WORST_CASE(Omega(n^1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l8 0: l0 -> l1 : __const_20^0'=__const_20^post_1, __const_5^0'=__const_5^post_1, __const_99^0'=__const_99^post_1, oldX0^0'=oldX0^post_1, oldX1^0'=oldX1^post_1, oldX2^0'=oldX2^post_1, oldX3^0'=oldX3^post_1, x0^0'=x0^post_1, x1^0'=x1^post_1, [ oldX0^post_1==x0^0 && oldX1^post_1==x1^0 && oldX2^post_1==oldX2^post_1 && oldX3^post_1==oldX3^post_1 && x0^post_1==oldX2^post_1 && x1^post_1==oldX3^post_1 && __const_20^0==__const_20^post_1 && __const_5^0==__const_5^post_1 && __const_99^0==__const_99^post_1 ], cost: 1 1: l2 -> l3 : __const_20^0'=__const_20^post_2, __const_5^0'=__const_5^post_2, __const_99^0'=__const_99^post_2, oldX0^0'=oldX0^post_2, oldX1^0'=oldX1^post_2, oldX2^0'=oldX2^post_2, oldX3^0'=oldX3^post_2, x0^0'=x0^post_2, x1^0'=x1^post_2, [ oldX0^post_2==x0^0 && oldX1^post_2==x1^0 && x0^post_2==oldX0^post_2 && x1^post_2==3+oldX1^post_2 && __const_20^0==__const_20^post_2 && __const_5^0==__const_5^post_2 && __const_99^0==__const_99^post_2 && oldX2^0==oldX2^post_2 && oldX3^0==oldX3^post_2 ], cost: 1 2: l3 -> l0 : __const_20^0'=__const_20^post_3, __const_5^0'=__const_5^post_3, __const_99^0'=__const_99^post_3, oldX0^0'=oldX0^post_3, oldX1^0'=oldX1^post_3, oldX2^0'=oldX2^post_3, oldX3^0'=oldX3^post_3, x0^0'=x0^post_3, x1^0'=x1^post_3, [ oldX0^post_3==x0^0 && oldX1^post_3==x1^0 && 1+__const_20^0<=oldX1^post_3 && x0^post_3==oldX0^post_3 && x1^post_3==oldX1^post_3 && __const_20^0==__const_20^post_3 && __const_5^0==__const_5^post_3 && __const_99^0==__const_99^post_3 && oldX2^0==oldX2^post_3 && oldX3^0==oldX3^post_3 ], cost: 1 3: l3 -> l2 : __const_20^0'=__const_20^post_4, __const_5^0'=__const_5^post_4, __const_99^0'=__const_99^post_4, oldX0^0'=oldX0^post_4, oldX1^0'=oldX1^post_4, oldX2^0'=oldX2^post_4, oldX3^0'=oldX3^post_4, x0^0'=x0^post_4, x1^0'=x1^post_4, [ oldX0^post_4==x0^0 && oldX1^post_4==x1^0 && oldX1^post_4<=__const_20^0 && x0^post_4==oldX0^post_4 && x1^post_4==oldX1^post_4 && __const_20^0==__const_20^post_4 && __const_5^0==__const_5^post_4 && __const_99^0==__const_99^post_4 && oldX2^0==oldX2^post_4 && oldX3^0==oldX3^post_4 ], cost: 1 4: l4 -> l5 : __const_20^0'=__const_20^post_5, __const_5^0'=__const_5^post_5, __const_99^0'=__const_99^post_5, oldX0^0'=oldX0^post_5, oldX1^0'=oldX1^post_5, oldX2^0'=oldX2^post_5, oldX3^0'=oldX3^post_5, x0^0'=x0^post_5, x1^0'=x1^post_5, [ oldX0^post_5==x0^0 && oldX1^post_5==x1^0 && oldX2^post_5==oldX2^post_5 && x0^post_5==1+oldX0^post_5 && x1^post_5==oldX2^post_5 && __const_20^0==__const_20^post_5 && __const_5^0==__const_5^post_5 && __const_99^0==__const_99^post_5 && oldX3^0==oldX3^post_5 ], cost: 1 5: l5 -> l3 : __const_20^0'=__const_20^post_6, __const_5^0'=__const_5^post_6, __const_99^0'=__const_99^post_6, oldX0^0'=oldX0^post_6, oldX1^0'=oldX1^post_6, oldX2^0'=oldX2^post_6, oldX3^0'=oldX3^post_6, x0^0'=x0^post_6, x1^0'=x1^post_6, [ oldX0^post_6==x0^0 && oldX1^post_6==x1^0 && 1+__const_99^0<=oldX0^post_6 && x0^post_6==oldX0^post_6 && x1^post_6==__const_5^0 && __const_20^0==__const_20^post_6 && __const_5^0==__const_5^post_6 && __const_99^0==__const_99^post_6 && oldX2^0==oldX2^post_6 && oldX3^0==oldX3^post_6 ], cost: 1 6: l5 -> l4 : __const_20^0'=__const_20^post_7, __const_5^0'=__const_5^post_7, __const_99^0'=__const_99^post_7, oldX0^0'=oldX0^post_7, oldX1^0'=oldX1^post_7, oldX2^0'=oldX2^post_7, oldX3^0'=oldX3^post_7, x0^0'=x0^post_7, x1^0'=x1^post_7, [ oldX0^post_7==x0^0 && oldX1^post_7==x1^0 && oldX2^post_7==oldX2^post_7 && oldX0^post_7<=__const_99^0 && x0^post_7==oldX0^post_7 && x1^post_7==oldX2^post_7 && __const_20^0==__const_20^post_7 && __const_5^0==__const_5^post_7 && __const_99^0==__const_99^post_7 && oldX3^0==oldX3^post_7 ], cost: 1 7: l6 -> l5 : __const_20^0'=__const_20^post_8, __const_5^0'=__const_5^post_8, __const_99^0'=__const_99^post_8, oldX0^0'=oldX0^post_8, oldX1^0'=oldX1^post_8, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_8, x0^0'=x0^post_8, x1^0'=x1^post_8, [ oldX0^post_8==x0^0 && oldX1^post_8==x1^0 && oldX2^post_8==oldX2^post_8 && x0^post_8==0 && x1^post_8==oldX2^post_8 && __const_20^0==__const_20^post_8 && __const_5^0==__const_5^post_8 && __const_99^0==__const_99^post_8 && oldX3^0==oldX3^post_8 ], cost: 1 8: l7 -> l6 : __const_20^0'=__const_20^post_9, __const_5^0'=__const_5^post_9, __const_99^0'=__const_99^post_9, oldX0^0'=oldX0^post_9, oldX1^0'=oldX1^post_9, oldX2^0'=oldX2^post_9, oldX3^0'=oldX3^post_9, x0^0'=x0^post_9, x1^0'=x1^post_9, [ oldX0^post_9==x0^0 && oldX1^post_9==x1^0 && oldX2^post_9==oldX2^post_9 && oldX3^post_9==oldX3^post_9 && x0^post_9==oldX2^post_9 && x1^post_9==oldX3^post_9 && __const_20^0==__const_20^post_9 && __const_5^0==__const_5^post_9 && __const_99^0==__const_99^post_9 ], cost: 1 9: l7 -> l1 : __const_20^0'=__const_20^post_10, __const_5^0'=__const_5^post_10, __const_99^0'=__const_99^post_10, oldX0^0'=oldX0^post_10, oldX1^0'=oldX1^post_10, oldX2^0'=oldX2^post_10, oldX3^0'=oldX3^post_10, x0^0'=x0^post_10, x1^0'=x1^post_10, [ __const_20^0==__const_20^post_10 && __const_5^0==__const_5^post_10 && __const_99^0==__const_99^post_10 && oldX0^0==oldX0^post_10 && oldX1^0==oldX1^post_10 && oldX2^0==oldX2^post_10 && oldX3^0==oldX3^post_10 && x0^0==x0^post_10 && x1^0==x1^post_10 ], cost: 1 10: l7 -> l0 : __const_20^0'=__const_20^post_11, __const_5^0'=__const_5^post_11, __const_99^0'=__const_99^post_11, oldX0^0'=oldX0^post_11, oldX1^0'=oldX1^post_11, oldX2^0'=oldX2^post_11, oldX3^0'=oldX3^post_11, x0^0'=x0^post_11, x1^0'=x1^post_11, [ __const_20^0==__const_20^post_11 && __const_5^0==__const_5^post_11 && __const_99^0==__const_99^post_11 && oldX0^0==oldX0^post_11 && oldX1^0==oldX1^post_11 && oldX2^0==oldX2^post_11 && oldX3^0==oldX3^post_11 && x0^0==x0^post_11 && x1^0==x1^post_11 ], cost: 1 11: l7 -> l2 : __const_20^0'=__const_20^post_12, __const_5^0'=__const_5^post_12, __const_99^0'=__const_99^post_12, oldX0^0'=oldX0^post_12, oldX1^0'=oldX1^post_12, oldX2^0'=oldX2^post_12, oldX3^0'=oldX3^post_12, x0^0'=x0^post_12, x1^0'=x1^post_12, [ __const_20^0==__const_20^post_12 && __const_5^0==__const_5^post_12 && __const_99^0==__const_99^post_12 && oldX0^0==oldX0^post_12 && oldX1^0==oldX1^post_12 && oldX2^0==oldX2^post_12 && oldX3^0==oldX3^post_12 && x0^0==x0^post_12 && x1^0==x1^post_12 ], cost: 1 12: l7 -> l3 : __const_20^0'=__const_20^post_13, __const_5^0'=__const_5^post_13, __const_99^0'=__const_99^post_13, oldX0^0'=oldX0^post_13, oldX1^0'=oldX1^post_13, oldX2^0'=oldX2^post_13, oldX3^0'=oldX3^post_13, x0^0'=x0^post_13, x1^0'=x1^post_13, [ __const_20^0==__const_20^post_13 && __const_5^0==__const_5^post_13 && __const_99^0==__const_99^post_13 && oldX0^0==oldX0^post_13 && oldX1^0==oldX1^post_13 && oldX2^0==oldX2^post_13 && oldX3^0==oldX3^post_13 && x0^0==x0^post_13 && x1^0==x1^post_13 ], cost: 1 13: l7 -> l4 : __const_20^0'=__const_20^post_14, __const_5^0'=__const_5^post_14, __const_99^0'=__const_99^post_14, oldX0^0'=oldX0^post_14, oldX1^0'=oldX1^post_14, oldX2^0'=oldX2^post_14, oldX3^0'=oldX3^post_14, x0^0'=x0^post_14, x1^0'=x1^post_14, [ __const_20^0==__const_20^post_14 && __const_5^0==__const_5^post_14 && __const_99^0==__const_99^post_14 && oldX0^0==oldX0^post_14 && oldX1^0==oldX1^post_14 && oldX2^0==oldX2^post_14 && oldX3^0==oldX3^post_14 && x0^0==x0^post_14 && x1^0==x1^post_14 ], cost: 1 14: l7 -> l5 : __const_20^0'=__const_20^post_15, __const_5^0'=__const_5^post_15, __const_99^0'=__const_99^post_15, oldX0^0'=oldX0^post_15, oldX1^0'=oldX1^post_15, oldX2^0'=oldX2^post_15, oldX3^0'=oldX3^post_15, x0^0'=x0^post_15, x1^0'=x1^post_15, [ __const_20^0==__const_20^post_15 && __const_5^0==__const_5^post_15 && __const_99^0==__const_99^post_15 && oldX0^0==oldX0^post_15 && oldX1^0==oldX1^post_15 && oldX2^0==oldX2^post_15 && oldX3^0==oldX3^post_15 && x0^0==x0^post_15 && x1^0==x1^post_15 ], cost: 1 15: l7 -> l6 : __const_20^0'=__const_20^post_16, __const_5^0'=__const_5^post_16, __const_99^0'=__const_99^post_16, oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, oldX2^0'=oldX2^post_16, oldX3^0'=oldX3^post_16, x0^0'=x0^post_16, x1^0'=x1^post_16, [ __const_20^0==__const_20^post_16 && __const_5^0==__const_5^post_16 && __const_99^0==__const_99^post_16 && oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && oldX2^0==oldX2^post_16 && oldX3^0==oldX3^post_16 && x0^0==x0^post_16 && x1^0==x1^post_16 ], cost: 1 16: l8 -> l7 : __const_20^0'=__const_20^post_17, __const_5^0'=__const_5^post_17, __const_99^0'=__const_99^post_17, oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, oldX2^0'=oldX2^post_17, oldX3^0'=oldX3^post_17, x0^0'=x0^post_17, x1^0'=x1^post_17, [ __const_20^0==__const_20^post_17 && __const_5^0==__const_5^post_17 && __const_99^0==__const_99^post_17 && oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 16: l8 -> l7 : __const_20^0'=__const_20^post_17, __const_5^0'=__const_5^post_17, __const_99^0'=__const_99^post_17, oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, oldX2^0'=oldX2^post_17, oldX3^0'=oldX3^post_17, x0^0'=x0^post_17, x1^0'=x1^post_17, [ __const_20^0==__const_20^post_17 && __const_5^0==__const_5^post_17 && __const_99^0==__const_99^post_17 && oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ], cost: 1 Removed unreachable and leaf rules: Start location: l8 1: l2 -> l3 : __const_20^0'=__const_20^post_2, __const_5^0'=__const_5^post_2, __const_99^0'=__const_99^post_2, oldX0^0'=oldX0^post_2, oldX1^0'=oldX1^post_2, oldX2^0'=oldX2^post_2, oldX3^0'=oldX3^post_2, x0^0'=x0^post_2, x1^0'=x1^post_2, [ oldX0^post_2==x0^0 && oldX1^post_2==x1^0 && x0^post_2==oldX0^post_2 && x1^post_2==3+oldX1^post_2 && __const_20^0==__const_20^post_2 && __const_5^0==__const_5^post_2 && __const_99^0==__const_99^post_2 && oldX2^0==oldX2^post_2 && oldX3^0==oldX3^post_2 ], cost: 1 3: l3 -> l2 : __const_20^0'=__const_20^post_4, __const_5^0'=__const_5^post_4, __const_99^0'=__const_99^post_4, oldX0^0'=oldX0^post_4, oldX1^0'=oldX1^post_4, oldX2^0'=oldX2^post_4, oldX3^0'=oldX3^post_4, x0^0'=x0^post_4, x1^0'=x1^post_4, [ oldX0^post_4==x0^0 && oldX1^post_4==x1^0 && oldX1^post_4<=__const_20^0 && x0^post_4==oldX0^post_4 && x1^post_4==oldX1^post_4 && __const_20^0==__const_20^post_4 && __const_5^0==__const_5^post_4 && __const_99^0==__const_99^post_4 && oldX2^0==oldX2^post_4 && oldX3^0==oldX3^post_4 ], cost: 1 4: l4 -> l5 : __const_20^0'=__const_20^post_5, __const_5^0'=__const_5^post_5, __const_99^0'=__const_99^post_5, oldX0^0'=oldX0^post_5, oldX1^0'=oldX1^post_5, oldX2^0'=oldX2^post_5, oldX3^0'=oldX3^post_5, x0^0'=x0^post_5, x1^0'=x1^post_5, [ oldX0^post_5==x0^0 && oldX1^post_5==x1^0 && oldX2^post_5==oldX2^post_5 && x0^post_5==1+oldX0^post_5 && x1^post_5==oldX2^post_5 && __const_20^0==__const_20^post_5 && __const_5^0==__const_5^post_5 && __const_99^0==__const_99^post_5 && oldX3^0==oldX3^post_5 ], cost: 1 5: l5 -> l3 : __const_20^0'=__const_20^post_6, __const_5^0'=__const_5^post_6, __const_99^0'=__const_99^post_6, oldX0^0'=oldX0^post_6, oldX1^0'=oldX1^post_6, oldX2^0'=oldX2^post_6, oldX3^0'=oldX3^post_6, x0^0'=x0^post_6, x1^0'=x1^post_6, [ oldX0^post_6==x0^0 && oldX1^post_6==x1^0 && 1+__const_99^0<=oldX0^post_6 && x0^post_6==oldX0^post_6 && x1^post_6==__const_5^0 && __const_20^0==__const_20^post_6 && __const_5^0==__const_5^post_6 && __const_99^0==__const_99^post_6 && oldX2^0==oldX2^post_6 && oldX3^0==oldX3^post_6 ], cost: 1 6: l5 -> l4 : __const_20^0'=__const_20^post_7, __const_5^0'=__const_5^post_7, __const_99^0'=__const_99^post_7, oldX0^0'=oldX0^post_7, oldX1^0'=oldX1^post_7, oldX2^0'=oldX2^post_7, oldX3^0'=oldX3^post_7, x0^0'=x0^post_7, x1^0'=x1^post_7, [ oldX0^post_7==x0^0 && oldX1^post_7==x1^0 && oldX2^post_7==oldX2^post_7 && oldX0^post_7<=__const_99^0 && x0^post_7==oldX0^post_7 && x1^post_7==oldX2^post_7 && __const_20^0==__const_20^post_7 && __const_5^0==__const_5^post_7 && __const_99^0==__const_99^post_7 && oldX3^0==oldX3^post_7 ], cost: 1 7: l6 -> l5 : __const_20^0'=__const_20^post_8, __const_5^0'=__const_5^post_8, __const_99^0'=__const_99^post_8, oldX0^0'=oldX0^post_8, oldX1^0'=oldX1^post_8, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_8, x0^0'=x0^post_8, x1^0'=x1^post_8, [ oldX0^post_8==x0^0 && oldX1^post_8==x1^0 && oldX2^post_8==oldX2^post_8 && x0^post_8==0 && x1^post_8==oldX2^post_8 && __const_20^0==__const_20^post_8 && __const_5^0==__const_5^post_8 && __const_99^0==__const_99^post_8 && oldX3^0==oldX3^post_8 ], cost: 1 8: l7 -> l6 : __const_20^0'=__const_20^post_9, __const_5^0'=__const_5^post_9, __const_99^0'=__const_99^post_9, oldX0^0'=oldX0^post_9, oldX1^0'=oldX1^post_9, oldX2^0'=oldX2^post_9, oldX3^0'=oldX3^post_9, x0^0'=x0^post_9, x1^0'=x1^post_9, [ oldX0^post_9==x0^0 && oldX1^post_9==x1^0 && oldX2^post_9==oldX2^post_9 && oldX3^post_9==oldX3^post_9 && x0^post_9==oldX2^post_9 && x1^post_9==oldX3^post_9 && __const_20^0==__const_20^post_9 && __const_5^0==__const_5^post_9 && __const_99^0==__const_99^post_9 ], cost: 1 11: l7 -> l2 : __const_20^0'=__const_20^post_12, __const_5^0'=__const_5^post_12, __const_99^0'=__const_99^post_12, oldX0^0'=oldX0^post_12, oldX1^0'=oldX1^post_12, oldX2^0'=oldX2^post_12, oldX3^0'=oldX3^post_12, x0^0'=x0^post_12, x1^0'=x1^post_12, [ __const_20^0==__const_20^post_12 && __const_5^0==__const_5^post_12 && __const_99^0==__const_99^post_12 && oldX0^0==oldX0^post_12 && oldX1^0==oldX1^post_12 && oldX2^0==oldX2^post_12 && oldX3^0==oldX3^post_12 && x0^0==x0^post_12 && x1^0==x1^post_12 ], cost: 1 12: l7 -> l3 : __const_20^0'=__const_20^post_13, __const_5^0'=__const_5^post_13, __const_99^0'=__const_99^post_13, oldX0^0'=oldX0^post_13, oldX1^0'=oldX1^post_13, oldX2^0'=oldX2^post_13, oldX3^0'=oldX3^post_13, x0^0'=x0^post_13, x1^0'=x1^post_13, [ __const_20^0==__const_20^post_13 && __const_5^0==__const_5^post_13 && __const_99^0==__const_99^post_13 && oldX0^0==oldX0^post_13 && oldX1^0==oldX1^post_13 && oldX2^0==oldX2^post_13 && oldX3^0==oldX3^post_13 && x0^0==x0^post_13 && x1^0==x1^post_13 ], cost: 1 13: l7 -> l4 : __const_20^0'=__const_20^post_14, __const_5^0'=__const_5^post_14, __const_99^0'=__const_99^post_14, oldX0^0'=oldX0^post_14, oldX1^0'=oldX1^post_14, oldX2^0'=oldX2^post_14, oldX3^0'=oldX3^post_14, x0^0'=x0^post_14, x1^0'=x1^post_14, [ __const_20^0==__const_20^post_14 && __const_5^0==__const_5^post_14 && __const_99^0==__const_99^post_14 && oldX0^0==oldX0^post_14 && oldX1^0==oldX1^post_14 && oldX2^0==oldX2^post_14 && oldX3^0==oldX3^post_14 && x0^0==x0^post_14 && x1^0==x1^post_14 ], cost: 1 14: l7 -> l5 : __const_20^0'=__const_20^post_15, __const_5^0'=__const_5^post_15, __const_99^0'=__const_99^post_15, oldX0^0'=oldX0^post_15, oldX1^0'=oldX1^post_15, oldX2^0'=oldX2^post_15, oldX3^0'=oldX3^post_15, x0^0'=x0^post_15, x1^0'=x1^post_15, [ __const_20^0==__const_20^post_15 && __const_5^0==__const_5^post_15 && __const_99^0==__const_99^post_15 && oldX0^0==oldX0^post_15 && oldX1^0==oldX1^post_15 && oldX2^0==oldX2^post_15 && oldX3^0==oldX3^post_15 && x0^0==x0^post_15 && x1^0==x1^post_15 ], cost: 1 15: l7 -> l6 : __const_20^0'=__const_20^post_16, __const_5^0'=__const_5^post_16, __const_99^0'=__const_99^post_16, oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, oldX2^0'=oldX2^post_16, oldX3^0'=oldX3^post_16, x0^0'=x0^post_16, x1^0'=x1^post_16, [ __const_20^0==__const_20^post_16 && __const_5^0==__const_5^post_16 && __const_99^0==__const_99^post_16 && oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && oldX2^0==oldX2^post_16 && oldX3^0==oldX3^post_16 && x0^0==x0^post_16 && x1^0==x1^post_16 ], cost: 1 16: l8 -> l7 : __const_20^0'=__const_20^post_17, __const_5^0'=__const_5^post_17, __const_99^0'=__const_99^post_17, oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, oldX2^0'=oldX2^post_17, oldX3^0'=oldX3^post_17, x0^0'=x0^post_17, x1^0'=x1^post_17, [ __const_20^0==__const_20^post_17 && __const_5^0==__const_5^post_17 && __const_99^0==__const_99^post_17 && oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ], cost: 1 Simplified all rules, resulting in: Start location: l8 1: l2 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [], cost: 1 3: l3 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ x1^0<=__const_20^0 ], cost: 1 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=__const_5^0, [ 1+__const_99^0<=x0^0 ], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 7: l6 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 1 8: l7 -> l6 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_9, oldX3^0'=oldX3^post_9, x0^0'=oldX2^post_9, x1^0'=oldX3^post_9, [], cost: 1 11: l7 -> l2 : [], cost: 1 12: l7 -> l3 : [], cost: 1 13: l7 -> l4 : [], cost: 1 14: l7 -> l5 : [], cost: 1 15: l7 -> l6 : [], cost: 1 16: l8 -> l7 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on tree-shaped paths): Start location: l8 1: l2 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [], cost: 1 3: l3 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ x1^0<=__const_20^0 ], cost: 1 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=__const_5^0, [ 1+__const_99^0<=x0^0 ], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 7: l6 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 1 17: l8 -> l6 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_9, oldX3^0'=oldX3^post_9, x0^0'=oldX2^post_9, x1^0'=oldX3^post_9, [], cost: 2 18: l8 -> l2 : [], cost: 2 19: l8 -> l3 : [], cost: 2 20: l8 -> l4 : [], cost: 2 21: l8 -> l5 : [], cost: 2 22: l8 -> l6 : [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l8 1: l2 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [], cost: 1 3: l3 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ x1^0<=__const_20^0 ], cost: 1 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=__const_5^0, [ 1+__const_99^0<=x0^0 ], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 18: l8 -> l2 : [], cost: 2 19: l8 -> l3 : [], cost: 2 20: l8 -> l4 : [], cost: 2 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 Eliminated location l2 (as a last resort): Start location: l8 25: l3 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [ x1^0<=__const_20^0 ], cost: 2 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=__const_5^0, [ 1+__const_99^0<=x0^0 ], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 19: l8 -> l3 : [], cost: 2 20: l8 -> l4 : [], cost: 2 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 26: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [], cost: 3 Accelerating simple loops of location 3. Accelerating the following rules: 25: l3 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [ x1^0<=__const_20^0 ], cost: 2 Accelerated rule 25 with metering function meter (where 3*meter==__const_20^0-x1^0), yielding the new rule 27. Removing the simple loops: 25. Accelerated all simple loops using metering functions (where possible): Start location: l8 27: l3 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2*meter 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=__const_5^0, [ 1+__const_99^0<=x0^0 ], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 19: l8 -> l3 : [], cost: 2 20: l8 -> l4 : [], cost: 2 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 26: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [], cost: 3 Chained accelerated rules (with incoming rules): Start location: l8 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=__const_5^0, [ 1+__const_99^0<=x0^0 ], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 28: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+__const_5^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 1+2*meter 19: l8 -> l3 : [], cost: 2 20: l8 -> l4 : [], cost: 2 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 26: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=3+x1^0, [], cost: 3 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter Removed unreachable locations (and leaf rules with constant cost): Start location: l8 4: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 1 6: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ x0^0<=__const_99^0 ], cost: 1 28: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+__const_5^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 1+2*meter 20: l8 -> l4 : [], cost: 2 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter Eliminated location l4 (as a last resort): Start location: l8 28: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+__const_5^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 1+2*meter 31: l5 -> l5 : oldX0^0'=x0^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [ x0^0<=__const_99^0 ], cost: 2 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter 32: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 3 Accelerating simple loops of location 5. Accelerating the following rules: 31: l5 -> l5 : oldX0^0'=x0^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [ x0^0<=__const_99^0 ], cost: 2 Accelerated rule 31 with metering function 1+__const_99^0-x0^0, yielding the new rule 33. Removing the simple loops: 31. Accelerated all simple loops using metering functions (where possible): Start location: l8 28: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+__const_5^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 1+2*meter 33: l5 -> l5 : oldX0^0'=__const_99^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=oldX2^post_5, [ x0^0<=__const_99^0 ], cost: 2+2*__const_99^0-2*x0^0 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter 32: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 3 Chained accelerated rules (with incoming rules): Start location: l8 28: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+__const_5^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 1+2*meter 21: l8 -> l5 : [], cost: 2 23: l8 -> l5 : oldX0^0'=oldX2^post_9, oldX1^0'=oldX3^post_9, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 24: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=oldX2^post_8, [], cost: 3 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter 32: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=oldX2^post_5, [], cost: 3 34: l8 -> l5 : oldX0^0'=__const_99^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=oldX2^post_5, [ x0^0<=__const_99^0 ], cost: 4+2*__const_99^0-2*x0^0 35: l8 -> l5 : oldX0^0'=__const_99^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, oldX3^0'=oldX3^post_9, x0^0'=1+__const_99^0, x1^0'=oldX2^post_5, [ 0<=__const_99^0 ], cost: 5+2*__const_99^0 36: l8 -> l5 : oldX0^0'=__const_99^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=oldX2^post_5, [ 0<=__const_99^0 ], cost: 5+2*__const_99^0 37: l8 -> l5 : oldX0^0'=__const_99^0, oldX1^0'=oldX2^post_7, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=oldX2^post_5, [ 1+x0^0<=__const_99^0 ], cost: 3+2*__const_99^0-2*x0^0 Eliminated locations (on tree-shaped paths): Start location: l8 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter 38: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+__const_5^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 3+2*meter 39: l8 -> l3 : oldX0^0'=0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter 40: l8 -> l3 : oldX0^0'=0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter 41: l8 -> l3 : oldX0^0'=1+x0^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=1+x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter 42: l8 -> l3 : oldX0^0'=1+__const_99^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=3*meter+__const_5^0, [ x0^0<=__const_99^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 5+2*__const_99^0+2*meter-2*x0^0 43: l8 -> l3 : oldX0^0'=1+__const_99^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, oldX3^0'=oldX3^post_9, x0^0'=1+__const_99^0, x1^0'=3*meter+__const_5^0, [ 0<=__const_99^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 6+2*__const_99^0+2*meter 44: l8 -> l3 : oldX0^0'=1+__const_99^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=3*meter+__const_5^0, [ 0<=__const_99^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 6+2*__const_99^0+2*meter 45: l8 -> l3 : oldX0^0'=1+__const_99^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+__const_99^0, x1^0'=3*meter+__const_5^0, [ 1+x0^0<=__const_99^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*__const_99^0+2*meter-2*x0^0 Applied pruning (of leafs and parallel rules): Start location: l8 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter 39: l8 -> l3 : oldX0^0'=0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_9, x0^0'=0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter 40: l8 -> l3 : oldX0^0'=0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter 41: l8 -> l3 : oldX0^0'=1+x0^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=1+x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l8 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ x1^0<=__const_20^0 && 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3+x1^0<=__const_20^0 && 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter 40: l8 -> l3 : oldX0^0'=0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter 41: l8 -> l3 : oldX0^0'=1+x0^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=1+x0^0 && __const_5^0<=__const_20^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter Computing asymptotic complexity for rule 29 Simplified the guard: 29: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-3+3*meter+x1^0, x1^0'=3*meter+x1^0, [ 3*meter==__const_20^0-x1^0 && meter>=1 ], cost: 2+2*meter Solved the limit problem by the following transformations: Created initial limit problem: 1-__const_20^0+3*meter+x1^0 (+/+!), 1+__const_20^0-3*meter-x1^0 (+/+!), 2+2*meter (+), meter (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {__const_20^0==0,meter==n,x1^0==-3*n} resulting limit problem: [solved] Solution: __const_20^0 / 0 meter / n x1^0 / -3*n Resulting cost 2+2*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 30 Simplified the guard: 30: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=3*meter+x1^0, x1^0'=3+3*meter+x1^0, [ 3*meter==-3+__const_20^0-x1^0 && meter>=1 ], cost: 3+2*meter Solved the limit problem by the following transformations: Created initial limit problem: -2+__const_20^0-3*meter-x1^0 (+/+!), 3+2*meter (+), meter (+/+!), 4-__const_20^0+3*meter+x1^0 (+/+!) [not solved] applying transformation rule (C) using substitution {__const_20^0==3+3*meter+x1^0} resulting limit problem: 1 (+/+!), 3+2*meter (+), meter (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+2*meter (+), meter (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n} resulting limit problem: [solved] Solution: __const_20^0 / 3+3*n meter / n x1^0 / 0 Resulting cost 3+2*n has complexity: Poly(n^1) Computing asymptotic complexity for rule 40 Simplified the guard: 40: l8 -> l3 : oldX0^0'=0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_8, x0^0'=0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter Solved the limit problem by the following transformations: Created initial limit problem: 1+__const_20^0-3*meter-__const_5^0 (+/+!), 1-__const_20^0+3*meter+__const_5^0 (+/+!), -__const_99^0 (+/+!), 4+2*meter (+), meter (+/+!) [not solved] applying transformation rule (C) using substitution {__const_20^0==3*meter+__const_5^0} resulting limit problem: 1 (+/+!), -__const_99^0 (+/+!), 4+2*meter (+), meter (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: -__const_99^0 (+/+!), 4+2*meter (+), meter (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {__const_99^0==-1,meter==n} resulting limit problem: [solved] Solution: __const_99^0 / -1 __const_20^0 / 3*n meter / n __const_5^0 / 0 Resulting cost 4+2*n has complexity: Poly(n^1) Computing asymptotic complexity for rule 41 Simplified the guard: 41: l8 -> l3 : oldX0^0'=1+x0^0, oldX1^0'=-3+3*meter+__const_5^0, oldX2^0'=oldX2^post_5, x0^0'=1+x0^0, x1^0'=3*meter+__const_5^0, [ 1+__const_99^0<=1+x0^0 && 3*meter==__const_20^0-__const_5^0 && meter>=1 ], cost: 4+2*meter Solved the limit problem by the following transformations: Created initial limit problem: 1+__const_20^0-3*meter-__const_5^0 (+/+!), 1-__const_20^0+3*meter+__const_5^0 (+/+!), 4+2*meter (+), meter (+/+!), 1-__const_99^0+x0^0 (+/+!) [not solved] applying transformation rule (C) using substitution {__const_20^0==3*meter+__const_5^0} resulting limit problem: 1 (+/+!), 4+2*meter (+), meter (+/+!), 1-__const_99^0+x0^0 (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 4+2*meter (+), meter (+/+!), 1-__const_99^0+x0^0 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {__const_99^0==0,meter==n,x0^0==0} resulting limit problem: [solved] Solution: __const_99^0 / 0 __const_20^0 / 3*n meter / n x0^0 / 0 __const_5^0 / 0 Resulting cost 4+2*n has complexity: Poly(n^1) Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 2+2*n Rule cost: 2+2*meter Rule guard: [ 3*meter==__const_20^0-x1^0 && meter>=1 ] WORST_CASE(Omega(n^1),?)