WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l15 0: l0 -> l1 : K^0'=K^post_1, N^0'=N^post_1, next^0'=next^post_1, pos^0'=pos^post_1, xx^0'=xx^post_1, yy^0'=yy^post_1, z^0'=z^post_1, [ K^post_1==-1+K^0 && N^0==N^post_1 && next^0==next^post_1 && pos^0==pos^post_1 && xx^0==xx^post_1 && yy^0==yy^post_1 && z^0==z^post_1 ], cost: 1 17: l1 -> l10 : K^0'=K^post_18, N^0'=N^post_18, next^0'=next^post_18, pos^0'=pos^post_18, xx^0'=xx^post_18, yy^0'=yy^post_18, z^0'=z^post_18, [ K^0==K^post_18 && N^0==N^post_18 && next^0==next^post_18 && pos^0==pos^post_18 && xx^0==xx^post_18 && yy^0==yy^post_18 && z^0==z^post_18 ], cost: 1 1: l2 -> l3 : K^0'=K^post_2, N^0'=N^post_2, next^0'=next^post_2, pos^0'=pos^post_2, xx^0'=xx^post_2, yy^0'=yy^post_2, z^0'=z^post_2, [ 3<=pos^0 && next^post_2==1+next^0 && z^post_2==z^post_2 && 0<=z^post_2 && pos^post_2==0 && K^0==K^post_2 && N^0==N^post_2 && xx^0==xx^post_2 && yy^0==yy^post_2 ], cost: 1 2: l2 -> l3 : K^0'=K^post_3, N^0'=N^post_3, next^0'=next^post_3, pos^0'=pos^post_3, xx^0'=xx^post_3, yy^0'=yy^post_3, z^0'=z^post_3, [ pos^0<=2 && yy^0<=0 && pos^post_3==1+pos^0 && K^0==K^post_3 && N^0==N^post_3 && next^0==next^post_3 && xx^0==xx^post_3 && yy^0==yy^post_3 && z^0==z^post_3 ], cost: 1 5: l3 -> l1 : K^0'=K^post_6, N^0'=N^post_6, next^0'=next^post_6, pos^0'=pos^post_6, xx^0'=xx^post_6, yy^0'=yy^post_6, z^0'=z^post_6, [ xx^0<=yy^0 && yy^0<=xx^0 && K^0==K^post_6 && N^0==N^post_6 && next^0==next^post_6 && pos^0==pos^post_6 && xx^0==xx^post_6 && yy^0==yy^post_6 && z^0==z^post_6 ], cost: 1 6: l3 -> l0 : K^0'=K^post_7, N^0'=N^post_7, next^0'=next^post_7, pos^0'=pos^post_7, xx^0'=xx^post_7, yy^0'=yy^post_7, z^0'=z^post_7, [ 1+yy^0<=xx^0 && K^0==K^post_7 && N^0==N^post_7 && next^0==next^post_7 && pos^0==pos^post_7 && xx^0==xx^post_7 && yy^0==yy^post_7 && z^0==z^post_7 ], cost: 1 7: l3 -> l0 : K^0'=K^post_8, N^0'=N^post_8, next^0'=next^post_8, pos^0'=pos^post_8, xx^0'=xx^post_8, yy^0'=yy^post_8, z^0'=z^post_8, [ 1+xx^0<=yy^0 && K^0==K^post_8 && N^0==N^post_8 && next^0==next^post_8 && pos^0==pos^post_8 && xx^0==xx^post_8 && yy^0==yy^post_8 && z^0==z^post_8 ], cost: 1 3: l4 -> l2 : K^0'=K^post_4, N^0'=N^post_4, next^0'=next^post_4, pos^0'=pos^post_4, xx^0'=xx^post_4, yy^0'=yy^post_4, z^0'=z^post_4, [ 2<=pos^0 && K^0==K^post_4 && N^0==N^post_4 && next^0==next^post_4 && pos^0==pos^post_4 && xx^0==xx^post_4 && yy^0==yy^post_4 && z^0==z^post_4 ], cost: 1 4: l4 -> l3 : K^0'=K^post_5, N^0'=N^post_5, next^0'=next^post_5, pos^0'=pos^post_5, xx^0'=xx^post_5, yy^0'=yy^post_5, z^0'=z^post_5, [ pos^0<=1 && 1<=yy^0 && pos^post_5==1+pos^0 && K^0==K^post_5 && N^0==N^post_5 && next^0==next^post_5 && xx^0==xx^post_5 && yy^0==yy^post_5 && z^0==z^post_5 ], cost: 1 8: l5 -> l4 : K^0'=K^post_9, N^0'=N^post_9, next^0'=next^post_9, pos^0'=pos^post_9, xx^0'=xx^post_9, yy^0'=yy^post_9, z^0'=z^post_9, [ 1<=pos^0 && K^0==K^post_9 && N^0==N^post_9 && next^0==next^post_9 && pos^0==pos^post_9 && xx^0==xx^post_9 && yy^0==yy^post_9 && z^0==z^post_9 ], cost: 1 9: l5 -> l3 : K^0'=K^post_10, N^0'=N^post_10, next^0'=next^post_10, pos^0'=pos^post_10, xx^0'=xx^post_10, yy^0'=yy^post_10, z^0'=z^post_10, [ pos^0<=0 && yy^0<=0 && pos^post_10==1+pos^0 && K^0==K^post_10 && N^0==N^post_10 && next^0==next^post_10 && xx^0==xx^post_10 && yy^0==yy^post_10 && z^0==z^post_10 ], cost: 1 10: l6 -> l3 : K^0'=K^post_11, N^0'=N^post_11, next^0'=next^post_11, pos^0'=pos^post_11, xx^0'=xx^post_11, yy^0'=yy^post_11, z^0'=z^post_11, [ 1<=z^0 && z^post_11==-1+z^0 && K^0==K^post_11 && N^0==N^post_11 && next^0==next^post_11 && pos^0==pos^post_11 && xx^0==xx^post_11 && yy^0==yy^post_11 ], cost: 1 11: l6 -> l5 : K^0'=K^post_12, N^0'=N^post_12, next^0'=next^post_12, pos^0'=pos^post_12, xx^0'=xx^post_12, yy^0'=yy^post_12, z^0'=z^post_12, [ z^0<=0 && K^0==K^post_12 && N^0==N^post_12 && next^0==next^post_12 && pos^0==pos^post_12 && xx^0==xx^post_12 && yy^0==yy^post_12 && z^0==z^post_12 ], cost: 1 12: l7 -> l8 : K^0'=K^post_13, N^0'=N^post_13, next^0'=next^post_13, pos^0'=pos^post_13, xx^0'=xx^post_13, yy^0'=yy^post_13, z^0'=z^post_13, [ 3<=pos^0 && next^post_13==1+next^0 && z^post_13==z^post_13 && 0<=z^post_13 && pos^post_13==0 && K^0==K^post_13 && N^0==N^post_13 && xx^0==xx^post_13 && yy^0==yy^post_13 ], cost: 1 13: l7 -> l8 : K^0'=K^post_14, N^0'=N^post_14, next^0'=next^post_14, pos^0'=pos^post_14, xx^0'=xx^post_14, yy^0'=yy^post_14, z^0'=z^post_14, [ pos^0<=2 && xx^0<=0 && pos^post_14==1+pos^0 && K^0==K^post_14 && N^0==N^post_14 && next^0==next^post_14 && xx^0==xx^post_14 && yy^0==yy^post_14 && z^0==z^post_14 ], cost: 1 16: l8 -> l6 : K^0'=K^post_17, N^0'=N^post_17, next^0'=next^post_17, pos^0'=pos^post_17, xx^0'=xx^post_17, yy^0'=yy^post_17, z^0'=z^post_17, [ yy^post_17==yy^post_17 && 0<=yy^post_17 && yy^post_17<=1 && K^0==K^post_17 && N^0==N^post_17 && next^0==next^post_17 && pos^0==pos^post_17 && xx^0==xx^post_17 && z^0==z^post_17 ], cost: 1 14: l9 -> l7 : K^0'=K^post_15, N^0'=N^post_15, next^0'=next^post_15, pos^0'=pos^post_15, xx^0'=xx^post_15, yy^0'=yy^post_15, z^0'=z^post_15, [ 2<=pos^0 && K^0==K^post_15 && N^0==N^post_15 && next^0==next^post_15 && pos^0==pos^post_15 && xx^0==xx^post_15 && yy^0==yy^post_15 && z^0==z^post_15 ], cost: 1 15: l9 -> l8 : K^0'=K^post_16, N^0'=N^post_16, next^0'=next^post_16, pos^0'=pos^post_16, xx^0'=xx^post_16, yy^0'=yy^post_16, z^0'=z^post_16, [ pos^0<=1 && 1<=xx^0 && pos^post_16==1+pos^0 && K^0==K^post_16 && N^0==N^post_16 && next^0==next^post_16 && xx^0==xx^post_16 && yy^0==yy^post_16 && z^0==z^post_16 ], cost: 1 22: l10 -> l13 : K^0'=K^post_23, N^0'=N^post_23, next^0'=next^post_23, pos^0'=pos^post_23, xx^0'=xx^post_23, yy^0'=yy^post_23, z^0'=z^post_23, [ K^0<=0 && K^0==K^post_23 && N^0==N^post_23 && next^0==next^post_23 && pos^0==pos^post_23 && xx^0==xx^post_23 && yy^0==yy^post_23 && z^0==z^post_23 ], cost: 1 23: l10 -> l12 : K^0'=K^post_24, N^0'=N^post_24, next^0'=next^post_24, pos^0'=pos^post_24, xx^0'=xx^post_24, yy^0'=yy^post_24, z^0'=z^post_24, [ 1<=K^0 && xx^post_24==xx^post_24 && 0<=xx^post_24 && xx^post_24<=1 && K^0==K^post_24 && N^0==N^post_24 && next^0==next^post_24 && pos^0==pos^post_24 && yy^0==yy^post_24 && z^0==z^post_24 ], cost: 1 18: l11 -> l9 : K^0'=K^post_19, N^0'=N^post_19, next^0'=next^post_19, pos^0'=pos^post_19, xx^0'=xx^post_19, yy^0'=yy^post_19, z^0'=z^post_19, [ 1<=pos^0 && K^0==K^post_19 && N^0==N^post_19 && next^0==next^post_19 && pos^0==pos^post_19 && xx^0==xx^post_19 && yy^0==yy^post_19 && z^0==z^post_19 ], cost: 1 19: l11 -> l8 : K^0'=K^post_20, N^0'=N^post_20, next^0'=next^post_20, pos^0'=pos^post_20, xx^0'=xx^post_20, yy^0'=yy^post_20, z^0'=z^post_20, [ pos^0<=0 && xx^0<=0 && pos^post_20==1+pos^0 && K^0==K^post_20 && N^0==N^post_20 && next^0==next^post_20 && xx^0==xx^post_20 && yy^0==yy^post_20 && z^0==z^post_20 ], cost: 1 20: l12 -> l8 : K^0'=K^post_21, N^0'=N^post_21, next^0'=next^post_21, pos^0'=pos^post_21, xx^0'=xx^post_21, yy^0'=yy^post_21, z^0'=z^post_21, [ 1<=z^0 && z^post_21==-1+z^0 && K^0==K^post_21 && N^0==N^post_21 && next^0==next^post_21 && pos^0==pos^post_21 && xx^0==xx^post_21 && yy^0==yy^post_21 ], cost: 1 21: l12 -> l11 : K^0'=K^post_22, N^0'=N^post_22, next^0'=next^post_22, pos^0'=pos^post_22, xx^0'=xx^post_22, yy^0'=yy^post_22, z^0'=z^post_22, [ z^0<=0 && K^0==K^post_22 && N^0==N^post_22 && next^0==next^post_22 && pos^0==pos^post_22 && xx^0==xx^post_22 && yy^0==yy^post_22 && z^0==z^post_22 ], cost: 1 24: l14 -> l1 : K^0'=K^post_25, N^0'=N^post_25, next^0'=next^post_25, pos^0'=pos^post_25, xx^0'=xx^post_25, yy^0'=yy^post_25, z^0'=z^post_25, [ z^post_25==z^post_25 && 0<=z^post_25 && pos^post_25==0 && next^post_25==1 && N^post_25==N^post_25 && 1<=N^post_25 && K^post_25==N^post_25 && xx^post_25==0 && yy^post_25==0 ], cost: 1 25: l15 -> l14 : K^0'=K^post_26, N^0'=N^post_26, next^0'=next^post_26, pos^0'=pos^post_26, xx^0'=xx^post_26, yy^0'=yy^post_26, z^0'=z^post_26, [ K^0==K^post_26 && N^0==N^post_26 && next^0==next^post_26 && pos^0==pos^post_26 && xx^0==xx^post_26 && yy^0==yy^post_26 && z^0==z^post_26 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 25: l15 -> l14 : K^0'=K^post_26, N^0'=N^post_26, next^0'=next^post_26, pos^0'=pos^post_26, xx^0'=xx^post_26, yy^0'=yy^post_26, z^0'=z^post_26, [ K^0==K^post_26 && N^0==N^post_26 && next^0==next^post_26 && pos^0==pos^post_26 && xx^0==xx^post_26 && yy^0==yy^post_26 && z^0==z^post_26 ], cost: 1 Removed unreachable and leaf rules: Start location: l15 0: l0 -> l1 : K^0'=K^post_1, N^0'=N^post_1, next^0'=next^post_1, pos^0'=pos^post_1, xx^0'=xx^post_1, yy^0'=yy^post_1, z^0'=z^post_1, [ K^post_1==-1+K^0 && N^0==N^post_1 && next^0==next^post_1 && pos^0==pos^post_1 && xx^0==xx^post_1 && yy^0==yy^post_1 && z^0==z^post_1 ], cost: 1 17: l1 -> l10 : K^0'=K^post_18, N^0'=N^post_18, next^0'=next^post_18, pos^0'=pos^post_18, xx^0'=xx^post_18, yy^0'=yy^post_18, z^0'=z^post_18, [ K^0==K^post_18 && N^0==N^post_18 && next^0==next^post_18 && pos^0==pos^post_18 && xx^0==xx^post_18 && yy^0==yy^post_18 && z^0==z^post_18 ], cost: 1 1: l2 -> l3 : K^0'=K^post_2, N^0'=N^post_2, next^0'=next^post_2, pos^0'=pos^post_2, xx^0'=xx^post_2, yy^0'=yy^post_2, z^0'=z^post_2, [ 3<=pos^0 && next^post_2==1+next^0 && z^post_2==z^post_2 && 0<=z^post_2 && pos^post_2==0 && K^0==K^post_2 && N^0==N^post_2 && xx^0==xx^post_2 && yy^0==yy^post_2 ], cost: 1 2: l2 -> l3 : K^0'=K^post_3, N^0'=N^post_3, next^0'=next^post_3, pos^0'=pos^post_3, xx^0'=xx^post_3, yy^0'=yy^post_3, z^0'=z^post_3, [ pos^0<=2 && yy^0<=0 && pos^post_3==1+pos^0 && K^0==K^post_3 && N^0==N^post_3 && next^0==next^post_3 && xx^0==xx^post_3 && yy^0==yy^post_3 && z^0==z^post_3 ], cost: 1 5: l3 -> l1 : K^0'=K^post_6, N^0'=N^post_6, next^0'=next^post_6, pos^0'=pos^post_6, xx^0'=xx^post_6, yy^0'=yy^post_6, z^0'=z^post_6, [ xx^0<=yy^0 && yy^0<=xx^0 && K^0==K^post_6 && N^0==N^post_6 && next^0==next^post_6 && pos^0==pos^post_6 && xx^0==xx^post_6 && yy^0==yy^post_6 && z^0==z^post_6 ], cost: 1 6: l3 -> l0 : K^0'=K^post_7, N^0'=N^post_7, next^0'=next^post_7, pos^0'=pos^post_7, xx^0'=xx^post_7, yy^0'=yy^post_7, z^0'=z^post_7, [ 1+yy^0<=xx^0 && K^0==K^post_7 && N^0==N^post_7 && next^0==next^post_7 && pos^0==pos^post_7 && xx^0==xx^post_7 && yy^0==yy^post_7 && z^0==z^post_7 ], cost: 1 7: l3 -> l0 : K^0'=K^post_8, N^0'=N^post_8, next^0'=next^post_8, pos^0'=pos^post_8, xx^0'=xx^post_8, yy^0'=yy^post_8, z^0'=z^post_8, [ 1+xx^0<=yy^0 && K^0==K^post_8 && N^0==N^post_8 && next^0==next^post_8 && pos^0==pos^post_8 && xx^0==xx^post_8 && yy^0==yy^post_8 && z^0==z^post_8 ], cost: 1 3: l4 -> l2 : K^0'=K^post_4, N^0'=N^post_4, next^0'=next^post_4, pos^0'=pos^post_4, xx^0'=xx^post_4, yy^0'=yy^post_4, z^0'=z^post_4, [ 2<=pos^0 && K^0==K^post_4 && N^0==N^post_4 && next^0==next^post_4 && pos^0==pos^post_4 && xx^0==xx^post_4 && yy^0==yy^post_4 && z^0==z^post_4 ], cost: 1 4: l4 -> l3 : K^0'=K^post_5, N^0'=N^post_5, next^0'=next^post_5, pos^0'=pos^post_5, xx^0'=xx^post_5, yy^0'=yy^post_5, z^0'=z^post_5, [ pos^0<=1 && 1<=yy^0 && pos^post_5==1+pos^0 && K^0==K^post_5 && N^0==N^post_5 && next^0==next^post_5 && xx^0==xx^post_5 && yy^0==yy^post_5 && z^0==z^post_5 ], cost: 1 8: l5 -> l4 : K^0'=K^post_9, N^0'=N^post_9, next^0'=next^post_9, pos^0'=pos^post_9, xx^0'=xx^post_9, yy^0'=yy^post_9, z^0'=z^post_9, [ 1<=pos^0 && K^0==K^post_9 && N^0==N^post_9 && next^0==next^post_9 && pos^0==pos^post_9 && xx^0==xx^post_9 && yy^0==yy^post_9 && z^0==z^post_9 ], cost: 1 9: l5 -> l3 : K^0'=K^post_10, N^0'=N^post_10, next^0'=next^post_10, pos^0'=pos^post_10, xx^0'=xx^post_10, yy^0'=yy^post_10, z^0'=z^post_10, [ pos^0<=0 && yy^0<=0 && pos^post_10==1+pos^0 && K^0==K^post_10 && N^0==N^post_10 && next^0==next^post_10 && xx^0==xx^post_10 && yy^0==yy^post_10 && z^0==z^post_10 ], cost: 1 10: l6 -> l3 : K^0'=K^post_11, N^0'=N^post_11, next^0'=next^post_11, pos^0'=pos^post_11, xx^0'=xx^post_11, yy^0'=yy^post_11, z^0'=z^post_11, [ 1<=z^0 && z^post_11==-1+z^0 && K^0==K^post_11 && N^0==N^post_11 && next^0==next^post_11 && pos^0==pos^post_11 && xx^0==xx^post_11 && yy^0==yy^post_11 ], cost: 1 11: l6 -> l5 : K^0'=K^post_12, N^0'=N^post_12, next^0'=next^post_12, pos^0'=pos^post_12, xx^0'=xx^post_12, yy^0'=yy^post_12, z^0'=z^post_12, [ z^0<=0 && K^0==K^post_12 && N^0==N^post_12 && next^0==next^post_12 && pos^0==pos^post_12 && xx^0==xx^post_12 && yy^0==yy^post_12 && z^0==z^post_12 ], cost: 1 12: l7 -> l8 : K^0'=K^post_13, N^0'=N^post_13, next^0'=next^post_13, pos^0'=pos^post_13, xx^0'=xx^post_13, yy^0'=yy^post_13, z^0'=z^post_13, [ 3<=pos^0 && next^post_13==1+next^0 && z^post_13==z^post_13 && 0<=z^post_13 && pos^post_13==0 && K^0==K^post_13 && N^0==N^post_13 && xx^0==xx^post_13 && yy^0==yy^post_13 ], cost: 1 13: l7 -> l8 : K^0'=K^post_14, N^0'=N^post_14, next^0'=next^post_14, pos^0'=pos^post_14, xx^0'=xx^post_14, yy^0'=yy^post_14, z^0'=z^post_14, [ pos^0<=2 && xx^0<=0 && pos^post_14==1+pos^0 && K^0==K^post_14 && N^0==N^post_14 && next^0==next^post_14 && xx^0==xx^post_14 && yy^0==yy^post_14 && z^0==z^post_14 ], cost: 1 16: l8 -> l6 : K^0'=K^post_17, N^0'=N^post_17, next^0'=next^post_17, pos^0'=pos^post_17, xx^0'=xx^post_17, yy^0'=yy^post_17, z^0'=z^post_17, [ yy^post_17==yy^post_17 && 0<=yy^post_17 && yy^post_17<=1 && K^0==K^post_17 && N^0==N^post_17 && next^0==next^post_17 && pos^0==pos^post_17 && xx^0==xx^post_17 && z^0==z^post_17 ], cost: 1 14: l9 -> l7 : K^0'=K^post_15, N^0'=N^post_15, next^0'=next^post_15, pos^0'=pos^post_15, xx^0'=xx^post_15, yy^0'=yy^post_15, z^0'=z^post_15, [ 2<=pos^0 && K^0==K^post_15 && N^0==N^post_15 && next^0==next^post_15 && pos^0==pos^post_15 && xx^0==xx^post_15 && yy^0==yy^post_15 && z^0==z^post_15 ], cost: 1 15: l9 -> l8 : K^0'=K^post_16, N^0'=N^post_16, next^0'=next^post_16, pos^0'=pos^post_16, xx^0'=xx^post_16, yy^0'=yy^post_16, z^0'=z^post_16, [ pos^0<=1 && 1<=xx^0 && pos^post_16==1+pos^0 && K^0==K^post_16 && N^0==N^post_16 && next^0==next^post_16 && xx^0==xx^post_16 && yy^0==yy^post_16 && z^0==z^post_16 ], cost: 1 23: l10 -> l12 : K^0'=K^post_24, N^0'=N^post_24, next^0'=next^post_24, pos^0'=pos^post_24, xx^0'=xx^post_24, yy^0'=yy^post_24, z^0'=z^post_24, [ 1<=K^0 && xx^post_24==xx^post_24 && 0<=xx^post_24 && xx^post_24<=1 && K^0==K^post_24 && N^0==N^post_24 && next^0==next^post_24 && pos^0==pos^post_24 && yy^0==yy^post_24 && z^0==z^post_24 ], cost: 1 18: l11 -> l9 : K^0'=K^post_19, N^0'=N^post_19, next^0'=next^post_19, pos^0'=pos^post_19, xx^0'=xx^post_19, yy^0'=yy^post_19, z^0'=z^post_19, [ 1<=pos^0 && K^0==K^post_19 && N^0==N^post_19 && next^0==next^post_19 && pos^0==pos^post_19 && xx^0==xx^post_19 && yy^0==yy^post_19 && z^0==z^post_19 ], cost: 1 19: l11 -> l8 : K^0'=K^post_20, N^0'=N^post_20, next^0'=next^post_20, pos^0'=pos^post_20, xx^0'=xx^post_20, yy^0'=yy^post_20, z^0'=z^post_20, [ pos^0<=0 && xx^0<=0 && pos^post_20==1+pos^0 && K^0==K^post_20 && N^0==N^post_20 && next^0==next^post_20 && xx^0==xx^post_20 && yy^0==yy^post_20 && z^0==z^post_20 ], cost: 1 20: l12 -> l8 : K^0'=K^post_21, N^0'=N^post_21, next^0'=next^post_21, pos^0'=pos^post_21, xx^0'=xx^post_21, yy^0'=yy^post_21, z^0'=z^post_21, [ 1<=z^0 && z^post_21==-1+z^0 && K^0==K^post_21 && N^0==N^post_21 && next^0==next^post_21 && pos^0==pos^post_21 && xx^0==xx^post_21 && yy^0==yy^post_21 ], cost: 1 21: l12 -> l11 : K^0'=K^post_22, N^0'=N^post_22, next^0'=next^post_22, pos^0'=pos^post_22, xx^0'=xx^post_22, yy^0'=yy^post_22, z^0'=z^post_22, [ z^0<=0 && K^0==K^post_22 && N^0==N^post_22 && next^0==next^post_22 && pos^0==pos^post_22 && xx^0==xx^post_22 && yy^0==yy^post_22 && z^0==z^post_22 ], cost: 1 24: l14 -> l1 : K^0'=K^post_25, N^0'=N^post_25, next^0'=next^post_25, pos^0'=pos^post_25, xx^0'=xx^post_25, yy^0'=yy^post_25, z^0'=z^post_25, [ z^post_25==z^post_25 && 0<=z^post_25 && pos^post_25==0 && next^post_25==1 && N^post_25==N^post_25 && 1<=N^post_25 && K^post_25==N^post_25 && xx^post_25==0 && yy^post_25==0 ], cost: 1 25: l15 -> l14 : K^0'=K^post_26, N^0'=N^post_26, next^0'=next^post_26, pos^0'=pos^post_26, xx^0'=xx^post_26, yy^0'=yy^post_26, z^0'=z^post_26, [ K^0==K^post_26 && N^0==N^post_26 && next^0==next^post_26 && pos^0==pos^post_26 && xx^0==xx^post_26 && yy^0==yy^post_26 && z^0==z^post_26 ], cost: 1 Simplified all rules, resulting in: Start location: l15 0: l0 -> l1 : K^0'=-1+K^0, [], cost: 1 17: l1 -> l10 : [], cost: 1 1: l2 -> l3 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_2, [ 3<=pos^0 && 0<=z^post_2 ], cost: 1 2: l2 -> l3 : pos^0'=1+pos^0, [ pos^0<=2 && yy^0<=0 ], cost: 1 5: l3 -> l1 : [ -yy^0+xx^0==0 ], cost: 1 6: l3 -> l0 : [ 1+yy^0<=xx^0 ], cost: 1 7: l3 -> l0 : [ 1+xx^0<=yy^0 ], cost: 1 3: l4 -> l2 : [ 2<=pos^0 ], cost: 1 4: l4 -> l3 : pos^0'=1+pos^0, [ pos^0<=1 && 1<=yy^0 ], cost: 1 8: l5 -> l4 : [ 1<=pos^0 ], cost: 1 9: l5 -> l3 : pos^0'=1+pos^0, [ pos^0<=0 && yy^0<=0 ], cost: 1 10: l6 -> l3 : z^0'=-1+z^0, [ 1<=z^0 ], cost: 1 11: l6 -> l5 : [ z^0<=0 ], cost: 1 12: l7 -> l8 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_13, [ 3<=pos^0 && 0<=z^post_13 ], cost: 1 13: l7 -> l8 : pos^0'=1+pos^0, [ pos^0<=2 && xx^0<=0 ], cost: 1 16: l8 -> l6 : yy^0'=yy^post_17, [ 0<=yy^post_17 && yy^post_17<=1 ], cost: 1 14: l9 -> l7 : [ 2<=pos^0 ], cost: 1 15: l9 -> l8 : pos^0'=1+pos^0, [ pos^0<=1 && 1<=xx^0 ], cost: 1 23: l10 -> l12 : xx^0'=xx^post_24, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 ], cost: 1 18: l11 -> l9 : [ 1<=pos^0 ], cost: 1 19: l11 -> l8 : pos^0'=1+pos^0, [ pos^0<=0 && xx^0<=0 ], cost: 1 20: l12 -> l8 : z^0'=-1+z^0, [ 1<=z^0 ], cost: 1 21: l12 -> l11 : [ z^0<=0 ], cost: 1 24: l14 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 1 25: l15 -> l14 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l15 0: l0 -> l1 : K^0'=-1+K^0, [], cost: 1 27: l1 -> l12 : xx^0'=xx^post_24, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 ], cost: 2 1: l2 -> l3 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_2, [ 3<=pos^0 && 0<=z^post_2 ], cost: 1 2: l2 -> l3 : pos^0'=1+pos^0, [ pos^0<=2 && yy^0<=0 ], cost: 1 5: l3 -> l1 : [ -yy^0+xx^0==0 ], cost: 1 6: l3 -> l0 : [ 1+yy^0<=xx^0 ], cost: 1 7: l3 -> l0 : [ 1+xx^0<=yy^0 ], cost: 1 3: l4 -> l2 : [ 2<=pos^0 ], cost: 1 4: l4 -> l3 : pos^0'=1+pos^0, [ pos^0<=1 && 1<=yy^0 ], cost: 1 8: l5 -> l4 : [ 1<=pos^0 ], cost: 1 9: l5 -> l3 : pos^0'=1+pos^0, [ pos^0<=0 && yy^0<=0 ], cost: 1 10: l6 -> l3 : z^0'=-1+z^0, [ 1<=z^0 ], cost: 1 11: l6 -> l5 : [ z^0<=0 ], cost: 1 12: l7 -> l8 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_13, [ 3<=pos^0 && 0<=z^post_13 ], cost: 1 13: l7 -> l8 : pos^0'=1+pos^0, [ pos^0<=2 && xx^0<=0 ], cost: 1 16: l8 -> l6 : yy^0'=yy^post_17, [ 0<=yy^post_17 && yy^post_17<=1 ], cost: 1 14: l9 -> l7 : [ 2<=pos^0 ], cost: 1 15: l9 -> l8 : pos^0'=1+pos^0, [ pos^0<=1 && 1<=xx^0 ], cost: 1 18: l11 -> l9 : [ 1<=pos^0 ], cost: 1 19: l11 -> l8 : pos^0'=1+pos^0, [ pos^0<=0 && xx^0<=0 ], cost: 1 20: l12 -> l8 : z^0'=-1+z^0, [ 1<=z^0 ], cost: 1 21: l12 -> l11 : [ z^0<=0 ], cost: 1 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l15 28: l1 -> l8 : xx^0'=xx^post_24, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 ], cost: 3 29: l1 -> l11 : xx^0'=xx^post_24, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 ], cost: 3 1: l2 -> l3 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_2, [ 3<=pos^0 && 0<=z^post_2 ], cost: 1 2: l2 -> l3 : pos^0'=1+pos^0, [ pos^0<=2 && yy^0<=0 ], cost: 1 5: l3 -> l1 : [ -yy^0+xx^0==0 ], cost: 1 32: l3 -> l1 : K^0'=-1+K^0, [ 1+yy^0<=xx^0 ], cost: 2 33: l3 -> l1 : K^0'=-1+K^0, [ 1+xx^0<=yy^0 ], cost: 2 9: l5 -> l3 : pos^0'=1+pos^0, [ pos^0<=0 && yy^0<=0 ], cost: 1 34: l5 -> l2 : [ 2<=pos^0 ], cost: 2 35: l5 -> l3 : pos^0'=1+pos^0, [ 1<=pos^0 && pos^0<=1 && 1<=yy^0 ], cost: 2 12: l7 -> l8 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_13, [ 3<=pos^0 && 0<=z^post_13 ], cost: 1 13: l7 -> l8 : pos^0'=1+pos^0, [ pos^0<=2 && xx^0<=0 ], cost: 1 30: l8 -> l3 : yy^0'=yy^post_17, z^0'=-1+z^0, [ 0<=yy^post_17 && yy^post_17<=1 && 1<=z^0 ], cost: 2 31: l8 -> l5 : yy^0'=yy^post_17, [ 0<=yy^post_17 && yy^post_17<=1 && z^0<=0 ], cost: 2 19: l11 -> l8 : pos^0'=1+pos^0, [ pos^0<=0 && xx^0<=0 ], cost: 1 36: l11 -> l7 : [ 2<=pos^0 ], cost: 2 37: l11 -> l8 : pos^0'=1+pos^0, [ 1<=pos^0 && pos^0<=1 && 1<=xx^0 ], cost: 2 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l15 28: l1 -> l8 : xx^0'=xx^post_24, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 ], cost: 3 38: l1 -> l8 : pos^0'=1+pos^0, xx^0'=xx^post_24, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && pos^0<=0 && xx^post_24<=0 ], cost: 4 39: l1 -> l7 : xx^0'=xx^post_24, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 2<=pos^0 ], cost: 5 40: l1 -> l8 : pos^0'=1+pos^0, xx^0'=xx^post_24, [ 1<=K^0 && xx^post_24<=1 && z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=xx^post_24 ], cost: 5 1: l2 -> l3 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_2, [ 3<=pos^0 && 0<=z^post_2 ], cost: 1 2: l2 -> l3 : pos^0'=1+pos^0, [ pos^0<=2 && yy^0<=0 ], cost: 1 5: l3 -> l1 : [ -yy^0+xx^0==0 ], cost: 1 32: l3 -> l1 : K^0'=-1+K^0, [ 1+yy^0<=xx^0 ], cost: 2 33: l3 -> l1 : K^0'=-1+K^0, [ 1+xx^0<=yy^0 ], cost: 2 12: l7 -> l8 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_13, [ 3<=pos^0 && 0<=z^post_13 ], cost: 1 13: l7 -> l8 : pos^0'=1+pos^0, [ pos^0<=2 && xx^0<=0 ], cost: 1 30: l8 -> l3 : yy^0'=yy^post_17, z^0'=-1+z^0, [ 0<=yy^post_17 && yy^post_17<=1 && 1<=z^0 ], cost: 2 41: l8 -> l3 : pos^0'=1+pos^0, yy^0'=yy^post_17, [ 0<=yy^post_17 && z^0<=0 && pos^0<=0 && yy^post_17<=0 ], cost: 3 42: l8 -> l2 : yy^0'=yy^post_17, [ 0<=yy^post_17 && yy^post_17<=1 && z^0<=0 && 2<=pos^0 ], cost: 4 43: l8 -> l3 : pos^0'=1+pos^0, yy^0'=yy^post_17, [ yy^post_17<=1 && z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=yy^post_17 ], cost: 4 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l15 46: l1 -> l3 : xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 ], cost: 5 47: l1 -> l3 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && -1+z^0<=0 && pos^0<=0 && yy^post_17<=0 ], cost: 6 48: l1 -> l2 : xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && yy^post_17<=1 && -1+z^0<=0 && 2<=pos^0 ], cost: 7 49: l1 -> l3 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && yy^post_17<=1 && -1+z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=yy^post_17 ], cost: 7 50: l1 -> l3 : pos^0'=2+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && xx^post_24<=0 && 0<=yy^post_17 && 1+pos^0<=0 && yy^post_17<=0 ], cost: 7 51: l1 -> l3 : pos^0'=2+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && pos^0<=0 && xx^post_24<=0 && yy^post_17<=1 && 1<=1+pos^0 && 1<=yy^post_17 ], cost: 8 52: l1 -> l2 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && xx^post_24<=1 && z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=xx^post_24 && 0<=yy^post_17 && yy^post_17<=1 ], cost: 9 53: l1 -> l3 : next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 ], cost: 8 54: l1 -> l3 : next^0'=1+next^0, pos^0'=1, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=z^post_13 && 0<=yy^post_17 && z^post_13<=0 && yy^post_17<=0 ], cost: 9 55: l1 -> l2 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && 2<=pos^0 && pos^0<=2 && xx^post_24<=0 && 0<=yy^post_17 && yy^post_17<=1 ], cost: 10 1: l2 -> l3 : next^0'=1+next^0, pos^0'=0, z^0'=z^post_2, [ 3<=pos^0 && 0<=z^post_2 ], cost: 1 2: l2 -> l3 : pos^0'=1+pos^0, [ pos^0<=2 && yy^0<=0 ], cost: 1 5: l3 -> l1 : [ -yy^0+xx^0==0 ], cost: 1 32: l3 -> l1 : K^0'=-1+K^0, [ 1+yy^0<=xx^0 ], cost: 2 33: l3 -> l1 : K^0'=-1+K^0, [ 1+xx^0<=yy^0 ], cost: 2 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l15 60: l1 -> l1 : xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && xx^post_24-yy^post_17==0 ], cost: 6 61: l1 -> l1 : K^0'=-1+K^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 1+yy^post_17<=xx^post_24 ], cost: 7 62: l1 -> l1 : K^0'=-1+K^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 1+xx^post_24<=yy^post_17 ], cost: 7 63: l1 -> l1 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && -1+z^0<=0 && pos^0<=0 && yy^post_17<=0 && xx^post_24-yy^post_17==0 ], cost: 7 64: l1 -> l1 : K^0'=-1+K^0, pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && -1+z^0<=0 && pos^0<=0 && yy^post_17<=0 && 1+yy^post_17<=xx^post_24 ], cost: 8 65: l1 -> l1 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && yy^post_17<=1 && -1+z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=yy^post_17 && xx^post_24-yy^post_17==0 ], cost: 8 66: l1 -> l1 : K^0'=-1+K^0, pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && yy^post_17<=1 && -1+z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=yy^post_17 && 1+xx^post_24<=yy^post_17 ], cost: 9 67: l1 -> l1 : pos^0'=2+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && xx^post_24<=0 && 0<=yy^post_17 && 1+pos^0<=0 && yy^post_17<=0 && xx^post_24-yy^post_17==0 ], cost: 8 68: l1 -> l1 : K^0'=-1+K^0, pos^0'=2+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && pos^0<=0 && xx^post_24<=0 && yy^post_17<=1 && 1<=1+pos^0 && 1<=yy^post_17 && 1+xx^post_24<=yy^post_17 ], cost: 10 69: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && xx^post_24-yy^post_17==0 ], cost: 9 70: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && 1+yy^post_17<=xx^post_24 ], cost: 10 71: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && 1+xx^post_24<=yy^post_17 ], cost: 10 72: l1 -> l1 : next^0'=1+next^0, pos^0'=1, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=z^post_13 && 0<=yy^post_17 && z^post_13<=0 && yy^post_17<=0 && xx^post_24-yy^post_17==0 ], cost: 10 73: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=1, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=z^post_13 && 0<=yy^post_17 && z^post_13<=0 && yy^post_17<=0 && 1+yy^post_17<=xx^post_24 ], cost: 11 74: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && yy^post_17<=1 && -1+z^0<=0 && 3<=pos^0 && 0<=z^post_2 && xx^post_24-yy^post_17==0 ], cost: 9 75: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && yy^post_17<=1 && -1+z^0<=0 && 3<=pos^0 && 0<=z^post_2 && 1+yy^post_17<=xx^post_24 ], cost: 10 76: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && yy^post_17<=1 && -1+z^0<=0 && 3<=pos^0 && 0<=z^post_2 && 1+xx^post_24<=yy^post_17 ], cost: 10 77: l1 -> l1 : pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && -1+z^0<=0 && 2<=pos^0 && pos^0<=2 && yy^post_17<=0 && xx^post_24-yy^post_17==0 ], cost: 9 78: l1 -> l1 : K^0'=-1+K^0, pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1<=z^0 && 0<=yy^post_17 && -1+z^0<=0 && 2<=pos^0 && pos^0<=2 && yy^post_17<=0 && 1+yy^post_17<=xx^post_24 ], cost: 10 79: l1 -> l1 : K^0'=-1+K^0, pos^0'=2+pos^0, xx^0'=xx^post_24, yy^0'=yy^post_17, [ 1<=K^0 && xx^post_24<=1 && z^0<=0 && 1<=pos^0 && pos^0<=1 && 1<=xx^post_24 && 0<=yy^post_17 && yy^post_17<=0 && 1+yy^post_17<=xx^post_24 ], cost: 12 80: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && 2<=pos^0 && pos^0<=2 && xx^post_24<=0 && 0<=yy^post_17 && yy^post_17<=1 && 0<=z^post_2 && xx^post_24-yy^post_17==0 ], cost: 12 81: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && z^0<=0 && 2<=pos^0 && pos^0<=2 && xx^post_24<=0 && 0<=yy^post_17 && yy^post_17<=1 && 0<=z^post_2 && 1+xx^post_24<=yy^post_17 ], cost: 13 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 60: l1 -> l1 : xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 ], cost: 6 61: l1 -> l1 : K^0'=-1+K^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 1+yy^post_17<=xx^post_24 ], cost: 7 62: l1 -> l1 : K^0'=-1+K^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2+z^0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 1+xx^post_24<=yy^post_17 ], cost: 7 63: l1 -> l1 : pos^0'=1+pos^0, xx^0'=0, yy^0'=0, z^0'=-1+z^0, [ 1<=K^0 && 1-z^0==0 && pos^0<=0 ], cost: 7 64: l1 -> l1 : K^0'=-1+K^0, pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=0, z^0'=-1+z^0, [ 1<=K^0 && xx^post_24<=1 && 1-z^0==0 && pos^0<=0 && 1<=xx^post_24 ], cost: 8 65: l1 -> l1 : pos^0'=1+pos^0, xx^0'=1, yy^0'=1, z^0'=-1+z^0, [ 1<=K^0 && 1-z^0==0 && 1-pos^0==0 ], cost: 8 66: l1 -> l1 : K^0'=-1+K^0, pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=1, z^0'=-1+z^0, [ 1<=K^0 && 0<=xx^post_24 && 1-z^0==0 && 1-pos^0==0 && 1+xx^post_24<=1 ], cost: 9 67: l1 -> l1 : pos^0'=2+pos^0, xx^0'=0, yy^0'=0, [ 1<=K^0 && z^0<=0 && 1+pos^0<=0 ], cost: 8 68: l1 -> l1 : K^0'=-1+K^0, pos^0'=2+pos^0, xx^0'=0, yy^0'=1, [ 1<=K^0 && z^0<=0 && pos^0==0 ], cost: 10 69: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && z^0<=0 && 3<=pos^0 && 1<=z^post_13 ], cost: 9 70: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && 1+yy^post_17<=xx^post_24 ], cost: 10 71: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && 1+xx^post_24<=yy^post_17 ], cost: 10 72: l1 -> l1 : next^0'=1+next^0, pos^0'=1, xx^0'=0, yy^0'=0, z^0'=0, [ 1<=K^0 && z^0<=0 && 3<=pos^0 ], cost: 10 73: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=1, xx^0'=xx^post_24, yy^0'=0, z^0'=0, [ 1<=K^0 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 1<=xx^post_24 ], cost: 11 74: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && 1-z^0==0 && 3<=pos^0 && 0<=z^post_2 ], cost: 9 75: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1-z^0==0 && 0<=yy^post_17 && yy^post_17<=1 && 3<=pos^0 && 0<=z^post_2 && 1+yy^post_17<=xx^post_24 ], cost: 10 76: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1-z^0==0 && 0<=yy^post_17 && yy^post_17<=1 && 3<=pos^0 && 0<=z^post_2 && 1+xx^post_24<=yy^post_17 ], cost: 10 77: l1 -> l1 : pos^0'=1+pos^0, xx^0'=0, yy^0'=0, z^0'=-1+z^0, [ 1<=K^0 && 1-z^0==0 && 2-pos^0==0 ], cost: 9 78: l1 -> l1 : K^0'=-1+K^0, pos^0'=1+pos^0, xx^0'=xx^post_24, yy^0'=0, z^0'=-1+z^0, [ 1<=K^0 && xx^post_24<=1 && 1-z^0==0 && 2-pos^0==0 && 1<=xx^post_24 ], cost: 10 79: l1 -> l1 : K^0'=-1+K^0, pos^0'=2+pos^0, xx^0'=1, yy^0'=0, [ 1<=K^0 && z^0<=0 && 1-pos^0==0 ], cost: 12 80: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_2, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && 0<=z^post_2 ], cost: 12 81: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=0, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && yy^post_17<=1 && 0<=z^post_2 && 1<=yy^post_17 ], cost: 13 Accelerated rule 60 with metering function meter (where 2*meter==-1+z^0), yielding the new rule 82. Accelerated rule 61 with metering function meter_1 (where 2*meter_1==-1+z^0) (after adding K^0>=z^0), yielding the new rule 83. Accelerated rule 62 with metering function meter_2 (where 2*meter_2==-1+z^0) (after adding K^0>=z^0), yielding the new rule 84. Accelerated rule 63 with metering function -1+z^0, yielding the new rule 85. Accelerated rule 64 with metering function -1+z^0, yielding the new rule 86. Accelerated rule 65 with metering function meter_3 (where 2*meter_3==z^0-pos^0), yielding the new rule 87. Accelerated rule 66 with metering function meter_4 (where 2*meter_4==z^0-pos^0), yielding the new rule 88. Accelerated rule 67 with metering function meter_5 (where 2*meter_5==-pos^0), yielding the new rule 89. Accelerated rule 68 with metering function meter_6 (where 2*meter_6==-pos^0), yielding the new rule 90. Found no metering function for rule 69. Found no metering function for rule 70. Found no metering function for rule 71. Found no metering function for rule 72. Found no metering function for rule 73. During metering: Instantiating temporary variables by {z^post_2==0} Accelerated rule 74 with metering function -1+z^0, yielding the new rule 91. During metering: Instantiating temporary variables by {z^post_2==0} Accelerated rule 75 with metering function -1+z^0, yielding the new rule 92. During metering: Instantiating temporary variables by {z^post_2==0} Accelerated rule 76 with metering function -1+z^0, yielding the new rule 93. Accelerated rule 77 with metering function meter_7 (where 2*meter_7==1+z^0-pos^0), yielding the new rule 94. Accelerated rule 78 with metering function meter_8 (where 2*meter_8==1+z^0-pos^0), yielding the new rule 95. Accelerated rule 79 with metering function meter_9 (where 2*meter_9==1-pos^0), yielding the new rule 96. Accelerated rule 80 with metering function meter_10 (where 2*meter_10==-2+pos^0), yielding the new rule 97. Accelerated rule 81 with metering function meter_11 (where 2*meter_11==-2+pos^0), yielding the new rule 98. During metering: Instantiating temporary variables by {meter==1} During metering: Instantiating temporary variables by {meter==1} During metering: Instantiating temporary variables by {meter==1} During metering: Instantiating temporary variables by {meter==1} Nested simple loops 65 (outer loop) and 82 (inner loop) with metering function 1-pos^0, resulting in the new rules: 99. Nested simple loops 66 (outer loop) and 82 (inner loop) with metering function 1-pos^0, resulting in the new rules: 100. During metering: Instantiating temporary variables by {meter==1,z^post_2==0} During metering: Instantiating temporary variables by {meter==1,z^post_2==0} During metering: Instantiating temporary variables by {meter==1,z^post_2==0} Nested simple loops 77 (outer loop) and 82 (inner loop) with metering function 2-pos^0, resulting in the new rules: 101. Nested simple loops 78 (outer loop) and 82 (inner loop) with metering function 2-pos^0, resulting in the new rules: 102. Nested simple loops 80 (outer loop) and 82 (inner loop) with metering function meter_19 (where 2*meter_19==-2+pos^0), resulting in the new rules: 103. Nested simple loops 81 (outer loop) and 82 (inner loop) with metering function meter_20 (where 2*meter_20==-2+pos^0), resulting in the new rules: 104. During metering: Instantiating temporary variables by {meter_1==1} During metering: Instantiating temporary variables by {meter_1==1} During metering: Instantiating temporary variables by {meter_1==1} Nested simple loops 65 (outer loop) and 83 (inner loop) with metering function 1-pos^0, resulting in the new rules: 105. During metering: Instantiating temporary variables by {z^post_2==0,meter_1==1} During metering: Instantiating temporary variables by {z^post_2==0,meter_1==1} Nested simple loops 77 (outer loop) and 83 (inner loop) with metering function 2-pos^0, resulting in the new rules: 106. Nested simple loops 78 (outer loop) and 83 (inner loop) with metering function 2-pos^0, resulting in the new rules: 107. Nested simple loops 80 (outer loop) and 83 (inner loop) with metering function meter_26 (where 2*meter_26==-2+pos^0), resulting in the new rules: 108. During metering: Instantiating temporary variables by {meter_2==1} During metering: Instantiating temporary variables by {meter_2==1} Nested simple loops 65 (outer loop) and 84 (inner loop) with metering function 1-pos^0, resulting in the new rules: 109. Nested simple loops 66 (outer loop) and 84 (inner loop) with metering function 1-pos^0, resulting in the new rules: 110. During metering: Instantiating temporary variables by {z^post_2==0,meter_2==1} During metering: Instantiating temporary variables by {z^post_2==0,meter_2==1} Nested simple loops 77 (outer loop) and 84 (inner loop) with metering function 2-pos^0, resulting in the new rules: 111. Nested simple loops 80 (outer loop) and 84 (inner loop) with metering function meter_31 (where 2*meter_31==-2+pos^0), resulting in the new rules: 112. Nested simple loops 81 (outer loop) and 84 (inner loop) with metering function meter_32 (where 2*meter_32==-2+pos^0), resulting in the new rules: 113. Nested simple loops 60 (outer loop) and 89 (inner loop) with metering function meter_33 (where 2*meter_33==-2+z^0), resulting in the new rules: 114. Nested simple loops 61 (outer loop) and 89 (inner loop) with metering function meter_34 (where 2*meter_34==-2+z^0), resulting in the new rules: 115. Nested simple loops 62 (outer loop) and 89 (inner loop) with metering function meter_35 (where 2*meter_35==-2+z^0), resulting in the new rules: 116. Nested simple loops 63 (outer loop) and 89 (inner loop) with metering function -1+z^0, resulting in the new rules: 117. Nested simple loops 64 (outer loop) and 89 (inner loop) with metering function -1+z^0, resulting in the new rules: 118. During metering: Instantiating temporary variables by {meter_5==1} Removing the simple loops: 60 61 62 63 64 65 66 67 68 74 75 76 77 78 79 80 81. Accelerated all simple loops using metering functions (where possible): Start location: l15 69: l1 -> l1 : next^0'=1+next^0, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && z^0<=0 && 3<=pos^0 && 1<=z^post_13 ], cost: 9 70: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && 1+yy^post_17<=xx^post_24 ], cost: 10 71: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-1+z^post_13, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=z^post_13 && 1+xx^post_24<=yy^post_17 ], cost: 10 72: l1 -> l1 : next^0'=1+next^0, pos^0'=1, xx^0'=0, yy^0'=0, z^0'=0, [ 1<=K^0 && z^0<=0 && 3<=pos^0 ], cost: 10 73: l1 -> l1 : K^0'=-1+K^0, next^0'=1+next^0, pos^0'=1, xx^0'=xx^post_24, yy^0'=0, z^0'=0, [ 1<=K^0 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 1<=xx^post_24 ], cost: 11 82: l1 -> l1 : xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=-2*meter+z^0, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 2*meter==-1+z^0 && meter>=1 ], cost: 6*meter 83: l1 -> l1 : K^0'=K^0-meter_1, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^0-2*meter_1, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 1+yy^post_17<=xx^post_24 && K^0>=z^0 && 2*meter_1==-1+z^0 && meter_1>=1 ], cost: 7*meter_1 84: l1 -> l1 : K^0'=K^0-meter_2, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^0-2*meter_2, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=-1+z^0 && 1+xx^post_24<=yy^post_17 && K^0>=z^0 && 2*meter_2==-1+z^0 && meter_2>=1 ], cost: 7*meter_2 85: l1 -> l1 : pos^0'=-1+z^0+pos^0, xx^0'=0, yy^0'=0, z^0'=1, [ 1<=K^0 && 1-z^0==0 && pos^0<=0 && -1+z^0>=1 ], cost: -7+7*z^0 86: l1 -> l1 : K^0'=1-z^0+K^0, pos^0'=-1+z^0+pos^0, xx^0'=xx^post_24, yy^0'=0, z^0'=1, [ 1<=K^0 && xx^post_24<=1 && 1-z^0==0 && pos^0<=0 && 1<=xx^post_24 && -1+z^0>=1 ], cost: -8+8*z^0 87: l1 -> l1 : pos^0'=meter_3+pos^0, xx^0'=1, yy^0'=1, z^0'=-meter_3+z^0, [ 1<=K^0 && 1-z^0==0 && 1-pos^0==0 && 2*meter_3==z^0-pos^0 && meter_3>=1 ], cost: 8*meter_3 88: l1 -> l1 : K^0'=K^0-meter_4, pos^0'=pos^0+meter_4, xx^0'=xx^post_24, yy^0'=1, z^0'=z^0-meter_4, [ 1<=K^0 && 0<=xx^post_24 && 1-z^0==0 && 1-pos^0==0 && 1+xx^post_24<=1 && 2*meter_4==z^0-pos^0 && meter_4>=1 ], cost: 9*meter_4 89: l1 -> l1 : pos^0'=2*meter_5+pos^0, xx^0'=0, yy^0'=0, [ 1<=K^0 && z^0<=0 && 1+pos^0<=0 && 2*meter_5==-pos^0 && meter_5>=1 ], cost: 8*meter_5 90: l1 -> l1 : K^0'=K^0-meter_6, pos^0'=pos^0+2*meter_6, xx^0'=0, yy^0'=1, [ 1<=K^0 && z^0<=0 && pos^0==0 && 2*meter_6==-pos^0 && meter_6>=1 ], cost: 10*meter_6 91: l1 -> l1 : next^0'=-1+next^0+z^0, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=0, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && 1-z^0==0 && 3<=pos^0 && -1+z^0>=1 ], cost: -9+9*z^0 92: l1 -> l1 : K^0'=1-z^0+K^0, next^0'=-1+next^0+z^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1-z^0==0 && 0<=yy^post_17 && yy^post_17<=1 && 3<=pos^0 && 1+yy^post_17<=xx^post_24 && -1+z^0>=1 ], cost: -10+10*z^0 93: l1 -> l1 : K^0'=1-z^0+K^0, next^0'=-1+next^0+z^0, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=0, [ 1<=K^0 && 0<=xx^post_24 && xx^post_24<=1 && 1-z^0==0 && 0<=yy^post_17 && yy^post_17<=1 && 3<=pos^0 && 1+xx^post_24<=yy^post_17 && -1+z^0>=1 ], cost: -10+10*z^0 94: l1 -> l1 : pos^0'=meter_7+pos^0, xx^0'=0, yy^0'=0, z^0'=-meter_7+z^0, [ 1<=K^0 && 1-z^0==0 && 2-pos^0==0 && 2*meter_7==1+z^0-pos^0 && meter_7>=1 ], cost: 9*meter_7 95: l1 -> l1 : K^0'=K^0-meter_8, pos^0'=pos^0+meter_8, xx^0'=xx^post_24, yy^0'=0, z^0'=z^0-meter_8, [ 1<=K^0 && xx^post_24<=1 && 1-z^0==0 && 2-pos^0==0 && 1<=xx^post_24 && 2*meter_8==1+z^0-pos^0 && meter_8>=1 ], cost: 10*meter_8 96: l1 -> l1 : K^0'=K^0-meter_9, pos^0'=pos^0+2*meter_9, xx^0'=1, yy^0'=0, [ 1<=K^0 && z^0<=0 && 1-pos^0==0 && 2*meter_9==1-pos^0 && meter_9>=1 ], cost: 12*meter_9 97: l1 -> l1 : next^0'=next^0+meter_10, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_2, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && 0<=z^post_2 && 2*meter_10==-2+pos^0 && meter_10>=1 ], cost: 12*meter_10 98: l1 -> l1 : K^0'=K^0-meter_11, next^0'=next^0+meter_11, pos^0'=0, xx^0'=0, yy^0'=yy^post_17, z^0'=z^post_2, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && yy^post_17<=1 && 0<=z^post_2 && 1<=yy^post_17 && 2*meter_11==-2+pos^0 && meter_11>=1 ], cost: 13*meter_11 99: l1 -> l1 : pos^0'=1, xx^0'=1, yy^0'=1, z^0'=-1+2*meter*(-1+pos^0)+z^0+pos^0, [ 1<=K^0 && 1<=-1+z^0 && 2*meter==-1+z^0 && meter>=1 && 1-pos^0==0 && 1-pos^0>=1 ], cost: 8-6*meter*(-1+pos^0)-8*pos^0 100: l1 -> l1 : K^0'=-1+pos^0+K^0, pos^0'=1, xx^0'=0, yy^0'=1, z^0'=-1+2*meter*(-1+pos^0)+z^0+pos^0, [ 1<=K^0 && 1<=-1+z^0 && 2*meter==-1+z^0 && meter>=1 && 1-pos^0==0 && 1-pos^0>=1 ], cost: 9-6*meter*(-1+pos^0)-9*pos^0 101: l1 -> l1 : pos^0'=2, xx^0'=0, yy^0'=0, z^0'=-2+z^0+pos^0+2*meter*(-2+pos^0), [ 1<=K^0 && 1<=-1+z^0 && 2*meter==-1+z^0 && meter>=1 && 2-pos^0==0 && 2-pos^0>=1 ], cost: 18-9*pos^0-6*meter*(-2+pos^0) 102: l1 -> l1 : K^0'=-2+pos^0+K^0, pos^0'=2, xx^0'=1, yy^0'=0, z^0'=-2+z^0+pos^0+2*meter*(-2+pos^0), [ 1<=K^0 && 1<=-1+z^0 && 2*meter==-1+z^0 && meter>=1 && 2-pos^0==0 && 2-pos^0>=1 ], cost: 20-10*pos^0-6*meter*(-2+pos^0) 103: l1 -> l1 : next^0'=next^0+meter_19, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=1, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter && meter>=1 && 2*meter_19==-2+pos^0 && meter_19>=1 ], cost: 6*meter*meter_19+12*meter_19 104: l1 -> l1 : K^0'=-meter_20+K^0, next^0'=meter_20+next^0, pos^0'=0, xx^0'=1, yy^0'=1, z^0'=1, [ z^0<=0 && 2-pos^0==0 && 1<=-1+K^0 && 1<=2*meter && meter>=1 && 2*meter_20==-2+pos^0 && meter_20>=1 ], cost: 13*meter_20+6*meter_20*meter 105: l1 -> l1 : K^0'=K^0+(-1+pos^0)*meter_1, pos^0'=1, xx^0'=1, yy^0'=1, z^0'=-1+z^0+pos^0+2*(-1+pos^0)*meter_1, [ 1<=K^0 && 1<=-1+z^0 && K^0>=z^0 && 2*meter_1==-1+z^0 && meter_1>=1 && 1<=K^0-meter_1 && 1-pos^0==0 && 1-pos^0>=1 ], cost: 8-8*pos^0-7*(-1+pos^0)*meter_1 106: l1 -> l1 : K^0'=(-2+pos^0)*meter_1+K^0, pos^0'=2, xx^0'=0, yy^0'=0, z^0'=-2+2*(-2+pos^0)*meter_1+z^0+pos^0, [ 1<=K^0 && 1<=-1+z^0 && K^0>=z^0 && 2*meter_1==-1+z^0 && meter_1>=1 && 1<=K^0-meter_1 && 2-pos^0==0 && 2-pos^0>=1 ], cost: 18-7*(-2+pos^0)*meter_1-9*pos^0 107: l1 -> l1 : K^0'=-2+(-2+pos^0)*meter_1+pos^0+K^0, pos^0'=2, xx^0'=1, yy^0'=0, z^0'=-2+2*(-2+pos^0)*meter_1+z^0+pos^0, [ 1<=K^0 && 1<=-1+z^0 && K^0>=z^0 && 2*meter_1==-1+z^0 && meter_1>=1 && 1<=K^0-meter_1 && 2-pos^0==0 && 2-pos^0>=1 ], cost: 20-7*(-2+pos^0)*meter_1-10*pos^0 108: l1 -> l1 : K^0'=K^0-meter_26*meter_1, next^0'=next^0+meter_26, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_1 && 1+yy^post_17<=xx^post_24 && K^0>=1+2*meter_1 && meter_1>=1 && 2*meter_26==-2+pos^0 && meter_26>=1 ], cost: 12*meter_26+7*meter_26*meter_1 109: l1 -> l1 : K^0'=K^0+(-1+pos^0)*meter_2, pos^0'=1, xx^0'=1, yy^0'=1, z^0'=-1+z^0+pos^0+2*(-1+pos^0)*meter_2, [ 1<=K^0 && 1<=-1+z^0 && K^0>=z^0 && 2*meter_2==-1+z^0 && meter_2>=1 && 1<=K^0-meter_2 && 1-pos^0==0 && 1-pos^0>=1 ], cost: 8-8*pos^0-7*(-1+pos^0)*meter_2 110: l1 -> l1 : K^0'=-1+pos^0+K^0+(-1+pos^0)*meter_2, pos^0'=1, xx^0'=0, yy^0'=1, z^0'=-1+z^0+pos^0+2*(-1+pos^0)*meter_2, [ 1<=K^0 && 1<=-1+z^0 && K^0>=z^0 && 2*meter_2==-1+z^0 && meter_2>=1 && 1<=K^0-meter_2 && 1-pos^0==0 && 1-pos^0>=1 ], cost: 9-9*pos^0-7*(-1+pos^0)*meter_2 111: l1 -> l1 : K^0'=(-2+pos^0)*meter_2+K^0, pos^0'=2, xx^0'=0, yy^0'=0, z^0'=-2+z^0+pos^0+2*(-2+pos^0)*meter_2, [ 1<=K^0 && 1<=-1+z^0 && K^0>=z^0 && 2*meter_2==-1+z^0 && meter_2>=1 && 1<=K^0-meter_2 && 2-pos^0==0 && 2-pos^0>=1 ], cost: 18-9*pos^0-7*(-2+pos^0)*meter_2 112: l1 -> l1 : K^0'=K^0-meter_2*meter_31, next^0'=next^0+meter_31, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^0 && z^0<=0 && 2-pos^0==0 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_2 && 1+xx^post_24<=yy^post_17 && K^0>=1+2*meter_2 && meter_2>=1 && 2*meter_31==-2+pos^0 && meter_31>=1 ], cost: 7*meter_2*meter_31+12*meter_31 113: l1 -> l1 : K^0'=-meter_32-meter_32*meter_2+K^0, next^0'=next^0+meter_32, pos^0'=0, xx^0'=xx^post_24, yy^0'=1, z^0'=1, [ z^0<=0 && 2-pos^0==0 && 1<=-1+K^0 && 0<=xx^post_24 && 1<=2*meter_2 && 1+xx^post_24<=1 && -1+K^0>=1+2*meter_2 && meter_2>=1 && 2*meter_32==-2+pos^0 && meter_32>=1 ], cost: 13*meter_32+7*meter_32*meter_2 114: l1 -> l1 : pos^0'=2*meter_5*meter_33+pos^0, xx^0'=0, yy^0'=0, z^0'=z^0-2*meter_33, [ 1<=K^0 && 2-z^0==0 && 1+pos^0<=0 && 2*meter_5==-pos^0 && meter_5>=1 && 2*meter_33==-2+z^0 && meter_33>=1 ], cost: 8*meter_5*meter_33+6*meter_33 115: l1 -> l1 : K^0'=-meter_34+K^0, pos^0'=pos^0+2*meter_34*meter_5, xx^0'=0, yy^0'=0, z^0'=-2*meter_34+z^0, [ 2-z^0==0 && 1<=-1+K^0 && 1+pos^0<=0 && 2*meter_5==-pos^0 && meter_5>=1 && 2*meter_34==-2+z^0 && meter_34>=1 ], cost: 7*meter_34+8*meter_34*meter_5 116: l1 -> l1 : K^0'=K^0-meter_35, pos^0'=2*meter_5*meter_35+pos^0, xx^0'=0, yy^0'=0, z^0'=z^0-2*meter_35, [ 2-z^0==0 && 1<=-1+K^0 && 1+pos^0<=0 && 2*meter_5==-pos^0 && meter_5>=1 && 2*meter_35==-2+z^0 && meter_35>=1 ], cost: 8*meter_5*meter_35+7*meter_35 117: l1 -> l1 : pos^0'=-1+z^0+pos^0+2*(-1+z^0)*meter_5, xx^0'=0, yy^0'=0, z^0'=1, [ 1<=K^0 && 1-z^0==0 && 2+pos^0<=0 && 2*meter_5==-1-pos^0 && meter_5>=1 && -1+z^0>=1 ], cost: -7+7*z^0+8*(-1+z^0)*meter_5 118: l1 -> l1 : K^0'=1-z^0+K^0, pos^0'=-1+z^0+pos^0+2*(-1+z^0)*meter_5, xx^0'=0, yy^0'=0, z^0'=1, [ 1-z^0==0 && 1<=-1+K^0 && 2+pos^0<=0 && 2*meter_5==-1-pos^0 && meter_5>=1 && -1+z^0>=1 ], cost: -8+8*z^0+8*(-1+z^0)*meter_5 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: l15 26: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=K^post_25 ], cost: 2 119: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter && meter>=1 ], cost: 2+6*meter 120: l15 -> l1 : K^0'=-meter_1+K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_1 && 1+yy^post_17<=xx^post_24 && K^post_25>=1+2*meter_1 && meter_1>=1 ], cost: 2+7*meter_1 121: l15 -> l1 : K^0'=K^post_25-meter_2, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_2 && 1+xx^post_24<=yy^post_17 && K^post_25>=1+2*meter_2 && meter_2>=1 ], cost: 2+7*meter_2 Removed unreachable locations (and leaf rules with constant cost): Start location: l15 119: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter && meter>=1 ], cost: 2+6*meter 120: l15 -> l1 : K^0'=-meter_1+K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_1 && 1+yy^post_17<=xx^post_24 && K^post_25>=1+2*meter_1 && meter_1>=1 ], cost: 2+7*meter_1 121: l15 -> l1 : K^0'=K^post_25-meter_2, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_2 && 1+xx^post_24<=yy^post_17 && K^post_25>=1+2*meter_2 && meter_2>=1 ], cost: 2+7*meter_2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l15 119: l15 -> l1 : K^0'=K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter && meter>=1 ], cost: 2+6*meter 120: l15 -> l1 : K^0'=-meter_1+K^post_25, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_1 && 1+yy^post_17<=xx^post_24 && K^post_25>=1+2*meter_1 && meter_1>=1 ], cost: 2+7*meter_1 121: l15 -> l1 : K^0'=K^post_25-meter_2, N^0'=K^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=1, [ 1<=K^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter_2 && 1+xx^post_24<=yy^post_17 && K^post_25>=1+2*meter_2 && meter_2>=1 ], cost: 2+7*meter_2 Computing asymptotic complexity for rule 119 Solved the limit problem by the following transformations: Created initial limit problem: 2*meter (+/+!), 2+6*meter (+), 2-yy^post_17 (+/+!), K^post_25 (+/+!), 1+yy^post_17 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,yy^post_17==0,K^post_25==1} resulting limit problem: [solved] Solution: meter / n yy^post_17 / 0 K^post_25 / 1 Resulting cost 2+6*n has complexity: Unbounded Found new complexity Unbounded. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Unbounded Cpx degree: Unbounded Solved cost: 2+6*n Rule cost: 2+6*meter Rule guard: [ 1<=K^post_25 && 0<=yy^post_17 && yy^post_17<=1 && 1<=2*meter ] WORST_CASE(INF,?)