NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l11 0: l0 -> l1 : a^0'=a^post_1, b^0'=b^post_1, c^0'=c^post_1, d^0'=d^post_1, e^0'=e^post_1, [ 0<=e^0 && e^1_1==e^0 && d^1_1==d^0 && c^1_1==c^0 && b^1_1==b^0 && a^1_1==a^0 && e^2_1==e^1_1 && d^2_1==d^1_1 && c^2_1==c^1_1 && b^2_1==b^1_1 && a^2_1==a^1_1 && e^3_1==e^2_1 && d^3_1==d^2_1 && c^3_1==c^2_1 && b^3_1==b^2_1 && a^3_1==a^2_1 && e^post_1==e^3_1 && d^post_1==d^3_1 && c^post_1==c^3_1 && b^post_1==b^3_1 && a^post_1==a^3_1 ], cost: 1 1: l0 -> l2 : a^0'=a^post_2, b^0'=b^post_2, c^0'=c^post_2, d^0'=d^post_2, e^0'=e^post_2, [ 1+e^0<=0 && e^post_2==e^0 && d^post_2==d^0 && c^post_2==c^0 && b^post_2==b^0 && a^post_2==a^0 ], cost: 1 6: l2 -> l5 : a^0'=a^post_7, b^0'=b^post_7, c^0'=c^post_7, d^0'=d^post_7, e^0'=e^post_7, [ 0<=a^0 && e^post_7==e^0 && d^post_7==d^0 && c^post_7==c^0 && b^post_7==b^0 && a^post_7==a^0 ], cost: 1 7: l2 -> l6 : a^0'=a^post_8, b^0'=b^post_8, c^0'=c^post_8, d^0'=d^post_8, e^0'=e^post_8, [ 1+a^0<=0 && e^1_2_1==e^0 && d^1_2_1==d^0 && c^1_2_1==c^0 && b^1_2_1==b^0 && a^1_2==a^0 && e^2_2_1==e^1_2_1 && d^2_2_1==d^1_2_1 && c^2_2_1==c^1_2_1 && b^2_2_1==b^1_2_1 && a^2_2_1==-a^1_2 && e^3_2_1==e^2_2_1 && d^3_2_1==d^2_2_1 && c^3_2_1==c^2_2_1 && b^3_2_1==-a^2_2_1+b^2_2_1 && a^3_2_1==a^2_2_1 && e^post_8==-a^3_2_1+e^3_2_1 && d^post_8==d^3_2_1 && c^post_8==c^3_2_1 && b^post_8==b^3_2_1 && a^post_8==a^3_2_1 ], cost: 1 2: l3 -> l0 : a^0'=a^post_3, b^0'=b^post_3, c^0'=c^post_3, d^0'=d^post_3, e^0'=e^post_3, [ d^0<=c^0 && e^post_3==e^0 && d^post_3==d^0 && c^post_3==c^0 && b^post_3==b^0 && a^post_3==a^0 ], cost: 1 3: l3 -> l2 : a^0'=a^post_4, b^0'=b^post_4, c^0'=c^post_4, d^0'=d^post_4, e^0'=e^post_4, [ 1+c^0<=d^0 && e^post_4==e^0 && d^post_4==d^0 && c^post_4==c^0 && b^post_4==b^0 && a^post_4==a^0 ], cost: 1 4: l4 -> l3 : a^0'=a^post_5, b^0'=b^post_5, c^0'=c^post_5, d^0'=d^post_5, e^0'=e^post_5, [ 0<=b^0 && e^post_5==e^0 && d^post_5==d^0 && c^post_5==c^0 && b^post_5==b^0 && a^post_5==a^0 ], cost: 1 5: l4 -> l2 : a^0'=a^post_6, b^0'=b^post_6, c^0'=c^post_6, d^0'=d^post_6, e^0'=e^post_6, [ 1+b^0<=0 && e^post_6==e^0 && d^post_6==d^0 && c^post_6==c^0 && b^post_6==b^0 && a^post_6==a^0 ], cost: 1 16: l5 -> l10 : a^0'=a^post_17, b^0'=b^post_17, c^0'=c^post_17, d^0'=d^post_17, e^0'=e^post_17, [ 0<=b^0 && e^post_17==e^0 && d^post_17==d^0 && c^post_17==c^0 && b^post_17==b^0 && a^post_17==a^0 ], cost: 1 17: l5 -> l6 : a^0'=a^post_18, b^0'=b^post_18, c^0'=c^post_18, d^0'=d^post_18, e^0'=e^post_18, [ 1+b^0<=0 && e^1_6_1==e^0 && d^1_6_1==d^0 && c^1_6_1==c^0 && b^1_6_1==b^0 && a^1_6==a^0 && e^2_6_1==e^1_6_1 && d^2_6_1==d^1_6_1 && c^2_6_1==c^1_6_1 && b^2_6_1==-b^1_6_1 && a^2_6_1==a^1_6 && e^3_6_1==e^2_6_1 && d^3_6_1==d^2_6_1 && c^3_6_1==c^2_6_1 && b^3_6_1==b^2_6_1 && a^3_6_1==a^2_6_1-b^3_6_1 && e^post_18==e^3_6_1 && d^post_18==d^3_6_1 && c^post_18==c^3_6_1-b^3_6_1 && b^post_18==b^3_6_1 && a^post_18==a^3_6_1 ], cost: 1 18: l6 -> l8 : a^0'=a^post_19, b^0'=b^post_19, c^0'=c^post_19, d^0'=d^post_19, e^0'=e^post_19, [ e^post_19==e^0 && d^post_19==d^0 && c^post_19==c^0 && b^post_19==b^0 && a^post_19==a^0 ], cost: 1 8: l7 -> l6 : a^0'=a^post_9, b^0'=b^post_9, c^0'=c^post_9, d^0'=d^post_9, e^0'=e^post_9, [ 0<=e^0 && e^post_9==e^0 && d^post_9==d^0 && c^post_9==c^0 && b^post_9==b^0 && a^post_9==a^0 ], cost: 1 9: l7 -> l6 : a^0'=a^post_10, b^0'=b^post_10, c^0'=c^post_10, d^0'=d^post_10, e^0'=e^post_10, [ 1+e^0<=0 && e^1_3_1==e^0 && d^1_3_1==d^0 && c^1_3_1==c^0 && b^1_3_1==b^0 && a^1_3==a^0 && e^2_3_1==-e^1_3_1 && d^2_3_1==d^1_3_1 && c^2_3_1==c^1_3_1 && b^2_3_1==b^1_3_1 && a^2_3_1==a^1_3 && e^3_3_1==e^2_3_1 && d^3_3_1==-e^3_3_1+d^2_3_1 && c^3_3_1==c^2_3_1 && b^3_3_1==b^2_3_1 && a^3_3_1==a^2_3_1 && e^post_10==e^3_3_1 && d^post_10==d^3_3_1 && c^post_10==c^3_3_1 && b^post_10==b^3_3_1 && a^post_10==a^3_3_1-e^post_10 ], cost: 1 10: l8 -> l4 : a^0'=a^post_11, b^0'=b^post_11, c^0'=c^post_11, d^0'=d^post_11, e^0'=e^post_11, [ 0<=a^0 && e^post_11==e^0 && d^post_11==d^0 && c^post_11==c^0 && b^post_11==b^0 && a^post_11==a^0 ], cost: 1 11: l8 -> l2 : a^0'=a^post_12, b^0'=b^post_12, c^0'=c^post_12, d^0'=d^post_12, e^0'=e^post_12, [ 1+a^0<=0 && e^post_12==e^0 && d^post_12==d^0 && c^post_12==c^0 && b^post_12==b^0 && a^post_12==a^0 ], cost: 1 12: l9 -> l7 : a^0'=a^post_13, b^0'=b^post_13, c^0'=c^post_13, d^0'=d^post_13, e^0'=e^post_13, [ 0<=d^0 && e^post_13==e^0 && d^post_13==d^0 && c^post_13==c^0 && b^post_13==b^0 && a^post_13==a^0 ], cost: 1 13: l9 -> l6 : a^0'=a^post_14, b^0'=b^post_14, c^0'=c^post_14, d^0'=d^post_14, e^0'=e^post_14, [ 1+d^0<=0 && e^1_4_1==e^0 && d^1_4_1==d^0 && c^1_4_1==c^0 && b^1_4_1==b^0 && a^1_4==a^0 && e^2_4_1==e^1_4_1 && d^2_4_1==-d^1_4_1 && c^2_4_1==c^1_4_1 && b^2_4_1==b^1_4_1 && a^2_4_1==a^1_4 && e^3_4_1==e^2_4_1 && d^3_4_1==d^2_4_1 && c^3_4_1==-d^3_4_1+c^2_4_1 && b^3_4_1==b^2_4_1 && a^3_4_1==a^2_4_1 && e^post_14==-d^3_4_1+e^3_4_1 && d^post_14==d^3_4_1 && c^post_14==c^3_4_1 && b^post_14==b^3_4_1 && a^post_14==a^3_4_1 ], cost: 1 14: l10 -> l9 : a^0'=a^post_15, b^0'=b^post_15, c^0'=c^post_15, d^0'=d^post_15, e^0'=e^post_15, [ 0<=c^0 && e^post_15==e^0 && d^post_15==d^0 && c^post_15==c^0 && b^post_15==b^0 && a^post_15==a^0 ], cost: 1 15: l10 -> l6 : a^0'=a^post_16, b^0'=b^post_16, c^0'=c^post_16, d^0'=d^post_16, e^0'=e^post_16, [ 1+c^0<=0 && e^1_5_1==e^0 && d^1_5_1==d^0 && c^1_5_1==c^0 && b^1_5_1==b^0 && a^1_5==a^0 && e^2_5_1==e^1_5_1 && d^2_5_1==d^1_5_1 && c^2_5_1==-c^1_5_1 && b^2_5_1==b^1_5_1 && a^2_5_1==a^1_5 && e^3_5_1==e^2_5_1 && d^3_5_1==d^2_5_1 && c^3_5_1==c^2_5_1 && b^3_5_1==-c^3_5_1+b^2_5_1 && a^3_5_1==a^2_5_1 && e^post_16==e^3_5_1 && d^post_16==-c^3_5_1+d^3_5_1 && c^post_16==c^3_5_1 && b^post_16==b^3_5_1 && a^post_16==a^3_5_1 ], cost: 1 19: l11 -> l6 : a^0'=a^post_20, b^0'=b^post_20, c^0'=c^post_20, d^0'=d^post_20, e^0'=e^post_20, [ a^0==a^post_20 && b^0==b^post_20 && c^0==c^post_20 && d^0==d^post_20 && e^0==e^post_20 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 19: l11 -> l6 : a^0'=a^post_20, b^0'=b^post_20, c^0'=c^post_20, d^0'=d^post_20, e^0'=e^post_20, [ a^0==a^post_20 && b^0==b^post_20 && c^0==c^post_20 && d^0==d^post_20 && e^0==e^post_20 ], cost: 1 Removed unreachable and leaf rules: Start location: l11 1: l0 -> l2 : a^0'=a^post_2, b^0'=b^post_2, c^0'=c^post_2, d^0'=d^post_2, e^0'=e^post_2, [ 1+e^0<=0 && e^post_2==e^0 && d^post_2==d^0 && c^post_2==c^0 && b^post_2==b^0 && a^post_2==a^0 ], cost: 1 6: l2 -> l5 : a^0'=a^post_7, b^0'=b^post_7, c^0'=c^post_7, d^0'=d^post_7, e^0'=e^post_7, [ 0<=a^0 && e^post_7==e^0 && d^post_7==d^0 && c^post_7==c^0 && b^post_7==b^0 && a^post_7==a^0 ], cost: 1 7: l2 -> l6 : a^0'=a^post_8, b^0'=b^post_8, c^0'=c^post_8, d^0'=d^post_8, e^0'=e^post_8, [ 1+a^0<=0 && e^1_2_1==e^0 && d^1_2_1==d^0 && c^1_2_1==c^0 && b^1_2_1==b^0 && a^1_2==a^0 && e^2_2_1==e^1_2_1 && d^2_2_1==d^1_2_1 && c^2_2_1==c^1_2_1 && b^2_2_1==b^1_2_1 && a^2_2_1==-a^1_2 && e^3_2_1==e^2_2_1 && d^3_2_1==d^2_2_1 && c^3_2_1==c^2_2_1 && b^3_2_1==-a^2_2_1+b^2_2_1 && a^3_2_1==a^2_2_1 && e^post_8==-a^3_2_1+e^3_2_1 && d^post_8==d^3_2_1 && c^post_8==c^3_2_1 && b^post_8==b^3_2_1 && a^post_8==a^3_2_1 ], cost: 1 2: l3 -> l0 : a^0'=a^post_3, b^0'=b^post_3, c^0'=c^post_3, d^0'=d^post_3, e^0'=e^post_3, [ d^0<=c^0 && e^post_3==e^0 && d^post_3==d^0 && c^post_3==c^0 && b^post_3==b^0 && a^post_3==a^0 ], cost: 1 3: l3 -> l2 : a^0'=a^post_4, b^0'=b^post_4, c^0'=c^post_4, d^0'=d^post_4, e^0'=e^post_4, [ 1+c^0<=d^0 && e^post_4==e^0 && d^post_4==d^0 && c^post_4==c^0 && b^post_4==b^0 && a^post_4==a^0 ], cost: 1 4: l4 -> l3 : a^0'=a^post_5, b^0'=b^post_5, c^0'=c^post_5, d^0'=d^post_5, e^0'=e^post_5, [ 0<=b^0 && e^post_5==e^0 && d^post_5==d^0 && c^post_5==c^0 && b^post_5==b^0 && a^post_5==a^0 ], cost: 1 5: l4 -> l2 : a^0'=a^post_6, b^0'=b^post_6, c^0'=c^post_6, d^0'=d^post_6, e^0'=e^post_6, [ 1+b^0<=0 && e^post_6==e^0 && d^post_6==d^0 && c^post_6==c^0 && b^post_6==b^0 && a^post_6==a^0 ], cost: 1 16: l5 -> l10 : a^0'=a^post_17, b^0'=b^post_17, c^0'=c^post_17, d^0'=d^post_17, e^0'=e^post_17, [ 0<=b^0 && e^post_17==e^0 && d^post_17==d^0 && c^post_17==c^0 && b^post_17==b^0 && a^post_17==a^0 ], cost: 1 17: l5 -> l6 : a^0'=a^post_18, b^0'=b^post_18, c^0'=c^post_18, d^0'=d^post_18, e^0'=e^post_18, [ 1+b^0<=0 && e^1_6_1==e^0 && d^1_6_1==d^0 && c^1_6_1==c^0 && b^1_6_1==b^0 && a^1_6==a^0 && e^2_6_1==e^1_6_1 && d^2_6_1==d^1_6_1 && c^2_6_1==c^1_6_1 && b^2_6_1==-b^1_6_1 && a^2_6_1==a^1_6 && e^3_6_1==e^2_6_1 && d^3_6_1==d^2_6_1 && c^3_6_1==c^2_6_1 && b^3_6_1==b^2_6_1 && a^3_6_1==a^2_6_1-b^3_6_1 && e^post_18==e^3_6_1 && d^post_18==d^3_6_1 && c^post_18==c^3_6_1-b^3_6_1 && b^post_18==b^3_6_1 && a^post_18==a^3_6_1 ], cost: 1 18: l6 -> l8 : a^0'=a^post_19, b^0'=b^post_19, c^0'=c^post_19, d^0'=d^post_19, e^0'=e^post_19, [ e^post_19==e^0 && d^post_19==d^0 && c^post_19==c^0 && b^post_19==b^0 && a^post_19==a^0 ], cost: 1 8: l7 -> l6 : a^0'=a^post_9, b^0'=b^post_9, c^0'=c^post_9, d^0'=d^post_9, e^0'=e^post_9, [ 0<=e^0 && e^post_9==e^0 && d^post_9==d^0 && c^post_9==c^0 && b^post_9==b^0 && a^post_9==a^0 ], cost: 1 9: l7 -> l6 : a^0'=a^post_10, b^0'=b^post_10, c^0'=c^post_10, d^0'=d^post_10, e^0'=e^post_10, [ 1+e^0<=0 && e^1_3_1==e^0 && d^1_3_1==d^0 && c^1_3_1==c^0 && b^1_3_1==b^0 && a^1_3==a^0 && e^2_3_1==-e^1_3_1 && d^2_3_1==d^1_3_1 && c^2_3_1==c^1_3_1 && b^2_3_1==b^1_3_1 && a^2_3_1==a^1_3 && e^3_3_1==e^2_3_1 && d^3_3_1==-e^3_3_1+d^2_3_1 && c^3_3_1==c^2_3_1 && b^3_3_1==b^2_3_1 && a^3_3_1==a^2_3_1 && e^post_10==e^3_3_1 && d^post_10==d^3_3_1 && c^post_10==c^3_3_1 && b^post_10==b^3_3_1 && a^post_10==a^3_3_1-e^post_10 ], cost: 1 10: l8 -> l4 : a^0'=a^post_11, b^0'=b^post_11, c^0'=c^post_11, d^0'=d^post_11, e^0'=e^post_11, [ 0<=a^0 && e^post_11==e^0 && d^post_11==d^0 && c^post_11==c^0 && b^post_11==b^0 && a^post_11==a^0 ], cost: 1 11: l8 -> l2 : a^0'=a^post_12, b^0'=b^post_12, c^0'=c^post_12, d^0'=d^post_12, e^0'=e^post_12, [ 1+a^0<=0 && e^post_12==e^0 && d^post_12==d^0 && c^post_12==c^0 && b^post_12==b^0 && a^post_12==a^0 ], cost: 1 12: l9 -> l7 : a^0'=a^post_13, b^0'=b^post_13, c^0'=c^post_13, d^0'=d^post_13, e^0'=e^post_13, [ 0<=d^0 && e^post_13==e^0 && d^post_13==d^0 && c^post_13==c^0 && b^post_13==b^0 && a^post_13==a^0 ], cost: 1 13: l9 -> l6 : a^0'=a^post_14, b^0'=b^post_14, c^0'=c^post_14, d^0'=d^post_14, e^0'=e^post_14, [ 1+d^0<=0 && e^1_4_1==e^0 && d^1_4_1==d^0 && c^1_4_1==c^0 && b^1_4_1==b^0 && a^1_4==a^0 && e^2_4_1==e^1_4_1 && d^2_4_1==-d^1_4_1 && c^2_4_1==c^1_4_1 && b^2_4_1==b^1_4_1 && a^2_4_1==a^1_4 && e^3_4_1==e^2_4_1 && d^3_4_1==d^2_4_1 && c^3_4_1==-d^3_4_1+c^2_4_1 && b^3_4_1==b^2_4_1 && a^3_4_1==a^2_4_1 && e^post_14==-d^3_4_1+e^3_4_1 && d^post_14==d^3_4_1 && c^post_14==c^3_4_1 && b^post_14==b^3_4_1 && a^post_14==a^3_4_1 ], cost: 1 14: l10 -> l9 : a^0'=a^post_15, b^0'=b^post_15, c^0'=c^post_15, d^0'=d^post_15, e^0'=e^post_15, [ 0<=c^0 && e^post_15==e^0 && d^post_15==d^0 && c^post_15==c^0 && b^post_15==b^0 && a^post_15==a^0 ], cost: 1 15: l10 -> l6 : a^0'=a^post_16, b^0'=b^post_16, c^0'=c^post_16, d^0'=d^post_16, e^0'=e^post_16, [ 1+c^0<=0 && e^1_5_1==e^0 && d^1_5_1==d^0 && c^1_5_1==c^0 && b^1_5_1==b^0 && a^1_5==a^0 && e^2_5_1==e^1_5_1 && d^2_5_1==d^1_5_1 && c^2_5_1==-c^1_5_1 && b^2_5_1==b^1_5_1 && a^2_5_1==a^1_5 && e^3_5_1==e^2_5_1 && d^3_5_1==d^2_5_1 && c^3_5_1==c^2_5_1 && b^3_5_1==-c^3_5_1+b^2_5_1 && a^3_5_1==a^2_5_1 && e^post_16==e^3_5_1 && d^post_16==-c^3_5_1+d^3_5_1 && c^post_16==c^3_5_1 && b^post_16==b^3_5_1 && a^post_16==a^3_5_1 ], cost: 1 19: l11 -> l6 : a^0'=a^post_20, b^0'=b^post_20, c^0'=c^post_20, d^0'=d^post_20, e^0'=e^post_20, [ a^0==a^post_20 && b^0==b^post_20 && c^0==c^post_20 && d^0==d^post_20 && e^0==e^post_20 ], cost: 1 Simplified all rules, resulting in: Start location: l11 1: l0 -> l2 : [ 1+e^0<=0 ], cost: 1 6: l2 -> l5 : [ 0<=a^0 ], cost: 1 7: l2 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 1 2: l3 -> l0 : [ d^0<=c^0 ], cost: 1 3: l3 -> l2 : [ 1+c^0<=d^0 ], cost: 1 4: l4 -> l3 : [ 0<=b^0 ], cost: 1 5: l4 -> l2 : [ 1+b^0<=0 ], cost: 1 16: l5 -> l10 : [ 0<=b^0 ], cost: 1 17: l5 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 1+b^0<=0 ], cost: 1 18: l6 -> l8 : [], cost: 1 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 10: l8 -> l4 : [ 0<=a^0 ], cost: 1 11: l8 -> l2 : [ 1+a^0<=0 ], cost: 1 12: l9 -> l7 : [ 0<=d^0 ], cost: 1 13: l9 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 1+d^0<=0 ], cost: 1 14: l10 -> l9 : [ 0<=c^0 ], cost: 1 15: l10 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 1+c^0<=0 ], cost: 1 19: l11 -> l6 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l11 6: l2 -> l5 : [ 0<=a^0 ], cost: 1 7: l2 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 1 3: l3 -> l2 : [ 1+c^0<=d^0 ], cost: 1 20: l3 -> l2 : [ d^0<=c^0 && 1+e^0<=0 ], cost: 2 4: l4 -> l3 : [ 0<=b^0 ], cost: 1 5: l4 -> l2 : [ 1+b^0<=0 ], cost: 1 16: l5 -> l10 : [ 0<=b^0 ], cost: 1 17: l5 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 1+b^0<=0 ], cost: 1 18: l6 -> l8 : [], cost: 1 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 10: l8 -> l4 : [ 0<=a^0 ], cost: 1 11: l8 -> l2 : [ 1+a^0<=0 ], cost: 1 12: l9 -> l7 : [ 0<=d^0 ], cost: 1 13: l9 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 1+d^0<=0 ], cost: 1 14: l10 -> l9 : [ 0<=c^0 ], cost: 1 15: l10 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 1+c^0<=0 ], cost: 1 19: l11 -> l6 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l11 7: l2 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 1 23: l2 -> l10 : [ 0<=a^0 && 0<=b^0 ], cost: 2 24: l2 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 2 5: l4 -> l2 : [ 1+b^0<=0 ], cost: 1 27: l4 -> l2 : [ 0<=b^0 && 1+c^0<=d^0 ], cost: 2 28: l4 -> l2 : [ 0<=b^0 && d^0<=c^0 && 1+e^0<=0 ], cost: 3 21: l6 -> l4 : [ 0<=a^0 ], cost: 2 22: l6 -> l2 : [ 1+a^0<=0 ], cost: 2 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 15: l10 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 1+c^0<=0 ], cost: 1 25: l10 -> l7 : [ 0<=c^0 && 0<=d^0 ], cost: 2 26: l10 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=c^0 && 1+d^0<=0 ], cost: 2 19: l11 -> l6 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l11 7: l2 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 1 24: l2 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 2 32: l2 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=0 ], cost: 3 33: l2 -> l7 : [ 0<=a^0 && 0<=b^0 && 0<=c^0 && 0<=d^0 ], cost: 4 34: l2 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && 0<=c^0 && 1+d^0<=0 ], cost: 4 22: l6 -> l2 : [ 1+a^0<=0 ], cost: 2 29: l6 -> l2 : [ 0<=a^0 && 1+b^0<=0 ], cost: 3 30: l6 -> l2 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 ], cost: 4 31: l6 -> l2 : [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 ], cost: 5 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 19: l11 -> l6 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: l11 35: l6 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 3 36: l6 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 5 37: l6 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 7 38: l6 -> l7 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 ], cost: 8 39: l6 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 1+c^0<=0 ], cost: 8 40: l6 -> l7 : [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 9 41: l6 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 9 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 19: l11 -> l6 : [], cost: 1 Accelerating simple loops of location 6. Accelerating the following rules: 35: l6 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 3 36: l6 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 5 37: l6 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 7 39: l6 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 1+c^0<=0 ], cost: 8 41: l6 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 9 Failed to prove monotonicity of the guard of rule 35. Failed to prove monotonicity of the guard of rule 36. Failed to prove monotonicity of the guard of rule 37. Failed to prove monotonicity of the guard of rule 39. Failed to prove monotonicity of the guard of rule 41. [accelerate] Nesting with 5 inner and 5 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: l11 35: l6 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 3 36: l6 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 5 37: l6 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 7 38: l6 -> l7 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 ], cost: 8 39: l6 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 1+c^0<=0 ], cost: 8 40: l6 -> l7 : [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 9 41: l6 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 9 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 19: l11 -> l6 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: l11 38: l6 -> l7 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 ], cost: 8 40: l6 -> l7 : [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 9 8: l7 -> l6 : [ 0<=e^0 ], cost: 1 9: l7 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 ], cost: 1 42: l7 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 0<=e^0 && 1+a^0<=0 ], cost: 4 43: l7 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 1+e^0<=0 && 1+e^0+a^0<=0 ], cost: 4 45: l7 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=e^0 && 0<=a^0 && 1+b^0<=0 ], cost: 6 46: l7 -> l6 : a^0'=e^0+b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, d^0'=e^0+d^0, e^0'=-e^0, [ 1+e^0<=0 && 0<=e^0+a^0 && 1+b^0<=0 ], cost: 6 48: l7 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=e^0 && 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 49: l7 -> l6 : a^0'=e^0+a^0, b^0'=b^0+c^0, c^0'=-c^0, d^0'=e^0+c^0+d^0, e^0'=-e^0, [ 1+e^0<=0 && 0<=e^0+a^0 && 0<=b^0 && 1+c^0<=e^0+d^0 && 1+c^0<=0 ], cost: 8 19: l11 -> l6 : [], cost: 1 44: l11 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 4 47: l11 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 6 50: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 51: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 1+c^0<=0 ], cost: 9 52: l11 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 10 Eliminated locations (on tree-shaped paths): Start location: l11 53: l6 -> l6 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: 9 54: l6 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 1+e^0<=0 ], cost: 9 55: l6 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 1+e^0<=0 && 1+e^0+a^0<=0 ], cost: 12 56: l6 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 10 57: l6 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0+a^0<=0 ], cost: 13 19: l11 -> l6 : [], cost: 1 44: l11 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 4 47: l11 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 6 50: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 51: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 1+c^0<=0 ], cost: 9 52: l11 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 10 Merged rules: Start location: l11 53: l6 -> l6 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: 9 58: l6 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 10 59: l6 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0+a^0<=0 ], cost: 13 19: l11 -> l6 : [], cost: 1 44: l11 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 4 47: l11 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 6 50: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 51: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 1+c^0<=0 ], cost: 9 52: l11 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 10 Applied pruning (of leafs and parallel rules): Start location: l11 53: l6 -> l6 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: 9 58: l6 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 10 59: l6 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0+a^0<=0 ], cost: 13 19: l11 -> l6 : [], cost: 1 44: l11 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 4 47: l11 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 6 50: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 52: l11 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 10 Accelerating simple loops of location 6. Accelerating the following rules: 53: l6 -> l6 : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: 9 58: l6 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 10 59: l6 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0+a^0<=0 ], cost: 13 Accelerated rule 53 with non-termination, yielding the new rule 60. Failed to prove monotonicity of the guard of rule 58. Failed to prove monotonicity of the guard of rule 59. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 53. Accelerated all simple loops using metering functions (where possible): Start location: l11 58: l6 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 10 59: l6 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0+a^0<=0 ], cost: 13 60: l6 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 19: l11 -> l6 : [], cost: 1 44: l11 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 4 47: l11 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 6 50: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 52: l11 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 10 Chained accelerated rules (with incoming rules): Start location: l11 19: l11 -> l6 : [], cost: 1 44: l11 -> l6 : a^0'=-a^0, b^0'=b^0+a^0, e^0'=e^0+a^0, [ 1+a^0<=0 ], cost: 4 47: l11 -> l6 : a^0'=b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, [ 0<=a^0 && 1+b^0<=0 ], cost: 6 50: l11 -> l6 : b^0'=b^0+c^0, c^0'=-c^0, d^0'=c^0+d^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 ], cost: 8 52: l11 -> l6 : c^0'=c^0+d^0, d^0'=-d^0, e^0'=e^0+d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 ], cost: 10 61: l11 -> l6 : a^0'=e^0+a^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 11 62: l11 -> l6 : a^0'=e^0, b^0'=b^0+a^0, d^0'=e^0+d^0+a^0, e^0'=-e^0-a^0, [ 1+a^0<=0 && 0<=b^0+a^0 && 1+e^0+a^0<=0 && 0<=c^0 && 0<=d^0 ], cost: 14 63: l11 -> l6 : a^0'=e^0+b^0+a^0, b^0'=-b^0, c^0'=b^0+c^0, d^0'=e^0+d^0, e^0'=-e^0, [ 0<=a^0 && 1+b^0<=0 && 0<=b^0+a^0 && 1+e^0<=0 && 0<=b^0+c^0 && 0<=d^0 ], cost: 16 64: l11 -> l6 : a^0'=e^0+a^0, b^0'=b^0+c^0, c^0'=-c^0, d^0'=e^0+c^0+d^0, e^0'=-e^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 && 0<=b^0+c^0 && 1+e^0<=0 && 0<=c^0+d^0 ], cost: 18 65: l11 -> l6 : a^0'=e^0+d^0+a^0, c^0'=c^0+d^0, d^0'=e^0, e^0'=-e^0-d^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 && 1+e^0+d^0<=0 && 0<=c^0+d^0 ], cost: 20 66: l11 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+e^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0+a^0<=0 ], cost: 14 67: l11 -> l6 : a^0'=-e^0, b^0'=e^0+b^0+a^0, d^0'=e^0+d^0+a^0, e^0'=-a^0, [ 1+a^0<=0 && 0<=b^0+a^0 && 1+e^0+a^0<=0 && 0<=c^0 && 0<=d^0 && 1+e^0<=0 ], cost: 17 68: l11 -> l6 : a^0'=-e^0-b^0-a^0, b^0'=e^0+a^0, c^0'=b^0+c^0, d^0'=e^0+d^0, e^0'=b^0+a^0, [ 0<=a^0 && 1+b^0<=0 && 0<=b^0+a^0 && 1+e^0<=0 && 0<=b^0+c^0 && 0<=d^0 && 1+e^0+b^0+a^0<=0 ], cost: 19 69: l11 -> l6 : a^0'=-e^0-a^0, b^0'=e^0+b^0+c^0+a^0, c^0'=-c^0, d^0'=e^0+c^0+d^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 && 0<=b^0+c^0 && 1+e^0<=0 && 0<=c^0+d^0 && 1+e^0+a^0<=0 ], cost: 21 70: l11 -> l6 : a^0'=-e^0-d^0-a^0, b^0'=e^0+b^0+d^0+a^0, c^0'=c^0+d^0, d^0'=e^0, e^0'=a^0, [ 0<=a^0 && 0<=b^0 && d^0<=c^0 && 1+e^0<=0 && 0<=c^0 && 1+d^0<=0 && 1+e^0+d^0<=0 && 0<=c^0+d^0 && 1+e^0+d^0+a^0<=0 ], cost: 23 71: l11 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 72: l11 -> [13] : [ 1+a^0<=0 && 0<=b^0+a^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0+a^0 ], cost: NONTERM 73: l11 -> [13] : [ 0<=a^0 && 1+b^0<=0 && 0<=b^0+a^0 && 1+b^0+c^0<=d^0 && 0<=b^0+c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 74: l11 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 && 0<=b^0+c^0 && 1-c^0<=c^0+d^0 && 0<=c^0+d^0 && 0<=e^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l11 71: l11 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 72: l11 -> [13] : [ 1+a^0<=0 && 0<=b^0+a^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0+a^0 ], cost: NONTERM 73: l11 -> [13] : [ 0<=a^0 && 1+b^0<=0 && 0<=b^0+a^0 && 1+b^0+c^0<=d^0 && 0<=b^0+c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 74: l11 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 && 0<=b^0+c^0 && 1-c^0<=c^0+d^0 && 0<=c^0+d^0 && 0<=e^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l11 71: l11 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 72: l11 -> [13] : [ 1+a^0<=0 && 0<=b^0+a^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=d^0 && 0<=e^0+a^0 ], cost: NONTERM 73: l11 -> [13] : [ 0<=a^0 && 1+b^0<=0 && 0<=b^0+a^0 && 1+b^0+c^0<=d^0 && 0<=b^0+c^0 && 0<=d^0 && 0<=e^0 ], cost: NONTERM 74: l11 -> [13] : [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 1+c^0<=0 && 0<=b^0+c^0 && 1-c^0<=c^0+d^0 && 0<=c^0+d^0 && 0<=e^0 ], cost: NONTERM Computing asymptotic complexity for rule 71 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ 0<=a^0 && 0<=b^0 && 1+c^0<=d^0 && 0<=c^0 && 0<=e^0 ] NO