WORST_CASE(Omega(1),?) ### 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 : [ xx^0-yy^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'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^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 : [ xx^0-yy^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'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^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 : [ xx^0-yy^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'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^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 : [ xx^0-yy^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'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^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 : [ xx^0-yy^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'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^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'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^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 backward acceleration, yielding the new rule 82. Accelerated rule 61 with backward acceleration, yielding the new rule 83. Accelerated rule 62 with backward acceleration, yielding the new rule 84. Failed to prove monotonicity of the guard of rule 63. Failed to prove monotonicity of the guard of rule 64. Failed to prove monotonicity of the guard of rule 65. Failed to prove monotonicity of the guard of rule 66. Accelerated rule 67 with backward acceleration, yielding the new rule 85. Failed to prove monotonicity of the guard of rule 68. Failed to prove monotonicity of the guard of rule 69. Failed to prove monotonicity of the guard of rule 70. Failed to prove monotonicity of the guard of rule 71. Failed to prove monotonicity of the guard of rule 72. Failed to prove monotonicity of the guard of rule 73. Failed to prove monotonicity of the guard of rule 74. Failed to prove monotonicity of the guard of rule 75. Failed to prove monotonicity of the guard of rule 76. Failed to prove monotonicity of the guard of rule 77. Failed to prove monotonicity of the guard of rule 78. Failed to prove monotonicity of the guard of rule 79. Failed to prove monotonicity of the guard of rule 80. Failed to prove monotonicity of the guard of rule 81. [accelerate] Nesting with 22 inner and 22 outer candidates Nested simple loops 80 (outer loop) and 68 (inner loop) with Rule(1 | z^0<=0, 2-pos^0==0, K^0>=1, 1<=1, | 22*K^0 || 1 | 0=0, 2=next^0+K^0, 3=2, 4=0, 5=1, 6=0, ), resulting in the new rules: 86, 87. Nested simple loops 81 (outer loop) and 68 (inner loop) with Rule(1 | z^0<=0, 2-pos^0==0, k_31>=1, 1<=1-2*k_31+K^0, | 23*k_31 || 1 | 0=-2*k_31+K^0, 2=k_31+next^0, 3=2, 4=0, 5=1, 6=0, ), resulting in the new rules: 88, 89. Nested simple loops 79 (outer loop) and 72 (inner loop) with Rule(1 | z^0<=0, 3<=pos^0, K^0>=1, 1<=1, | 22*K^0 || 1 | 0=0, 2=next^0+K^0, 3=3, 4=1, 5=0, 6=0, ), resulting in the new rules: 90, 91. Nested simple loops 79 (outer loop) and 73 (inner loop) with Rule(1 | z^0<=0, 3<=pos^0, k_33>=1, 1<=1-2*k_33+K^0, | 23*k_33 || 1 | 0=-2*k_33+K^0, 2=next^0+k_33, 3=3, 4=1, 5=0, 6=0, ), resulting in the new rules: 92, 93. Nested simple loops 72 (outer loop) and 79 (inner loop) with Rule(1 | z^0<=0, 1-pos^0==0, -1+K^0>=1, 1<=1, | -22+22*K^0 || 1 | 0=1, 2=-1+next^0+K^0, 3=1, 4=0, 5=0, 6=0, ), resulting in the new rules: 94, 95. Nested simple loops 73 (outer loop) and 79 (inner loop) with Rule(1 | z^0<=0, 1-pos^0==0, k_35>=1, 1<=1-2*k_35+K^0, | 23*k_35 || 1 | 0=-2*k_35+K^0, 2=next^0+k_35, 3=1, 4=1, 5=0, 6=0, ), resulting in the new rules: 96, 97. Nested simple loops 68 (outer loop) and 80 (inner loop) with Rule(1 | z^0<=0, 2-pos^0==0, K^0>=1, 1<=1, | 22*K^0 || 1 | 0=0, 2=next^0+K^0, 3=2, 4=0, 5=1, 6=0, ), resulting in the new rules: 98, 99. Nested simple loops 68 (outer loop) and 81 (inner loop) with Rule(1 | z^0<=0, 2-pos^0==0, k_37>=1, 1<=1+K^0-2*k_37, | 23*k_37 || 1 | 0=K^0-2*k_37, 2=next^0+k_37, 3=2, 4=0, 5=1, 6=0, ), resulting in the new rules: 100, 101. Removing the simple loops: 60 61 62 67 68 72 73 79 80 81. Also removing duplicate rules: 86 87. Accelerated all simple loops using metering functions (where possible): Start location: l15 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 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 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 82: l1 -> l1 : xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=z^0-2*k, [ 1<=K^0 && 0<=yy^post_17 && yy^post_17<=1 && k>=1 && 1<=1+z^0-2*k ], cost: 6*k 83: l1 -> l1 : K^0'=-k_1+K^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^0-2*k_1, [ 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+yy^post_17<=xx^post_24 && k_1>=1 && 1<=1-k_1+K^0 && 1<=1+z^0-2*k_1 ], cost: 7*k_1 84: l1 -> l1 : K^0'=-k_2+K^0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2*k_2+z^0, [ 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+xx^post_24<=yy^post_17 && k_2>=1 && 1<=1-k_2+K^0 && 1<=1-2*k_2+z^0 ], cost: 7*k_2 85: l1 -> l1 : pos^0'=2*k_7+pos^0, xx^0'=0, yy^0'=0, [ 1<=K^0 && z^0<=0 && k_7>=1 && -1+2*k_7+pos^0<=0 ], cost: 8*k_7 88: l1 -> l1 : K^0'=-2*k_31+K^0, next^0'=k_31+next^0, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ z^0<=0 && 2-pos^0==0 && k_31>=1 && 1<=1-2*k_31+K^0 ], cost: 23*k_31 89: l1 -> l1 : K^0'=-1-2*k_31+K^0, next^0'=k_31+next^0, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=K^0 && z^0<=0 && pos^0==0 && -pos^0==0 && k_31>=1 && 1<=-2*k_31+K^0 ], cost: 10+23*k_31 90: l1 -> l1 : K^0'=0, next^0'=next^0+K^0, pos^0'=3, xx^0'=1, yy^0'=0, z^0'=0, [ z^0<=0 && 3<=pos^0 && K^0>=1 ], cost: 22*K^0 91: l1 -> l1 : K^0'=0, next^0'=-1+next^0+K^0, pos^0'=3, xx^0'=1, yy^0'=0, z^0'=0, [ z^0<=0 && 1-pos^0==0 && -1+K^0>=1 ], cost: -10+22*K^0 92: l1 -> l1 : K^0'=-2*k_33+K^0, next^0'=next^0+k_33, pos^0'=3, xx^0'=1, yy^0'=0, z^0'=0, [ z^0<=0 && 3<=pos^0 && k_33>=1 && 1<=1-2*k_33+K^0 ], cost: 23*k_33 93: l1 -> l1 : K^0'=-1-2*k_33+K^0, next^0'=next^0+k_33, pos^0'=3, xx^0'=1, yy^0'=0, z^0'=0, [ 1<=K^0 && z^0<=0 && 1-pos^0==0 && k_33>=1 && 1<=-2*k_33+K^0 ], cost: 12+23*k_33 94: l1 -> l1 : K^0'=1, next^0'=-1+next^0+K^0, pos^0'=1, xx^0'=0, yy^0'=0, z^0'=0, [ z^0<=0 && 1-pos^0==0 && -1+K^0>=1 ], cost: -22+22*K^0 95: l1 -> l1 : K^0'=1, next^0'=next^0+K^0, pos^0'=1, xx^0'=0, yy^0'=0, z^0'=0, [ z^0<=0 && 3<=pos^0 && -1+K^0>=1 ], cost: -12+22*K^0 96: l1 -> l1 : K^0'=-2*k_35+K^0, next^0'=next^0+k_35, pos^0'=1, xx^0'=1, yy^0'=0, z^0'=0, [ z^0<=0 && 1-pos^0==0 && k_35>=1 && 1<=1-2*k_35+K^0 ], cost: 23*k_35 97: l1 -> l1 : K^0'=-1-2*k_35+K^0, next^0'=1+next^0+k_35, pos^0'=1, xx^0'=1, yy^0'=0, z^0'=0, [ 1<=K^0 && xx^post_24<=1 && z^0<=0 && 3<=pos^0 && 1<=xx^post_24 && k_35>=1 && 1<=-2*k_35+K^0 ], cost: 11+23*k_35 98: l1 -> l1 : K^0'=0, next^0'=next^0+K^0, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ z^0<=0 && 2-pos^0==0 && K^0>=1 ], cost: 22*K^0 99: l1 -> l1 : K^0'=0, next^0'=-1+next^0+K^0, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ z^0<=0 && pos^0==0 && -pos^0==0 && -1+K^0>=1 ], cost: -12+22*K^0 100: l1 -> l1 : K^0'=K^0-2*k_37, next^0'=next^0+k_37, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ z^0<=0 && 2-pos^0==0 && k_37>=1 && 1<=1+K^0-2*k_37 ], cost: 23*k_37 101: l1 -> l1 : K^0'=-1+K^0-2*k_37, next^0'=next^0+k_37, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=K^0 && z^0<=0 && pos^0==0 && -pos^0==0 && k_37>=1 && 1<=K^0-2*k_37 ], cost: 10+23*k_37 26: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^post_25 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: l15 26: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=0, yy^0'=0, z^0'=z^post_25, [ 0<=z^post_25 && 1<=N^post_25 ], cost: 2 102: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=1, xx^0'=0, yy^0'=0, z^0'=0, [ 1<=N^post_25 ], cost: 9 103: l15 -> l1 : K^0'=-1+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=1, xx^0'=1, yy^0'=0, z^0'=0, [ 1<=N^post_25 ], cost: 10 104: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=z^post_25-2*k, [ 0<=z^post_25 && 1<=N^post_25 && 0<=yy^post_17 && yy^post_17<=1 && k>=1 && 1<=1+z^post_25-2*k ], cost: 2+6*k 105: l15 -> l1 : K^0'=-k_1+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_25-2*k_1, [ 0<=z^post_25 && 1<=N^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+yy^post_17<=xx^post_24 && k_1>=1 && 1<=1-k_1+N^post_25 && 1<=1+z^post_25-2*k_1 ], cost: 2+7*k_1 106: l15 -> l1 : K^0'=-k_2+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2*k_2+z^post_25, [ 0<=z^post_25 && 1<=N^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+xx^post_24<=yy^post_17 && k_2>=1 && 1<=1-k_2+N^post_25 && 1<=1-2*k_2+z^post_25 ], cost: 2+7*k_2 107: l15 -> l1 : K^0'=-1-2*k_31+N^post_25, N^0'=N^post_25, next^0'=1+k_31, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=N^post_25 && k_31>=1 && 1<=-2*k_31+N^post_25 ], cost: 12+23*k_31 108: l15 -> l1 : K^0'=0, N^0'=N^post_25, next^0'=N^post_25, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ -1+N^post_25>=1 ], cost: -10+22*N^post_25 109: l15 -> l1 : K^0'=-1+N^post_25-2*k_37, N^0'=N^post_25, next^0'=1+k_37, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=N^post_25 && k_37>=1 && 1<=N^post_25-2*k_37 ], cost: 12+23*k_37 Removed unreachable locations (and leaf rules with constant cost): Start location: l15 104: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=z^post_25-2*k, [ 0<=z^post_25 && 1<=N^post_25 && 0<=yy^post_17 && yy^post_17<=1 && k>=1 && 1<=1+z^post_25-2*k ], cost: 2+6*k 105: l15 -> l1 : K^0'=-k_1+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_25-2*k_1, [ 0<=z^post_25 && 1<=N^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+yy^post_17<=xx^post_24 && k_1>=1 && 1<=1-k_1+N^post_25 && 1<=1+z^post_25-2*k_1 ], cost: 2+7*k_1 106: l15 -> l1 : K^0'=-k_2+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2*k_2+z^post_25, [ 0<=z^post_25 && 1<=N^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+xx^post_24<=yy^post_17 && k_2>=1 && 1<=1-k_2+N^post_25 && 1<=1-2*k_2+z^post_25 ], cost: 2+7*k_2 107: l15 -> l1 : K^0'=-1-2*k_31+N^post_25, N^0'=N^post_25, next^0'=1+k_31, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=N^post_25 && k_31>=1 && 1<=-2*k_31+N^post_25 ], cost: 12+23*k_31 108: l15 -> l1 : K^0'=0, N^0'=N^post_25, next^0'=N^post_25, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ -1+N^post_25>=1 ], cost: -10+22*N^post_25 109: l15 -> l1 : K^0'=-1+N^post_25-2*k_37, N^0'=N^post_25, next^0'=1+k_37, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=N^post_25 && k_37>=1 && 1<=N^post_25-2*k_37 ], cost: 12+23*k_37 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l15 104: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=z^post_25-2*k, [ 0<=z^post_25 && 1<=N^post_25 && 0<=yy^post_17 && yy^post_17<=1 && k>=1 && 1<=1+z^post_25-2*k ], cost: 2+6*k 105: l15 -> l1 : K^0'=-k_1+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_25-2*k_1, [ 0<=z^post_25 && 1<=N^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+yy^post_17<=xx^post_24 && k_1>=1 && 1<=1-k_1+N^post_25 && 1<=1+z^post_25-2*k_1 ], cost: 2+7*k_1 106: l15 -> l1 : K^0'=-k_2+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2*k_2+z^post_25, [ 0<=z^post_25 && 1<=N^post_25 && 0<=xx^post_24 && xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+xx^post_24<=yy^post_17 && k_2>=1 && 1<=1-k_2+N^post_25 && 1<=1-2*k_2+z^post_25 ], cost: 2+7*k_2 107: l15 -> l1 : K^0'=-1-2*k_31+N^post_25, N^0'=N^post_25, next^0'=1+k_31, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=N^post_25 && k_31>=1 && 1<=-2*k_31+N^post_25 ], cost: 12+23*k_31 108: l15 -> l1 : K^0'=0, N^0'=N^post_25, next^0'=N^post_25, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ -1+N^post_25>=1 ], cost: -10+22*N^post_25 109: l15 -> l1 : K^0'=-1+N^post_25-2*k_37, N^0'=N^post_25, next^0'=1+k_37, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ 1<=N^post_25 && k_37>=1 && 1<=N^post_25-2*k_37 ], cost: 12+23*k_37 Computing asymptotic complexity for rule 108 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 107 Simplified the guard: 107: l15 -> l1 : K^0'=-1-2*k_31+N^post_25, N^0'=N^post_25, next^0'=1+k_31, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ k_31>=1 && 1<=-2*k_31+N^post_25 ], cost: 12+23*k_31 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 109 Simplified the guard: 109: l15 -> l1 : K^0'=-1+N^post_25-2*k_37, N^0'=N^post_25, next^0'=1+k_37, pos^0'=2, xx^0'=0, yy^0'=1, z^0'=0, [ k_37>=1 && 1<=N^post_25-2*k_37 ], cost: 12+23*k_37 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 104 Simplified the guard: 104: l15 -> l1 : K^0'=N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=yy^post_17, yy^0'=yy^post_17, z^0'=z^post_25-2*k, [ 1<=N^post_25 && 0<=yy^post_17 && yy^post_17<=1 && k>=1 && 1<=1+z^post_25-2*k ], cost: 2+6*k Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 105 Simplified the guard: 105: l15 -> l1 : K^0'=-k_1+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=z^post_25-2*k_1, [ xx^post_24<=1 && 0<=yy^post_17 && yy^post_17<=1 && 1+yy^post_17<=xx^post_24 && k_1>=1 && 1<=1-k_1+N^post_25 && 1<=1+z^post_25-2*k_1 ], cost: 2+7*k_1 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 106 Simplified the guard: 106: l15 -> l1 : K^0'=-k_2+N^post_25, N^0'=N^post_25, next^0'=1, pos^0'=0, xx^0'=xx^post_24, yy^0'=yy^post_17, z^0'=-2*k_2+z^post_25, [ 0<=xx^post_24 && 0<=yy^post_17 && yy^post_17<=1 && 1+xx^post_24<=yy^post_17 && k_2>=1 && 1<=1-k_2+N^post_25 && 1<=1-2*k_2+z^post_25 ], cost: 2+7*k_2 Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ 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 ] WORST_CASE(Omega(1),?)