0==n^post_14 && tmp^0==tmp^post_14 && tmp___0^0==tmp___0^post_14 && x^0==x^post_14 && y^0==y^post_14 ], cost: 1 14: l13 -> l12 : i^0'=i^post_15, j^0'=j^post_15, m^0'=m^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, tmp___0^0'=tmp___0^post_15, x^0'=x^post_15, y^0'=y^post_15, [ 1+y^0<=0 && i^0==i^post_15 && j^0==j^post_15 && m^0==m^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 && tmp___0^0==tmp___0^post_15 && x^0==x^post_15 && y^0==y^post_15 ], cost: 1 15: l14 -> l4 : i^0'=i^post_16, j^0'=j^post_16, m^0'=m^post_16, n^0'=n^post_16, tmp^0'=tmp^post_16, tmp___0^0'=tmp___0^post_16, x^0'=x^post_16, y^0'=y^post_16, [ 1+n^0<=i^0 && i^0==i^post_16 && j^0==j^post_16 && m^0==m^post_16 && n^0==n^post_16 && tmp^0==tmp^post_16 && tmp___0^0==tmp___0^post_16 && x^0==x^post_16 && y^0==y^post_16 ], cost: 1 16: l14 -> l13 : i^0'=i^post_17, j^0'=j^post_17, m^0'=m^post_17, n^0'=n^post_17, tmp^0'=tmp^post_17, tmp___0^0'=tmp___0^post_17, x^0'=x^post_17, y^0'=y^post_17, [ i^0<=n^0 && y^post_17==y^post_17 && i^0==i^post_17 && j^0==j^post_17 && m^0==m^post_17 && n^0==n^post_17 && tmp^0==tmp^post_17 && tmp___0^0==tmp___0^post_17 && x^0==x^post_17 ], cost: 1 18: l15 -> l4 : i^0'=i^post_19, j^0'=j^post_19, m^0'=m^post_19, n^0'=n^post_19, tmp^0'=tmp^post_19, tmp___0^0'=tmp___0^post_19, x^0'=x^post_19, y^0'=y^post_19, [ x^0<=0 && 0<=x^0 && i^0==i^post_19 && j^0==j^post_19 && m^0==m^post_19 && n^0==n^post_19 && tmp^0==tmp^post_19 && tmp___0^0==tmp___0^post_19 && x^0==x^post_19 && y^0==y^post_19 ], cost: 1 19: l15 -> l7 : i^0'=i^post_20, j^0'=j^post_20, m^0'=m^post_20, n^0'=n^post_20, tmp^0'=tmp^post_20, tmp___0^0'=tmp___0^post_20, x^0'=x^post_20, y^0'=y^post_20, [ 1<=x^0 && i^0==i^post_20 && j^0==j^post_20 && m^0==m^post_20 && n^0==n^post_20 && tmp^0==tmp^post_20 && tmp___0^0==tmp___0^post_20 && x^0==x^post_20 && y^0==y^post_20 ], cost: 1 20: l15 -> l7 : i^0'=i^post_21, j^0'=j^post_21, m^0'=m^post_21, n^0'=n^post_21, tmp^0'=tmp^post_21, tmp___0^0'=tmp___0^post_21, x^0'=x^post_21, y^0'=y^post_21, [ 1+x^0<=0 && i^0==i^post_21 && j^0==j^post_21 && m^0==m^post_21 && n^0==n^post_21 && tmp^0==tmp^post_21 && tmp___0^0==tmp___0^post_21 && x^0==x^post_21 && y^0==y^post_21 ], cost: 1 22: l16 -> l3 : i^0'=i^post_23, j^0'=j^post_23, m^0'=m^post_23, n^0'=n^post_23, tmp^0'=tmp^post_23, tmp___0^0'=tmp___0^post_23, x^0'=x^post_23, y^0'=y^post_23, [ 1+m^0<=n^0 && x^post_23==0 && i^post_23==m^0 && j^0==j^post_23 && m^0==m^post_23 && n^0==n^post_23 && tmp^0==tmp^post_23 && tmp___0^0==tmp___0^post_23 && y^0==y^post_23 ], cost: 1 23: l18 -> l15 : i^0'=i^post_24, j^0'=j^post_24, m^0'=m^post_24, n^0'=n^post_24, tmp^0'=tmp^post_24, tmp___0^0'=tmp___0^post_24, x^0'=x^post_24, y^0'=y^post_24, [ 1+n^0<=j^0 && i^0==i^post_24 && j^0==j^post_24 && m^0==m^post_24 && n^0==n^post_24 && tmp^0==tmp^post_24 && tmp___0^0==tmp___0^post_24 && x^0==x^post_24 && y^0==y^post_24 ], cost: 1 24: l18 -> l19 : i^0'=i^post_25, j^0'=j^post_25, m^0'=m^post_25, n^0'=n^post_25, tmp^0'=tmp^post_25, tmp___0^0'=tmp___0^post_25, x^0'=x^post_25, y^0'=y^post_25, [ j^0<=n^0 && y^post_25==y^post_25 && j^post_25==1+j^0 && i^0==i^post_25 && m^0==m^post_25 && n^0==n^post_25 && tmp^0==tmp^post_25 && tmp___0^0==tmp___0^post_25 && x^0==x^post_25 ], cost: 1 25: l19 -> l18 : i^0'=i^post_26, j^0'=j^post_26, m^0'=m^post_26, n^0'=n^post_26, tmp^0'=tmp^post_26, tmp___0^0'=tmp___0^post_26, x^0'=x^post_26, y^0'=y^post_26, [ i^0==i^post_26 && j^0==j^post_26 && m^0==m^post_26 && n^0==n^post_26 && tmp^0==tmp^post_26 && tmp___0^0==tmp___0^post_26 && x^0==x^post_26 && y^0==y^post_26 ], cost: 1 27: l20 -> l19 : i^0'=i^post_28, j^0'=j^post_28, m^0'=m^post_28, n^0'=n^post_28, tmp^0'=tmp^post_28, tmp___0^0'=tmp___0^post_28, x^0'=x^post_28, y^0'=y^post_28, [ 1+n^0<=j^0 && i^0==i^post_28 && j^0==j^post_28 && m^0==m^post_28 && n^0==n^post_28 && tmp^0==tmp^post_28 && tmp___0^0==tmp___0^post_28 && x^0==x^post_28 && y^0==y^post_28 ], cost: 1 28: l20 -> l21 : i^0'=i^post_29, j^0'=j^post_29, m^0'=m^post_29, n^0'=n^post_29, tmp^0'=tmp^post_29, tmp___0^0'=tmp___0^post_29, x^0'=x^post_29, y^0'=y^post_29, [ j^0<=n^0 && y^post_29==y^post_29 && j^post_29==1+j^0 && i^0==i^post_29 && m^0==m^post_29 && n^0==n^post_29 && tmp^0==tmp^post_29 && tmp___0^0==tmp___0^post_29 && x^0==x^post_29 ], cost: 1 29: l21 -> l20 : i^0'=i^post_30, j^0'=j^post_30, m^0'=m^post_30, n^0'=n^post_30, tmp^0'=tmp^post_30, tmp___0^0'=tmp___0^post_30, x^0'=x^post_30, y^0'=y^post_30, [ i^0==i^post_30 && j^0==j^post_30 && m^0==m^post_30 && n^0==n^post_30 && tmp^0==tmp^post_30 && tmp___0^0==tmp___0^post_30 && x^0==x^post_30 && y^0==y^post_30 ], cost: 1 33: l22 -> l3 : i^0'=i^post_34, j^0'=j^post_34, m^0'=m^post_34, n^0'=n^post_34, tmp^0'=tmp^post_34, tmp___0^0'=tmp___0^post_34, x^0'=x^post_34, y^0'=y^post_34, [ j^post_34==1+j^0 && i^0==i^post_34 && m^0==m^post_34 && n^0==n^post_34 && tmp^0==tmp^post_34 && tmp___0^0==tmp___0^post_34 && x^0==x^post_34 && y^0==y^post_34 ], cost: 1 36: l23 -> l5 : i^0'=i^post_37, j^0'=j^post_37, m^0'=m^post_37, n^0'=n^post_37, tmp^0'=tmp^post_37, tmp___0^0'=tmp___0^post_37, x^0'=x^post_37, y^0'=y^post_37, [ i^0==i^post_37 && j^0==j^post_37 && m^0==m^post_37 && n^0==n^post_37 && tmp^0==tmp^post_37 && tmp___0^0==tmp___0^post_37 && x^0==x^post_37 && y^0==y^post_37 ], cost: 1 Simplified all rules, resulting in: Start location: l23 0: l0 -> l1 : [ 1+n^0<=j^0 ], cost: 1 1: l0 -> l2 : tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 ], cost: 1 30: l1 -> l15 : [ -m^0+i^0==0 ], cost: 1 31: l1 -> l21 : [ 1+m^0<=i^0 ], cost: 1 32: l1 -> l21 : [ 1+i^0<=m^0 ], cost: 1 34: l2 -> l22 : [ tmp^0<=tmp___0^0 ], cost: 1 35: l2 -> l22 : i^0'=j^0, x^0'=x^post_36, [ 1+tmp___0^0<=tmp^0 ], cost: 1 2: l3 -> l0 : [], cost: 1 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 26: l5 -> l16 : [], cost: 1 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 17: l7 -> l14 : [], cost: 1 5: l8 -> l6 : [ 1+n^0<=j^0 ], cost: 1 6: l8 -> l9 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 1 7: l9 -> l8 : [], cost: 1 8: l10 -> l9 : [ 1+n^0<=j^0 ], cost: 1 9: l10 -> l11 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 1 10: l11 -> l10 : [], cost: 1 11: l12 -> l11 : y^0'=y^post_12, [], cost: 1 12: l13 -> l6 : [ y^0==0 ], cost: 1 13: l13 -> l12 : [ 1<=y^0 ], cost: 1 14: l13 -> l12 : [ 1+y^0<=0 ], cost: 1 15: l14 -> l4 : [ 1+n^0<=i^0 ], cost: 1 16: l14 -> l13 : y^0'=y^post_17, [ i^0<=n^0 ], cost: 1 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 22: l16 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 1 23: l18 -> l15 : [ 1+n^0<=j^0 ], cost: 1 24: l18 -> l19 : j^0'=1+j^0, y^0'=y^post_25, [ j^0<=n^0 ], cost: 1 25: l19 -> l18 : [], cost: 1 27: l20 -> l19 : [ 1+n^0<=j^0 ], cost: 1 28: l20 -> l21 : j^0'=1+j^0, y^0'=y^post_29, [ j^0<=n^0 ], cost: 1 29: l21 -> l20 : [], cost: 1 33: l22 -> l3 : j^0'=1+j^0, [], cost: 1 36: l23 -> l5 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l23 0: l0 -> l1 : [ 1+n^0<=j^0 ], cost: 1 1: l0 -> l2 : tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 ], cost: 1 30: l1 -> l15 : [ -m^0+i^0==0 ], cost: 1 31: l1 -> l21 : [ 1+m^0<=i^0 ], cost: 1 32: l1 -> l21 : [ 1+i^0<=m^0 ], cost: 1 34: l2 -> l22 : [ tmp^0<=tmp___0^0 ], cost: 1 35: l2 -> l22 : i^0'=j^0, x^0'=x^post_36, [ 1+tmp___0^0<=tmp^0 ], cost: 1 2: l3 -> l0 : [], cost: 1 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 17: l7 -> l14 : [], cost: 1 5: l8 -> l6 : [ 1+n^0<=j^0 ], cost: 1 6: l8 -> l9 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 1 7: l9 -> l8 : [], cost: 1 8: l10 -> l9 : [ 1+n^0<=j^0 ], cost: 1 9: l10 -> l11 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 1 10: l11 -> l10 : [], cost: 1 11: l12 -> l11 : y^0'=y^post_12, [], cost: 1 12: l13 -> l6 : [ y^0==0 ], cost: 1 13: l13 -> l12 : [ 1<=y^0 ], cost: 1 14: l13 -> l12 : [ 1+y^0<=0 ], cost: 1 15: l14 -> l4 : [ 1+n^0<=i^0 ], cost: 1 16: l14 -> l13 : y^0'=y^post_17, [ i^0<=n^0 ], cost: 1 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 23: l18 -> l15 : [ 1+n^0<=j^0 ], cost: 1 24: l18 -> l19 : j^0'=1+j^0, y^0'=y^post_25, [ j^0<=n^0 ], cost: 1 25: l19 -> l18 : [], cost: 1 27: l20 -> l19 : [ 1+n^0<=j^0 ], cost: 1 28: l20 -> l21 : j^0'=1+j^0, y^0'=y^post_29, [ j^0<=n^0 ], cost: 1 29: l21 -> l20 : [], cost: 1 33: l22 -> l3 : j^0'=1+j^0, [], cost: 1 36: l23 -> l5 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l23 30: l1 -> l15 : [ -m^0+i^0==0 ], cost: 1 31: l1 -> l21 : [ 1+m^0<=i^0 ], cost: 1 32: l1 -> l21 : [ 1+i^0<=m^0 ], cost: 1 52: l2 -> l3 : j^0'=1+j^0, [ tmp^0<=tmp___0^0 ], cost: 2 53: l2 -> l3 : i^0'=j^0, j^0'=1+j^0, x^0'=x^post_36, [ 1+tmp___0^0<=tmp^0 ], cost: 2 38: l3 -> l1 : [ 1+n^0<=j^0 ], cost: 2 39: l3 -> l2 : tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 ], cost: 2 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 41: l7 -> l13 : y^0'=y^post_17, [ i^0<=n^0 ], cost: 2 46: l9 -> l6 : [ 1+n^0<=j^0 ], cost: 2 47: l9 -> l9 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 2 44: l11 -> l9 : [ 1+n^0<=j^0 ], cost: 2 45: l11 -> l11 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 2 12: l13 -> l6 : [ y^0==0 ], cost: 1 42: l13 -> l11 : y^0'=y^post_12, [ 1<=y^0 ], cost: 2 43: l13 -> l11 : y^0'=y^post_12, [ 1+y^0<=0 ], cost: 2 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 50: l19 -> l15 : [ 1+n^0<=j^0 ], cost: 2 51: l19 -> l19 : j^0'=1+j^0, y^0'=y^post_25, [ j^0<=n^0 ], cost: 2 48: l21 -> l19 : [ 1+n^0<=j^0 ], cost: 2 49: l21 -> l21 : j^0'=1+j^0, y^0'=y^post_29, [ j^0<=n^0 ], cost: 2 36: l23 -> l5 : [], cost: 1 Accelerating simple loops of location 9. Accelerating the following rules: 47: l9 -> l9 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 2 Accelerated rule 47 with backward acceleration, yielding the new rule 54. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 47. Accelerating simple loops of location 11. Accelerating the following rules: 45: l11 -> l11 : j^0'=1+j^0, [ j^0<=n^0 ], cost: 2 Accelerated rule 45 with backward acceleration, yielding the new rule 55. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 45. Accelerating simple loops of location 19. Accelerating the following rules: 51: l19 -> l19 : j^0'=1+j^0, y^0'=y^post_25, [ j^0<=n^0 ], cost: 2 Accelerated rule 51 with backward acceleration, yielding the new rule 56. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 51. Accelerating simple loops of location 21. Accelerating the following rules: 49: l21 -> l21 : j^0'=1+j^0, y^0'=y^post_29, [ j^0<=n^0 ], cost: 2 Accelerated rule 49 with backward acceleration, yielding the new rule 57. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 49. Accelerated all simple loops using metering functions (where possible): Start location: l23 30: l1 -> l15 : [ -m^0+i^0==0 ], cost: 1 31: l1 -> l21 : [ 1+m^0<=i^0 ], cost: 1 32: l1 -> l21 : [ 1+i^0<=m^0 ], cost: 1 52: l2 -> l3 : j^0'=1+j^0, [ tmp^0<=tmp___0^0 ], cost: 2 53: l2 -> l3 : i^0'=j^0, j^0'=1+j^0, x^0'=x^post_36, [ 1+tmp___0^0<=tmp^0 ], cost: 2 38: l3 -> l1 : [ 1+n^0<=j^0 ], cost: 2 39: l3 -> l2 : tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 ], cost: 2 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 41: l7 -> l13 : y^0'=y^post_17, [ i^0<=n^0 ], cost: 2 46: l9 -> l6 : [ 1+n^0<=j^0 ], cost: 2 54: l9 -> l9 : j^0'=1+n^0, [ 1-j^0+n^0>=0 ], cost: 2-2*j^0+2*n^0 44: l11 -> l9 : [ 1+n^0<=j^0 ], cost: 2 55: l11 -> l11 : j^0'=1+n^0, [ 1-j^0+n^0>=0 ], cost: 2-2*j^0+2*n^0 12: l13 -> l6 : [ y^0==0 ], cost: 1 42: l13 -> l11 : y^0'=y^post_12, [ 1<=y^0 ], cost: 2 43: l13 -> l11 : y^0'=y^post_12, [ 1+y^0<=0 ], cost: 2 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 50: l19 -> l15 : [ 1+n^0<=j^0 ], cost: 2 56: l19 -> l19 : j^0'=1+n^0, y^0'=y^post_25, [ 1-j^0+n^0>=1 ], cost: 2-2*j^0+2*n^0 48: l21 -> l19 : [ 1+n^0<=j^0 ], cost: 2 57: l21 -> l21 : j^0'=1+n^0, y^0'=y^post_29, [ 1-j^0+n^0>=1 ], cost: 2-2*j^0+2*n^0 36: l23 -> l5 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: l23 30: l1 -> l15 : [ -m^0+i^0==0 ], cost: 1 31: l1 -> l21 : [ 1+m^0<=i^0 ], cost: 1 32: l1 -> l21 : [ 1+i^0<=m^0 ], cost: 1 61: l1 -> l21 : j^0'=1+n^0, y^0'=y^post_29, [ 1+m^0<=i^0 && 1-j^0+n^0>=1 ], cost: 3-2*j^0+2*n^0 62: l1 -> l21 : j^0'=1+n^0, y^0'=y^post_29, [ 1+i^0<=m^0 && 1-j^0+n^0>=1 ], cost: 3-2*j^0+2*n^0 52: l2 -> l3 : j^0'=1+j^0, [ tmp^0<=tmp___0^0 ], cost: 2 53: l2 -> l3 : i^0'=j^0, j^0'=1+j^0, x^0'=x^post_36, [ 1+tmp___0^0<=tmp^0 ], cost: 2 38: l3 -> l1 : [ 1+n^0<=j^0 ], cost: 2 39: l3 -> l2 : tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 ], cost: 2 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 41: l7 -> l13 : y^0'=y^post_17, [ i^0<=n^0 ], cost: 2 46: l9 -> l6 : [ 1+n^0<=j^0 ], cost: 2 44: l11 -> l9 : [ 1+n^0<=j^0 ], cost: 2 58: l11 -> l9 : j^0'=1+n^0, [ 1-j^0+n^0==0 ], cost: 4-2*j^0+2*n^0 12: l13 -> l6 : [ y^0==0 ], cost: 1 42: l13 -> l11 : y^0'=y^post_12, [ 1<=y^0 ], cost: 2 43: l13 -> l11 : y^0'=y^post_12, [ 1+y^0<=0 ], cost: 2 59: l13 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ 1<=y^0 && 1-j^0+n^0>=0 ], cost: 4-2*j^0+2*n^0 60: l13 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ 1+y^0<=0 && 1-j^0+n^0>=0 ], cost: 4-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 50: l19 -> l15 : [ 1+n^0<=j^0 ], cost: 2 48: l21 -> l19 : [ 1+n^0<=j^0 ], cost: 2 36: l23 -> l5 : [], cost: 1 Eliminated locations (on linear paths): Start location: l23 30: l1 -> l15 : [ -m^0+i^0==0 ], cost: 1 31: l1 -> l21 : [ 1+m^0<=i^0 ], cost: 1 32: l1 -> l21 : [ 1+i^0<=m^0 ], cost: 1 61: l1 -> l21 : j^0'=1+n^0, y^0'=y^post_29, [ 1+m^0<=i^0 && 1-j^0+n^0>=1 ], cost: 3-2*j^0+2*n^0 62: l1 -> l21 : j^0'=1+n^0, y^0'=y^post_29, [ 1+i^0<=m^0 && 1-j^0+n^0>=1 ], cost: 3-2*j^0+2*n^0 52: l2 -> l3 : j^0'=1+j^0, [ tmp^0<=tmp___0^0 ], cost: 2 53: l2 -> l3 : i^0'=j^0, j^0'=1+j^0, x^0'=x^post_36, [ 1+tmp___0^0<=tmp^0 ], cost: 2 38: l3 -> l1 : [ 1+n^0<=j^0 ], cost: 2 39: l3 -> l2 : tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 ], cost: 2 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 41: l7 -> l13 : y^0'=y^post_17, [ i^0<=n^0 ], cost: 2 46: l9 -> l6 : [ 1+n^0<=j^0 ], cost: 2 44: l11 -> l9 : [ 1+n^0<=j^0 ], cost: 2 58: l11 -> l9 : j^0'=1+n^0, [ 1-j^0+n^0==0 ], cost: 4-2*j^0+2*n^0 12: l13 -> l6 : [ y^0==0 ], cost: 1 42: l13 -> l11 : y^0'=y^post_12, [ 1<=y^0 ], cost: 2 43: l13 -> l11 : y^0'=y^post_12, [ 1+y^0<=0 ], cost: 2 59: l13 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ 1<=y^0 && 1-j^0+n^0>=0 ], cost: 4-2*j^0+2*n^0 60: l13 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ 1+y^0<=0 && 1-j^0+n^0>=0 ], cost: 4-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l23 64: l3 -> l15 : [ 1+n^0<=j^0 && -m^0+i^0==0 ], cost: 3 65: l3 -> l21 : [ 1+n^0<=j^0 && 1+m^0<=i^0 ], cost: 3 66: l3 -> l21 : [ 1+n^0<=j^0 && 1+i^0<=m^0 ], cost: 3 67: l3 -> l3 : j^0'=1+j^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 && tmp^post_2<=tmp___0^post_2 ], cost: 4 68: l3 -> l3 : i^0'=j^0, j^0'=1+j^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ j^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 ], cost: 4 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 69: l7 -> l6 : y^0'=y^post_17, [ i^0<=n^0 && y^post_17==0 ], cost: 3 70: l7 -> l11 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 ], cost: 4 71: l7 -> l11 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 ], cost: 4 72: l7 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 6-2*j^0+2*n^0 73: l7 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 6-2*j^0+2*n^0 74: l11 -> l6 : [ 1+n^0<=j^0 ], cost: 4 75: l11 -> l6 : j^0'=1+n^0, [ 1-j^0+n^0==0 ], cost: 6-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Accelerating simple loops of location 3. Accelerating the following rules: 67: l3 -> l3 : j^0'=1+j^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ j^0<=n^0 && tmp^post_2<=tmp___0^post_2 ], cost: 4 68: l3 -> l3 : i^0'=j^0, j^0'=1+j^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ j^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 ], cost: 4 Accelerated rule 67 with backward acceleration, yielding the new rule 76. Accelerated rule 68 with backward acceleration, yielding the new rule 77. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 67 68. Accelerated all simple loops using metering functions (where possible): Start location: l23 64: l3 -> l15 : [ 1+n^0<=j^0 && -m^0+i^0==0 ], cost: 3 65: l3 -> l21 : [ 1+n^0<=j^0 && 1+m^0<=i^0 ], cost: 3 66: l3 -> l21 : [ 1+n^0<=j^0 && 1+i^0<=m^0 ], cost: 3 76: l3 -> l3 : j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 4-4*j^0+4*n^0 77: l3 -> l3 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 4-4*j^0+4*n^0 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 69: l7 -> l6 : y^0'=y^post_17, [ i^0<=n^0 && y^post_17==0 ], cost: 3 70: l7 -> l11 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 ], cost: 4 71: l7 -> l11 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 ], cost: 4 72: l7 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 6-2*j^0+2*n^0 73: l7 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 6-2*j^0+2*n^0 74: l11 -> l6 : [ 1+n^0<=j^0 ], cost: 4 75: l11 -> l6 : j^0'=1+n^0, [ 1-j^0+n^0==0 ], cost: 6-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: l23 64: l3 -> l15 : [ 1+n^0<=j^0 && -m^0+i^0==0 ], cost: 3 65: l3 -> l21 : [ 1+n^0<=j^0 && 1+m^0<=i^0 ], cost: 3 66: l3 -> l21 : [ 1+n^0<=j^0 && 1+i^0<=m^0 ], cost: 3 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 37: l5 -> l3 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 ], cost: 2 78: l5 -> l3 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 79: l5 -> l3 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 69: l7 -> l6 : y^0'=y^post_17, [ i^0<=n^0 && y^post_17==0 ], cost: 3 70: l7 -> l11 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 ], cost: 4 71: l7 -> l11 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 ], cost: 4 72: l7 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 6-2*j^0+2*n^0 73: l7 -> l11 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 6-2*j^0+2*n^0 74: l11 -> l6 : [ 1+n^0<=j^0 ], cost: 4 75: l11 -> l6 : j^0'=1+n^0, [ 1-j^0+n^0==0 ], cost: 6-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 80: l5 -> l15 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 5 81: l5 -> l15 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 82: l5 -> l21 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 83: l5 -> [29] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 84: l5 -> [29] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 69: l7 -> l6 : y^0'=y^post_17, [ i^0<=n^0 && y^post_17==0 ], cost: 3 85: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1+n^0<=j^0 ], cost: 8 86: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0==0 ], cost: 10-2*j^0+2*n^0 87: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1+n^0<=j^0 ], cost: 8 88: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0==0 ], cost: 10-2*j^0+2*n^0 89: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 90: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 91: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 92: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Merged rules: Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 80: l5 -> l15 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 5 81: l5 -> l15 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 82: l5 -> l21 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 69: l7 -> l6 : y^0'=y^post_17, [ i^0<=n^0 && y^post_17==0 ], cost: 3 85: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1+n^0<=j^0 ], cost: 8 86: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0==0 ], cost: 10-2*j^0+2*n^0 87: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1+n^0<=j^0 ], cost: 8 88: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0==0 ], cost: 10-2*j^0+2*n^0 94: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 95: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Applied pruning (of leafs and parallel rules): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 80: l5 -> l15 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 5 81: l5 -> l15 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 82: l5 -> l21 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 85: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1+n^0<=j^0 ], cost: 8 87: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1+n^0<=j^0 ], cost: 8 88: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0==0 ], cost: 10-2*j^0+2*n^0 94: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 95: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 63: l21 -> l15 : [ 1+n^0<=j^0 ], cost: 4 36: l23 -> l5 : [], cost: 1 Eliminated locations (on linear paths): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 80: l5 -> l15 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 5 81: l5 -> l15 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 96: l5 -> l15 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 13-4*j^0+4*n^0 4: l6 -> l7 : i^0'=1+i^0, [], cost: 1 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 85: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1+n^0<=j^0 ], cost: 8 87: l7 -> l6 : y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1+n^0<=j^0 ], cost: 8 88: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0==0 ], cost: 10-2*j^0+2*n^0 94: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 95: l7 -> l6 : j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 10-2*j^0+2*n^0 18: l15 -> l4 : [ x^0==0 ], cost: 1 19: l15 -> l7 : [ 1<=x^0 ], cost: 1 20: l15 -> l7 : [ 1+x^0<=0 ], cost: 1 36: l23 -> l5 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 97: l5 -> l4 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 6 98: l5 -> l4 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 10-4*j^0+4*n^0 99: l5 -> l4 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && x^post_36==0 ], cost: 14-4*j^0+4*n^0 100: l5 -> l7 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 101: l5 -> l7 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 103: l7 -> l7 : i^0'=1+i^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1+n^0<=j^0 ], cost: 9 104: l7 -> l7 : i^0'=1+i^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1+n^0<=j^0 ], cost: 9 105: l7 -> l7 : i^0'=1+i^0, j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0==0 ], cost: 11-2*j^0+2*n^0 106: l7 -> l7 : i^0'=1+i^0, j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1<=y^post_17 && 1-j^0+n^0>=0 ], cost: 11-2*j^0+2*n^0 107: l7 -> l7 : i^0'=1+i^0, j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1+y^post_17<=0 && 1-j^0+n^0>=0 ], cost: 11-2*j^0+2*n^0 36: l23 -> l5 : [], cost: 1 Accelerating simple loops of location 7. [accelerate] Removed some duplicate simple loops Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 104: l7 -> l7 : i^0'=1+i^0, y^0'=y^post_12, [ i^0<=n^0 && 1+n^0<=j^0 ], cost: 9 105: l7 -> l7 : i^0'=1+i^0, j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1-j^0+n^0==0 ], cost: 11-2*j^0+2*n^0 107: l7 -> l7 : i^0'=1+i^0, j^0'=1+n^0, y^0'=y^post_12, [ i^0<=n^0 && 1-j^0+n^0>=0 ], cost: 11-2*j^0+2*n^0 Accelerated rule 104 with backward acceleration, yielding the new rule 108. Accelerated rule 105 with backward acceleration, yielding the new rule 109. Accelerated rule 107 with backward acceleration, yielding the new rule 110. [accelerate] Nesting with 3 inner and 3 outer candidates Removing the simple loops: 104 105 107. Accelerated all simple loops using metering functions (where possible): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 97: l5 -> l4 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 6 98: l5 -> l4 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 10-4*j^0+4*n^0 99: l5 -> l4 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && x^post_36==0 ], cost: 14-4*j^0+4*n^0 100: l5 -> l7 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 101: l5 -> l7 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 108: l7 -> l7 : i^0'=1+n^0, y^0'=y^post_12, [ 1+n^0<=j^0 && 1+n^0-i^0>=1 ], cost: 9+9*n^0-9*i^0 109: l7 -> l7 : i^0'=1+n^0, j^0'=1+n^0, y^0'=y^post_12, [ 1-j^0+n^0==0 && 1+n^0-i^0>=1 ], cost: 9+9*n^0-9*i^0 110: l7 -> l7 : i^0'=1+n^0, j^0'=1+n^0, y^0'=y^post_12, [ 1-j^0+n^0>=0 && 1+n^0-i^0>=1 ], cost: 9+9*n^0-9*i^0 36: l23 -> l5 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 97: l5 -> l4 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 6 98: l5 -> l4 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 10-4*j^0+4*n^0 99: l5 -> l4 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && x^post_36==0 ], cost: 14-4*j^0+4*n^0 100: l5 -> l7 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 101: l5 -> l7 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 111: l5 -> l7 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 23-4*j^0+4*n^0 112: l5 -> l7 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 23-4*j^0+4*n^0 113: l5 -> l7 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 23-4*j^0+4*n^0 114: l5 -> l7 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 23-4*j^0+4*n^0 115: l5 -> l7 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 23-4*j^0+4*n^0 116: l5 -> l7 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 23-4*j^0+4*n^0 40: l7 -> l4 : [ 1+n^0<=i^0 ], cost: 2 36: l23 -> l5 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 97: l5 -> l4 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 6 98: l5 -> l4 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 10-4*j^0+4*n^0 99: l5 -> l4 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && x^post_36==0 ], cost: 14-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 117: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 25-4*j^0+4*n^0 118: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 25-4*j^0+4*n^0 119: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 25-4*j^0+4*n^0 120: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 25-4*j^0+4*n^0 121: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 25-4*j^0+4*n^0 122: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 25-4*j^0+4*n^0 123: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 124: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 36: l23 -> l5 : [], cost: 1 Merged rules: Start location: l23 3: l4 -> l5 : m^0'=1+m^0, [], cost: 1 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 97: l5 -> l4 : i^0'=m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 6 98: l5 -> l4 : i^0'=m^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 10-4*j^0+4*n^0 99: l5 -> l4 : i^0'=n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && x^post_36==0 ], cost: 14-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 123: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 124: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 127: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 25-4*j^0+4*n^0 128: l5 -> l4 : i^0'=1+n^0, j^0'=1+n^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 25-4*j^0+4*n^0 36: l23 -> l5 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l23 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 123: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 124: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 129: l5 -> l5 : i^0'=m^0, m^0'=1+m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 7 130: l5 -> l5 : i^0'=m^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 11-4*j^0+4*n^0 131: l5 -> l5 : i^0'=n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && x^post_36==0 ], cost: 15-4*j^0+4*n^0 132: l5 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 26-4*j^0+4*n^0 133: l5 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 26-4*j^0+4*n^0 36: l23 -> l5 : [], cost: 1 Accelerating simple loops of location 5. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 129: l5 -> l5 : i^0'=m^0, m^0'=1+m^0, x^0'=0, [ 1+m^0<=n^0 && 1+n^0<=j^0 ], cost: 7 130: l5 -> l5 : i^0'=m^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 11-4*j^0+4*n^0 131: l5 -> l5 : i^0'=n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 15-4*j^0+4*n^0 132: l5 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 26-4*j^0+4*n^0 133: l5 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 26-4*j^0+4*n^0 Accelerated rule 129 with backward acceleration, yielding the new rule 134. Failed to prove monotonicity of the guard of rule 130. Failed to prove monotonicity of the guard of rule 131. Failed to prove monotonicity of the guard of rule 132. Failed to prove monotonicity of the guard of rule 133. [accelerate] Nesting with 5 inner and 5 outer candidates Removing the simple loops: 129. Accelerated all simple loops using metering functions (where possible): Start location: l23 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 123: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 124: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 130: l5 -> l5 : i^0'=m^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 11-4*j^0+4*n^0 131: l5 -> l5 : i^0'=n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 15-4*j^0+4*n^0 132: l5 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 26-4*j^0+4*n^0 133: l5 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 26-4*j^0+4*n^0 134: l5 -> l5 : i^0'=-1+n^0, m^0'=n^0, x^0'=0, [ 1+n^0<=j^0 && -m^0+n^0>=1 ], cost: -7*m^0+7*n^0 36: l23 -> l5 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: l23 93: l5 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 6-4*j^0+4*n^0 102: l5 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 9-4*j^0+4*n^0 123: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 14-4*j^0+4*n^0 124: l5 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 14-4*j^0+4*n^0 36: l23 -> l5 : [], cost: 1 135: l23 -> l5 : i^0'=m^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 12-4*j^0+4*n^0 136: l23 -> l5 : i^0'=n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=0, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 16-4*j^0+4*n^0 137: l23 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 27-4*j^0+4*n^0 138: l23 -> l5 : i^0'=1+n^0, j^0'=1+n^0, m^0'=1+m^0, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, x^0'=x^post_36, y^0'=y^post_12, [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 27-4*j^0+4*n^0 139: l23 -> l5 : i^0'=-1+n^0, m^0'=n^0, x^0'=0, [ 1+n^0<=j^0 && -m^0+n^0>=1 ], cost: 1-7*m^0+7*n^0 Eliminated locations (on tree-shaped paths): Start location: l23 140: l23 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 7-4*j^0+4*n^0 141: l23 -> [30] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 10-4*j^0+4*n^0 142: l23 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 15-4*j^0+4*n^0 143: l23 -> [32] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 15-4*j^0+4*n^0 144: l23 -> [34] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 12-4*j^0+4*n^0 145: l23 -> [34] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 16-4*j^0+4*n^0 146: l23 -> [34] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 27-4*j^0+4*n^0 147: l23 -> [34] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 27-4*j^0+4*n^0 148: l23 -> [34] : [ 1+n^0<=j^0 && -m^0+n^0>=1 ], cost: 1-7*m^0+7*n^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l23 140: l23 -> [29] : [ 1+m^0<=n^0 && 1-j^0+n^0>=1 ], cost: 7-4*j^0+4*n^0 144: l23 -> [34] : [ 1+m^0<=n^0 && tmp^post_2<=tmp___0^post_2 && 1-j^0+n^0>=1 ], cost: 12-4*j^0+4*n^0 145: l23 -> [34] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 ], cost: 16-4*j^0+4*n^0 146: l23 -> [34] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1<=x^post_36 ], cost: 27-4*j^0+4*n^0 147: l23 -> [34] : [ 1+m^0<=n^0 && 1+tmp___0^post_2<=tmp^post_2 && 1-j^0+n^0>=1 && 1+x^post_36<=0 ], cost: 27-4*j^0+4*n^0 148: l23 -> [34] : [ 1+n^0<=j^0 && -m^0+n^0>=1 ], cost: 1-7*m^0+7*n^0 Computing asymptotic complexity for rule 140 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 148 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 144 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 145 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 146 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 147 Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ i^0==i^post_37 && j^0==j^post_37 && m^0==m^post_37 && n^0==n^post_37 && tmp^0==tmp^post_37 && tmp___0^0==tmp___0^post_37 && x^0==x^post_37 && y^0==y^post_37 ] WORST_CASE(Omega(1),?)