NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l31 0: l0 -> l1 : r0^0'=r0^post_1, r^0'=r^post_1, x1^0'=x1^post_1, x^0'=x^post_1, [ r0^0<=0 && 0<=r0^0 && r^0==r^post_1 && r0^0==r0^post_1 && x^0==x^post_1 && x1^0==x1^post_1 ], cost: 1 1: l2 -> l3 : r0^0'=r0^post_2, r^0'=r^post_2, x1^0'=x1^post_2, x^0'=x^post_2, [ r^0<=1 && 1<=r^0 && r^0==r^post_2 && r0^0==r0^post_2 && x^0==x^post_2 && x1^0==x1^post_2 ], cost: 1 2: l4 -> l3 : r0^0'=r0^post_3, r^0'=r^post_3, x1^0'=x1^post_3, x^0'=x^post_3, [ r^0<=1 && 1<=r^0 && r^0==r^post_3 && r0^0==r0^post_3 && x^0==x^post_3 && x1^0==x1^post_3 ], cost: 1 3: l5 -> l3 : r0^0'=r0^post_4, r^0'=r^post_4, x1^0'=x1^post_4, x^0'=x^post_4, [ r^0<=1 && 1<=r^0 && r^0==r^post_4 && r0^0==r0^post_4 && x^0==x^post_4 && x1^0==x1^post_4 ], cost: 1 4: l6 -> l7 : r0^0'=r0^post_5, r^0'=r^post_5, x1^0'=x1^post_5, x^0'=x^post_5, [ x1^post_5==x^0 && r^0==r^post_5 && r0^0==r0^post_5 && x^0==x^post_5 ], cost: 1 5: l6 -> l8 : r0^0'=r0^post_6, r^0'=r^post_6, x1^0'=x1^post_6, x^0'=x^post_6, [ r^0==r^post_6 && r0^0==r0^post_6 && x^0==x^post_6 && x1^0==x1^post_6 ], cost: 1 7: l6 -> l3 : r0^0'=r0^post_8, r^0'=r^post_8, x1^0'=x1^post_8, x^0'=x^post_8, [ r^0==r^post_8 && r0^0==r0^post_8 && x^0==x^post_8 && x1^0==x1^post_8 ], cost: 1 8: l7 -> l9 : r0^0'=r0^post_9, r^0'=r^post_9, x1^0'=x1^post_9, x^0'=x^post_9, [ 1+x1^0<=2 && r^0==r^post_9 && r0^0==r0^post_9 && x^0==x^post_9 && x1^0==x1^post_9 ], cost: 1 9: l7 -> l9 : r0^0'=r0^post_10, r^0'=r^post_10, x1^0'=x1^post_10, x^0'=x^post_10, [ 3<=x1^0 && r^0==r^post_10 && r0^0==r0^post_10 && x^0==x^post_10 && x1^0==x1^post_10 ], cost: 1 11: l7 -> l2 : r0^0'=r0^post_12, r^0'=r^post_12, x1^0'=x1^post_12, x^0'=x^post_12, [ r^post_12==1 && r0^0==r0^post_12 && x^0==x^post_12 && x1^0==x1^post_12 ], cost: 1 12: l7 -> l10 : r0^0'=r0^post_13, r^0'=r^post_13, x1^0'=x1^post_13, x^0'=x^post_13, [ r^0==r^post_13 && r0^0==r0^post_13 && x^0==x^post_13 && x1^0==x1^post_13 ], cost: 1 6: l8 -> l6 : r0^0'=r0^post_7, r^0'=r^post_7, x1^0'=x1^post_7, x^0'=x^post_7, [ r^0==r^post_7 && r0^0==r0^post_7 && x^0==x^post_7 && x1^0==x1^post_7 ], cost: 1 10: l9 -> l2 : r0^0'=r0^post_11, r^0'=r^post_11, x1^0'=x1^post_11, x^0'=x^post_11, [ r^post_11==0 && r0^0==r0^post_11 && x^0==x^post_11 && x1^0==x1^post_11 ], cost: 1 13: l10 -> l7 : r0^0'=r0^post_14, r^0'=r^post_14, x1^0'=x1^post_14, x^0'=x^post_14, [ r^0==r^post_14 && r0^0==r0^post_14 && x^0==x^post_14 && x1^0==x1^post_14 ], cost: 1 14: l11 -> l12 : r0^0'=r0^post_15, r^0'=r^post_15, x1^0'=x1^post_15, x^0'=x^post_15, [ 1+x1^0<=2 && r^0==r^post_15 && r0^0==r0^post_15 && x^0==x^post_15 && x1^0==x1^post_15 ], cost: 1 15: l11 -> l12 : r0^0'=r0^post_16, r^0'=r^post_16, x1^0'=x1^post_16, x^0'=x^post_16, [ 3<=x1^0 && r^0==r^post_16 && r0^0==r0^post_16 && x^0==x^post_16 && x1^0==x1^post_16 ], cost: 1 17: l11 -> l4 : r0^0'=r0^post_18, r^0'=r^post_18, x1^0'=x1^post_18, x^0'=x^post_18, [ r^post_18==1 && r0^0==r0^post_18 && x^0==x^post_18 && x1^0==x1^post_18 ], cost: 1 18: l11 -> l13 : r0^0'=r0^post_19, r^0'=r^post_19, x1^0'=x1^post_19, x^0'=x^post_19, [ r^0==r^post_19 && r0^0==r0^post_19 && x^0==x^post_19 && x1^0==x1^post_19 ], cost: 1 16: l12 -> l4 : r0^0'=r0^post_17, r^0'=r^post_17, x1^0'=x1^post_17, x^0'=x^post_17, [ r^post_17==0 && r0^0==r0^post_17 && x^0==x^post_17 && x1^0==x1^post_17 ], cost: 1 19: l13 -> l11 : r0^0'=r0^post_20, r^0'=r^post_20, x1^0'=x1^post_20, x^0'=x^post_20, [ r^0==r^post_20 && r0^0==r0^post_20 && x^0==x^post_20 && x1^0==x1^post_20 ], cost: 1 20: l14 -> l15 : r0^0'=r0^post_21, r^0'=r^post_21, x1^0'=x1^post_21, x^0'=x^post_21, [ 1+x1^0<=2 && r^0==r^post_21 && r0^0==r0^post_21 && x^0==x^post_21 && x1^0==x1^post_21 ], cost: 1 21: l14 -> l15 : r0^0'=r0^post_22, r^0'=r^post_22, x1^0'=x1^post_22, x^0'=x^post_22, [ 3<=x1^0 && r^0==r^post_22 && r0^0==r0^post_22 && x^0==x^post_22 && x1^0==x1^post_22 ], cost: 1 23: l14 -> l5 : r0^0'=r0^post_24, r^0'=r^post_24, x1^0'=x1^post_24, x^0'=x^post_24, [ r^post_24==1 && r0^0==r0^post_24 && x^0==x^post_24 && x1^0==x1^post_24 ], cost: 1 24: l14 -> l16 : r0^0'=r0^post_25, r^0'=r^post_25, x1^0'=x1^post_25, x^0'=x^post_25, [ r^0==r^post_25 && r0^0==r0^post_25 && x^0==x^post_25 && x1^0==x1^post_25 ], cost: 1 22: l15 -> l5 : r0^0'=r0^post_23, r^0'=r^post_23, x1^0'=x1^post_23, x^0'=x^post_23, [ r^post_23==0 && r0^0==r0^post_23 && x^0==x^post_23 && x1^0==x1^post_23 ], cost: 1 25: l16 -> l14 : r0^0'=r0^post_26, r^0'=r^post_26, x1^0'=x1^post_26, x^0'=x^post_26, [ r^0==r^post_26 && r0^0==r0^post_26 && x^0==x^post_26 && x1^0==x1^post_26 ], cost: 1 26: l17 -> l18 : r0^0'=r0^post_27, r^0'=r^post_27, x1^0'=x1^post_27, x^0'=x^post_27, [ 1+x1^0<=2 && r^0==r^post_27 && r0^0==r0^post_27 && x^0==x^post_27 && x1^0==x1^post_27 ], cost: 1 27: l17 -> l18 : r0^0'=r0^post_28, r^0'=r^post_28, x1^0'=x1^post_28, x^0'=x^post_28, [ 3<=x1^0 && r^0==r^post_28 && r0^0==r0^post_28 && x^0==x^post_28 && x1^0==x1^post_28 ], cost: 1 29: l17 -> l2 : r0^0'=r0^post_30, r^0'=r^post_30, x1^0'=x1^post_30, x^0'=x^post_30, [ r^post_30==1 && r0^0==r0^post_30 && x^0==x^post_30 && x1^0==x1^post_30 ], cost: 1 30: l17 -> l7 : r0^0'=r0^post_31, r^0'=r^post_31, x1^0'=x1^post_31, x^0'=x^post_31, [ x^post_31==2 && r^0==r^post_31 && r0^0==r0^post_31 && x1^0==x1^post_31 ], cost: 1 28: l18 -> l2 : r0^0'=r0^post_29, r^0'=r^post_29, x1^0'=x1^post_29, x^0'=x^post_29, [ r^post_29==0 && r0^0==r0^post_29 && x^0==x^post_29 && x1^0==x1^post_29 ], cost: 1 31: l19 -> l20 : r0^0'=r0^post_32, r^0'=r^post_32, x1^0'=x1^post_32, x^0'=x^post_32, [ 1+x1^0<=2 && r^0==r^post_32 && r0^0==r0^post_32 && x^0==x^post_32 && x1^0==x1^post_32 ], cost: 1 32: l19 -> l20 : r0^0'=r0^post_33, r^0'=r^post_33, x1^0'=x1^post_33, x^0'=x^post_33, [ 3<=x1^0 && r^0==r^post_33 && r0^0==r0^post_33 && x^0==x^post_33 && x1^0==x1^post_33 ], cost: 1 34: l19 -> l4 : r0^0'=r0^post_35, r^0'=r^post_35, x1^0'=x1^post_35, x^0'=x^post_35, [ r^post_35==1 && r0^0==r0^post_35 && x^0==x^post_35 && x1^0==x1^post_35 ], cost: 1 35: l19 -> l11 : r0^0'=r0^post_36, r^0'=r^post_36, x1^0'=x1^post_36, x^0'=x^post_36, [ x^post_36==2 && r^0==r^post_36 && r0^0==r0^post_36 && x1^0==x1^post_36 ], cost: 1 33: l20 -> l4 : r0^0'=r0^post_34, r^0'=r^post_34, x1^0'=x1^post_34, x^0'=x^post_34, [ r^post_34==0 && r0^0==r0^post_34 && x^0==x^post_34 && x1^0==x1^post_34 ], cost: 1 36: l21 -> l22 : r0^0'=r0^post_37, r^0'=r^post_37, x1^0'=x1^post_37, x^0'=x^post_37, [ 1+x1^0<=2 && r^0==r^post_37 && r0^0==r0^post_37 && x^0==x^post_37 && x1^0==x1^post_37 ], cost: 1 37: l21 -> l22 : r0^0'=r0^post_38, r^0'=r^post_38, x1^0'=x1^post_38, x^0'=x^post_38, [ 3<=x1^0 && r^0==r^post_38 && r0^0==r0^post_38 && x^0==x^post_38 && x1^0==x1^post_38 ], cost: 1 39: l21 -> l5 : r0^0'=r0^post_40, r^0'=r^post_40, x1^0'=x1^post_40, x^0'=x^post_40, [ r^post_40==1 && r0^0==r0^post_40 && x^0==x^post_40 && x1^0==x1^post_40 ], cost: 1 40: l21 -> l14 : r0^0'=r0^post_41, r^0'=r^post_41, x1^0'=x1^post_41, x^0'=x^post_41, [ x^post_41==2 && r^0==r^post_41 && r0^0==r0^post_41 && x1^0==x1^post_41 ], cost: 1 38: l22 -> l5 : r0^0'=r0^post_39, r^0'=r^post_39, x1^0'=x1^post_39, x^0'=x^post_39, [ r^post_39==0 && r0^0==r0^post_39 && x^0==x^post_39 && x1^0==x1^post_39 ], cost: 1 41: l23 -> l24 : r0^0'=r0^post_42, r^0'=r^post_42, x1^0'=x1^post_42, x^0'=x^post_42, [ 1+x1^0<=2 && r^0==r^post_42 && r0^0==r0^post_42 && x^0==x^post_42 && x1^0==x1^post_42 ], cost: 1 42: l23 -> l24 : r0^0'=r0^post_43, r^0'=r^post_43, x1^0'=x1^post_43, x^0'=x^post_43, [ 3<=x1^0 && r^0==r^post_43 && r0^0==r0^post_43 && x^0==x^post_43 && x1^0==x1^post_43 ], cost: 1 44: l23 -> l2 : r0^0'=r0^post_45, r^0'=r^post_45, x1^0'=x1^post_45, x^0'=x^post_45, [ r^post_45==1 && r0^0==r0^post_45 && x^0==x^post_45 && x1^0==x1^post_45 ], cost: 1 45: l23 -> l17 : r0^0'=r0^post_46, r^0'=r^post_46, x1^0'=x1^post_46, x^0'=x^post_46, [ x^post_46==1 && r^0==r^post_46 && r0^0==r0^post_46 && x1^0==x1^post_46 ], cost: 1 43: l24 -> l2 : r0^0'=r0^post_44, r^0'=r^post_44, x1^0'=x1^post_44, x^0'=x^post_44, [ r^post_44==0 && r0^0==r0^post_44 && x^0==x^post_44 && x1^0==x1^post_44 ], cost: 1 46: l25 -> l26 : r0^0'=r0^post_47, r^0'=r^post_47, x1^0'=x1^post_47, x^0'=x^post_47, [ 1+x1^0<=2 && r^0==r^post_47 && r0^0==r0^post_47 && x^0==x^post_47 && x1^0==x1^post_47 ], cost: 1 47: l25 -> l26 : r0^0'=r0^post_48, r^0'=r^post_48, x1^0'=x1^post_48, x^0'=x^post_48, [ 3<=x1^0 && r^0==r^post_48 && r0^0==r0^post_48 && x^0==x^post_48 && x1^0==x1^post_48 ], cost: 1 49: l25 -> l4 : r0^0'=r0^post_50, r^0'=r^post_50, x1^0'=x1^post_50, x^0'=x^post_50, [ r^post_50==1 && r0^0==r0^post_50 && x^0==x^post_50 && x1^0==x1^post_50 ], cost: 1 50: l25 -> l19 : r0^0'=r0^post_51, r^0'=r^post_51, x1^0'=x1^post_51, x^0'=x^post_51, [ x^post_51==1 && r^0==r^post_51 && r0^0==r0^post_51 && x1^0==x1^post_51 ], cost: 1 48: l26 -> l4 : r0^0'=r0^post_49, r^0'=r^post_49, x1^0'=x1^post_49, x^0'=x^post_49, [ r^post_49==0 && r0^0==r0^post_49 && x^0==x^post_49 && x1^0==x1^post_49 ], cost: 1 51: l27 -> l28 : r0^0'=r0^post_52, r^0'=r^post_52, x1^0'=x1^post_52, x^0'=x^post_52, [ 1+x1^0<=2 && r^0==r^post_52 && r0^0==r0^post_52 && x^0==x^post_52 && x1^0==x1^post_52 ], cost: 1 52: l27 -> l28 : r0^0'=r0^post_53, r^0'=r^post_53, x1^0'=x1^post_53, x^0'=x^post_53, [ 3<=x1^0 && r^0==r^post_53 && r0^0==r0^post_53 && x^0==x^post_53 && x1^0==x1^post_53 ], cost: 1 54: l27 -> l5 : r0^0'=r0^post_55, r^0'=r^post_55, x1^0'=x1^post_55, x^0'=x^post_55, [ r^post_55==1 && r0^0==r0^post_55 && x^0==x^post_55 && x1^0==x1^post_55 ], cost: 1 55: l27 -> l21 : r0^0'=r0^post_56, r^0'=r^post_56, x1^0'=x1^post_56, x^0'=x^post_56, [ x^post_56==1 && r^0==r^post_56 && r0^0==r0^post_56 && x1^0==x1^post_56 ], cost: 1 53: l28 -> l5 : r0^0'=r0^post_54, r^0'=r^post_54, x1^0'=x1^post_54, x^0'=x^post_54, [ r^post_54==0 && r0^0==r0^post_54 && x^0==x^post_54 && x1^0==x1^post_54 ], cost: 1 56: l29 -> l19 : r0^0'=r0^post_57, r^0'=r^post_57, x1^0'=x1^post_57, x^0'=x^post_57, [ x1^post_57==x^0 && r^0==r^post_57 && r0^0==r0^post_57 && x^0==x^post_57 ], cost: 1 57: l29 -> l6 : r0^0'=r0^post_58, r^0'=r^post_58, x1^0'=x1^post_58, x^0'=x^post_58, [ x^post_58==2 && r^0==r^post_58 && r0^0==r0^post_58 && x1^0==x1^post_58 ], cost: 1 58: l29 -> l3 : r0^0'=r0^post_59, r^0'=r^post_59, x1^0'=x1^post_59, x^0'=x^post_59, [ r^0==r^post_59 && r0^0==r0^post_59 && x^0==x^post_59 && x1^0==x1^post_59 ], cost: 1 59: l30 -> l27 : r0^0'=r0^post_60, r^0'=r^post_60, x1^0'=x1^post_60, x^0'=x^post_60, [ x1^post_60==x^0 && r^0==r^post_60 && r0^0==r0^post_60 && x^0==x^post_60 ], cost: 1 60: l30 -> l29 : r0^0'=r0^post_61, r^0'=r^post_61, x1^0'=x1^post_61, x^0'=x^post_61, [ x^post_61==1 && r^0==r^post_61 && r0^0==r0^post_61 && x1^0==x1^post_61 ], cost: 1 61: l30 -> l3 : r0^0'=r0^post_62, r^0'=r^post_62, x1^0'=x1^post_62, x^0'=x^post_62, [ r^0==r^post_62 && r0^0==r0^post_62 && x^0==x^post_62 && x1^0==x1^post_62 ], cost: 1 62: l31 -> l30 : r0^0'=r0^post_63, r^0'=r^post_63, x1^0'=x1^post_63, x^0'=x^post_63, [ r^0==r^post_63 && r0^0==r0^post_63 && x^0==x^post_63 && x1^0==x1^post_63 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 62: l31 -> l30 : r0^0'=r0^post_63, r^0'=r^post_63, x1^0'=x1^post_63, x^0'=x^post_63, [ r^0==r^post_63 && r0^0==r0^post_63 && x^0==x^post_63 && x1^0==x1^post_63 ], cost: 1 Removed unreachable and leaf rules: Start location: l31 4: l6 -> l7 : r0^0'=r0^post_5, r^0'=r^post_5, x1^0'=x1^post_5, x^0'=x^post_5, [ x1^post_5==x^0 && r^0==r^post_5 && r0^0==r0^post_5 && x^0==x^post_5 ], cost: 1 5: l6 -> l8 : r0^0'=r0^post_6, r^0'=r^post_6, x1^0'=x1^post_6, x^0'=x^post_6, [ r^0==r^post_6 && r0^0==r0^post_6 && x^0==x^post_6 && x1^0==x1^post_6 ], cost: 1 12: l7 -> l10 : r0^0'=r0^post_13, r^0'=r^post_13, x1^0'=x1^post_13, x^0'=x^post_13, [ r^0==r^post_13 && r0^0==r0^post_13 && x^0==x^post_13 && x1^0==x1^post_13 ], cost: 1 6: l8 -> l6 : r0^0'=r0^post_7, r^0'=r^post_7, x1^0'=x1^post_7, x^0'=x^post_7, [ r^0==r^post_7 && r0^0==r0^post_7 && x^0==x^post_7 && x1^0==x1^post_7 ], cost: 1 13: l10 -> l7 : r0^0'=r0^post_14, r^0'=r^post_14, x1^0'=x1^post_14, x^0'=x^post_14, [ r^0==r^post_14 && r0^0==r0^post_14 && x^0==x^post_14 && x1^0==x1^post_14 ], cost: 1 18: l11 -> l13 : r0^0'=r0^post_19, r^0'=r^post_19, x1^0'=x1^post_19, x^0'=x^post_19, [ r^0==r^post_19 && r0^0==r0^post_19 && x^0==x^post_19 && x1^0==x1^post_19 ], cost: 1 19: l13 -> l11 : r0^0'=r0^post_20, r^0'=r^post_20, x1^0'=x1^post_20, x^0'=x^post_20, [ r^0==r^post_20 && r0^0==r0^post_20 && x^0==x^post_20 && x1^0==x1^post_20 ], cost: 1 24: l14 -> l16 : r0^0'=r0^post_25, r^0'=r^post_25, x1^0'=x1^post_25, x^0'=x^post_25, [ r^0==r^post_25 && r0^0==r0^post_25 && x^0==x^post_25 && x1^0==x1^post_25 ], cost: 1 25: l16 -> l14 : r0^0'=r0^post_26, r^0'=r^post_26, x1^0'=x1^post_26, x^0'=x^post_26, [ r^0==r^post_26 && r0^0==r0^post_26 && x^0==x^post_26 && x1^0==x1^post_26 ], cost: 1 35: l19 -> l11 : r0^0'=r0^post_36, r^0'=r^post_36, x1^0'=x1^post_36, x^0'=x^post_36, [ x^post_36==2 && r^0==r^post_36 && r0^0==r0^post_36 && x1^0==x1^post_36 ], cost: 1 40: l21 -> l14 : r0^0'=r0^post_41, r^0'=r^post_41, x1^0'=x1^post_41, x^0'=x^post_41, [ x^post_41==2 && r^0==r^post_41 && r0^0==r0^post_41 && x1^0==x1^post_41 ], cost: 1 55: l27 -> l21 : r0^0'=r0^post_56, r^0'=r^post_56, x1^0'=x1^post_56, x^0'=x^post_56, [ x^post_56==1 && r^0==r^post_56 && r0^0==r0^post_56 && x1^0==x1^post_56 ], cost: 1 56: l29 -> l19 : r0^0'=r0^post_57, r^0'=r^post_57, x1^0'=x1^post_57, x^0'=x^post_57, [ x1^post_57==x^0 && r^0==r^post_57 && r0^0==r0^post_57 && x^0==x^post_57 ], cost: 1 57: l29 -> l6 : r0^0'=r0^post_58, r^0'=r^post_58, x1^0'=x1^post_58, x^0'=x^post_58, [ x^post_58==2 && r^0==r^post_58 && r0^0==r0^post_58 && x1^0==x1^post_58 ], cost: 1 59: l30 -> l27 : r0^0'=r0^post_60, r^0'=r^post_60, x1^0'=x1^post_60, x^0'=x^post_60, [ x1^post_60==x^0 && r^0==r^post_60 && r0^0==r0^post_60 && x^0==x^post_60 ], cost: 1 60: l30 -> l29 : r0^0'=r0^post_61, r^0'=r^post_61, x1^0'=x1^post_61, x^0'=x^post_61, [ x^post_61==1 && r^0==r^post_61 && r0^0==r0^post_61 && x1^0==x1^post_61 ], cost: 1 62: l31 -> l30 : r0^0'=r0^post_63, r^0'=r^post_63, x1^0'=x1^post_63, x^0'=x^post_63, [ r^0==r^post_63 && r0^0==r0^post_63 && x^0==x^post_63 && x1^0==x1^post_63 ], cost: 1 Removed unreachable and leaf rules: Start location: l31 4: l6 -> l7 : r0^0'=r0^post_5, r^0'=r^post_5, x1^0'=x1^post_5, x^0'=x^post_5, [ x1^post_5==x^0 && r^0==r^post_5 && r0^0==r0^post_5 && x^0==x^post_5 ], cost: 1 5: l6 -> l8 : r0^0'=r0^post_6, r^0'=r^post_6, x1^0'=x1^post_6, x^0'=x^post_6, [ r^0==r^post_6 && r0^0==r0^post_6 && x^0==x^post_6 && x1^0==x1^post_6 ], cost: 1 12: l7 -> l10 : r0^0'=r0^post_13, r^0'=r^post_13, x1^0'=x1^post_13, x^0'=x^post_13, [ r^0==r^post_13 && r0^0==r0^post_13 && x^0==x^post_13 && x1^0==x1^post_13 ], cost: 1 6: l8 -> l6 : r0^0'=r0^post_7, r^0'=r^post_7, x1^0'=x1^post_7, x^0'=x^post_7, [ r^0==r^post_7 && r0^0==r0^post_7 && x^0==x^post_7 && x1^0==x1^post_7 ], cost: 1 13: l10 -> l7 : r0^0'=r0^post_14, r^0'=r^post_14, x1^0'=x1^post_14, x^0'=x^post_14, [ r^0==r^post_14 && r0^0==r0^post_14 && x^0==x^post_14 && x1^0==x1^post_14 ], cost: 1 18: l11 -> l13 : r0^0'=r0^post_19, r^0'=r^post_19, x1^0'=x1^post_19, x^0'=x^post_19, [ r^0==r^post_19 && r0^0==r0^post_19 && x^0==x^post_19 && x1^0==x1^post_19 ], cost: 1 19: l13 -> l11 : r0^0'=r0^post_20, r^0'=r^post_20, x1^0'=x1^post_20, x^0'=x^post_20, [ r^0==r^post_20 && r0^0==r0^post_20 && x^0==x^post_20 && x1^0==x1^post_20 ], cost: 1 24: l14 -> l16 : r0^0'=r0^post_25, r^0'=r^post_25, x1^0'=x1^post_25, x^0'=x^post_25, [ r^0==r^post_25 && r0^0==r0^post_25 && x^0==x^post_25 && x1^0==x1^post_25 ], cost: 1 25: l16 -> l14 : r0^0'=r0^post_26, r^0'=r^post_26, x1^0'=x1^post_26, x^0'=x^post_26, [ r^0==r^post_26 && r0^0==r0^post_26 && x^0==x^post_26 && x1^0==x1^post_26 ], cost: 1 35: l19 -> l11 : r0^0'=r0^post_36, r^0'=r^post_36, x1^0'=x1^post_36, x^0'=x^post_36, [ x^post_36==2 && r^0==r^post_36 && r0^0==r0^post_36 && x1^0==x1^post_36 ], cost: 1 40: l21 -> l14 : r0^0'=r0^post_41, r^0'=r^post_41, x1^0'=x1^post_41, x^0'=x^post_41, [ x^post_41==2 && r^0==r^post_41 && r0^0==r0^post_41 && x1^0==x1^post_41 ], cost: 1 55: l27 -> l21 : r0^0'=r0^post_56, r^0'=r^post_56, x1^0'=x1^post_56, x^0'=x^post_56, [ x^post_56==1 && r^0==r^post_56 && r0^0==r0^post_56 && x1^0==x1^post_56 ], cost: 1 56: l29 -> l19 : r0^0'=r0^post_57, r^0'=r^post_57, x1^0'=x1^post_57, x^0'=x^post_57, [ x1^post_57==x^0 && r^0==r^post_57 && r0^0==r0^post_57 && x^0==x^post_57 ], cost: 1 57: l29 -> l6 : r0^0'=r0^post_58, r^0'=r^post_58, x1^0'=x1^post_58, x^0'=x^post_58, [ x^post_58==2 && r^0==r^post_58 && r0^0==r0^post_58 && x1^0==x1^post_58 ], cost: 1 59: l30 -> l27 : r0^0'=r0^post_60, r^0'=r^post_60, x1^0'=x1^post_60, x^0'=x^post_60, [ x1^post_60==x^0 && r^0==r^post_60 && r0^0==r0^post_60 && x^0==x^post_60 ], cost: 1 60: l30 -> l29 : r0^0'=r0^post_61, r^0'=r^post_61, x1^0'=x1^post_61, x^0'=x^post_61, [ x^post_61==1 && r^0==r^post_61 && r0^0==r0^post_61 && x1^0==x1^post_61 ], cost: 1 62: l31 -> l30 : r0^0'=r0^post_63, r^0'=r^post_63, x1^0'=x1^post_63, x^0'=x^post_63, [ r^0==r^post_63 && r0^0==r0^post_63 && x^0==x^post_63 && x1^0==x1^post_63 ], cost: 1 Simplified all rules, resulting in: Start location: l31 4: l6 -> l7 : x1^0'=x^0, [], cost: 1 5: l6 -> l8 : [], cost: 1 12: l7 -> l10 : [], cost: 1 6: l8 -> l6 : [], cost: 1 13: l10 -> l7 : [], cost: 1 18: l11 -> l13 : [], cost: 1 19: l13 -> l11 : [], cost: 1 24: l14 -> l16 : [], cost: 1 25: l16 -> l14 : [], cost: 1 35: l19 -> l11 : x^0'=2, [], cost: 1 40: l21 -> l14 : x^0'=2, [], cost: 1 55: l27 -> l21 : x^0'=1, [], cost: 1 56: l29 -> l19 : x1^0'=x^0, [], cost: 1 57: l29 -> l6 : x^0'=2, [], cost: 1 59: l30 -> l27 : x1^0'=x^0, [], cost: 1 60: l30 -> l29 : x^0'=1, [], cost: 1 62: l31 -> l30 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l31 4: l6 -> l7 : x1^0'=x^0, [], cost: 1 67: l6 -> l6 : [], cost: 2 68: l7 -> l7 : [], cost: 2 69: l11 -> l11 : [], cost: 2 65: l14 -> l14 : [], cost: 2 57: l29 -> l6 : x^0'=2, [], cost: 1 66: l29 -> l11 : x1^0'=x^0, x^0'=2, [], cost: 2 60: l30 -> l29 : x^0'=1, [], cost: 1 64: l30 -> l14 : x1^0'=x^0, x^0'=2, [], cost: 3 62: l31 -> l30 : [], cost: 1 Accelerating simple loops of location 6. Accelerating the following rules: 67: l6 -> l6 : [], cost: 2 Accelerated rule 67 with non-termination, yielding the new rule 70. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 67. Accelerating simple loops of location 7. Accelerating the following rules: 68: l7 -> l7 : [], cost: 2 Accelerated rule 68 with non-termination, yielding the new rule 71. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 68. Accelerating simple loops of location 11. Accelerating the following rules: 69: l11 -> l11 : [], cost: 2 Accelerated rule 69 with non-termination, yielding the new rule 72. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 69. Accelerating simple loops of location 14. Accelerating the following rules: 65: l14 -> l14 : [], cost: 2 Accelerated rule 65 with non-termination, yielding the new rule 73. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 65. Accelerated all simple loops using metering functions (where possible): Start location: l31 4: l6 -> l7 : x1^0'=x^0, [], cost: 1 70: l6 -> [32] : [], cost: NONTERM 71: l7 -> [33] : [], cost: NONTERM 72: l11 -> [34] : [], cost: NONTERM 73: l14 -> [35] : [], cost: NONTERM 57: l29 -> l6 : x^0'=2, [], cost: 1 66: l29 -> l11 : x1^0'=x^0, x^0'=2, [], cost: 2 60: l30 -> l29 : x^0'=1, [], cost: 1 64: l30 -> l14 : x1^0'=x^0, x^0'=2, [], cost: 3 62: l31 -> l30 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: l31 4: l6 -> l7 : x1^0'=x^0, [], cost: 1 75: l6 -> [33] : [], cost: NONTERM 57: l29 -> l6 : x^0'=2, [], cost: 1 66: l29 -> l11 : x1^0'=x^0, x^0'=2, [], cost: 2 74: l29 -> [32] : [], cost: NONTERM 76: l29 -> [34] : [], cost: NONTERM 60: l30 -> l29 : x^0'=1, [], cost: 1 64: l30 -> l14 : x1^0'=x^0, x^0'=2, [], cost: 3 77: l30 -> [35] : [], cost: NONTERM 62: l31 -> l30 : [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: l31 75: l6 -> [33] : [], cost: NONTERM 57: l29 -> l6 : x^0'=2, [], cost: 1 74: l29 -> [32] : [], cost: NONTERM 76: l29 -> [34] : [], cost: NONTERM 60: l30 -> l29 : x^0'=1, [], cost: 1 77: l30 -> [35] : [], cost: NONTERM 62: l31 -> l30 : [], cost: 1 Eliminated locations (on linear paths): Start location: l31 74: l29 -> [32] : [], cost: NONTERM 76: l29 -> [34] : [], cost: NONTERM 78: l29 -> [33] : [], cost: NONTERM 60: l30 -> l29 : x^0'=1, [], cost: 1 77: l30 -> [35] : [], cost: NONTERM 62: l31 -> l30 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l31 74: l29 -> [32] : [], cost: NONTERM 76: l29 -> [34] : [], cost: NONTERM 78: l29 -> [33] : [], cost: NONTERM 79: l31 -> l29 : x^0'=1, [], cost: 2 80: l31 -> [35] : [], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l31 80: l31 -> [35] : [], cost: NONTERM 81: l31 -> [32] : [], cost: NONTERM 82: l31 -> [34] : [], cost: NONTERM 83: l31 -> [33] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l31 83: l31 -> [33] : [], cost: NONTERM Computing asymptotic complexity for rule 83 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: [] NO