WORST_CASE(Omega(0),?) Initial ITS Start location: l10 0: l0 -> l1 : tmp^0'=tmp^post0, i^0'=i^post0, k^0'=k^post0, __const_100^0'=__const_100^post0, tmp___0^0'=tmp___0^post0, j^0'=j^post0, (0 == 0 /\ k^0-__const_100^0 <= 0 /\ -k^post0+k^0 == 0 /\ -__const_100^post0+__const_100^0 == 0 /\ -j^post0+j^0 == 0 /\ i^post0 == 0 /\ tmp^0-tmp^post0 == 0), cost: 1 1: l0 -> l2 : tmp^0'=tmp^post1, i^0'=i^post1, k^0'=k^post1, __const_100^0'=__const_100^post1, tmp___0^0'=tmp___0^post1, j^0'=j^post1, (-tmp___0^post1+tmp___0^0 == 0 /\ -__const_100^post1+__const_100^0 == 0 /\ -j^post1+j^0 == 0 /\ 1-k^0+__const_100^0 <= 0 /\ tmp^0-tmp^post1 == 0 /\ k^0-k^post1 == 0 /\ i^0-i^post1 == 0), cost: 1 4: l1 -> l4 : tmp^0'=tmp^post4, i^0'=i^post4, k^0'=k^post4, __const_100^0'=__const_100^post4, tmp___0^0'=tmp___0^post4, j^0'=j^post4, (k^0-k^post4 == 0 /\ __const_100^0-__const_100^post4 == 0 /\ -i^post4+i^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ -j^post4+j^0 == 0 /\ -tmp___0^post4+tmp___0^0 == 0), cost: 1 2: l3 -> l0 : tmp^0'=tmp^post2, i^0'=i^post2, k^0'=k^post2, __const_100^0'=__const_100^post2, tmp___0^0'=tmp___0^post2, j^0'=j^post2, (-j^post2+j^0 == 0 /\ 1-k^0 <= 0 /\ __const_100^0-__const_100^post2 == 0 /\ i^0-i^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ k^0-k^post2 == 0 /\ -tmp___0^post2+tmp___0^0 == 0), cost: 1 3: l3 -> l2 : tmp^0'=tmp^post3, i^0'=i^post3, k^0'=k^post3, __const_100^0'=__const_100^post3, tmp___0^0'=tmp___0^post3, j^0'=j^post3, (__const_100^0-__const_100^post3 == 0 /\ -j^post3+j^0 == 0 /\ k^0-k^post3 == 0 /\ i^0-i^post3 == 0 /\ tmp^0-tmp^post3 == 0 /\ k^0 <= 0 /\ -tmp___0^post3+tmp___0^0 == 0), cost: 1 11: l4 -> l7 : tmp^0'=tmp^post11, i^0'=i^post11, k^0'=k^post11, __const_100^0'=__const_100^post11, tmp___0^0'=tmp___0^post11, j^0'=j^post11, (__const_100^0-__const_100^post11 == 0 /\ -j^post11+j^0 == 0 /\ tmp^0-tmp^post11 == 0 /\ -i^0+k^0 <= 0 /\ k^0-k^post11 == 0 /\ i^0-k^0 <= 0 /\ i^0-i^post11 == 0 /\ tmp___0^0-tmp___0^post11 == 0), cost: 1 12: l4 -> l8 : tmp^0'=tmp^post12, i^0'=i^post12, k^0'=k^post12, __const_100^0'=__const_100^post12, tmp___0^0'=tmp___0^post12, j^0'=j^post12, (tmp^0-tmp^post12 == 0 /\ tmp___0^0-tmp___0^post12 == 0 /\ 1-i^0+k^0 <= 0 /\ i^0-i^post12 == 0 /\ -j^post12+j^0 == 0 /\ -k^post12+k^0 == 0 /\ -__const_100^post12+__const_100^0 == 0), cost: 1 13: l4 -> l8 : tmp^0'=tmp^post13, i^0'=i^post13, k^0'=k^post13, __const_100^0'=__const_100^post13, tmp___0^0'=tmp___0^post13, j^0'=j^post13, (tmp^0-tmp^post13 == 0 /\ i^0-i^post13 == 0 /\ -k^post13+k^0 == 0 /\ -j^post13+j^0 == 0 /\ -__const_100^post13+__const_100^0 == 0 /\ tmp___0^0-tmp___0^post13 == 0 /\ 1+i^0-k^0 <= 0), cost: 1 5: l5 -> l2 : tmp^0'=tmp^post5, i^0'=i^post5, k^0'=k^post5, __const_100^0'=__const_100^post5, tmp___0^0'=tmp___0^post5, j^0'=j^post5, (-j^post5+j^0 == 0 /\ -k^post5+k^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ i^0-j^0 <= 0 /\ __const_100^0-__const_100^post5 == 0 /\ tmp___0^0-tmp___0^post5 == 0 /\ i^0-i^post5 == 0), cost: 1 6: l5 -> l6 : tmp^0'=tmp^post6, i^0'=i^post6, k^0'=k^post6, __const_100^0'=__const_100^post6, tmp___0^0'=tmp___0^post6, j^0'=j^post6, (tmp^0-tmp^post6 == 0 /\ -k^post6+k^0 == 0 /\ tmp___0^0-tmp___0^post6 == 0 /\ -__const_100^post6+__const_100^0 == 0 /\ i^0-i^post6 == 0 /\ -1+j^post6-j^0 == 0 /\ 1-i^0+j^0 <= 0), cost: 1 8: l6 -> l5 : tmp^0'=tmp^post8, i^0'=i^post8, k^0'=k^post8, __const_100^0'=__const_100^post8, tmp___0^0'=tmp___0^post8, j^0'=j^post8, (-tmp___0^post8+tmp___0^0 == 0 /\ -j^post8+j^0 == 0 /\ -__const_100^post8+__const_100^0 == 0 /\ k^0-k^post8 == 0 /\ i^0-i^post8 == 0 /\ tmp^0-tmp^post8 == 0), cost: 1 7: l7 -> l6 : tmp^0'=tmp^post7, i^0'=i^post7, k^0'=k^post7, __const_100^0'=__const_100^post7, tmp___0^0'=tmp___0^post7, j^0'=j^post7, (1-i^0+i^post7 == 0 /\ -tmp___0^post7+tmp___0^0 == 0 /\ tmp^0-tmp^post7 == 0 /\ k^0-k^post7 == 0 /\ -__const_100^post7+__const_100^0 == 0 /\ j^post7 == 0), cost: 1 9: l8 -> l1 : tmp^0'=tmp^post9, i^0'=i^post9, k^0'=k^post9, __const_100^0'=__const_100^post9, tmp___0^0'=tmp___0^post9, j^0'=j^post9, (-1-i^0+i^post9 == 0 /\ -tmp___0^post9+tmp___0^0 == 0 /\ -__const_100^post9+__const_100^0 == 0 /\ -j^post9+j^0 == 0 /\ k^0-k^post9 == 0 /\ -tmp^post9+tmp^0 == 0), cost: 1 10: l8 -> l7 : tmp^0'=tmp^post10, i^0'=i^post10, k^0'=k^post10, __const_100^0'=__const_100^post10, tmp___0^0'=tmp___0^post10, j^0'=j^post10, (tmp^0-tmp^post10 == 0 /\ -i^post10+i^0 == 0 /\ k^0-k^post10 == 0 /\ __const_100^0-__const_100^post10 == 0 /\ -j^post10+j^0 == 0 /\ -tmp___0^post10+tmp___0^0 == 0), cost: 1 14: l9 -> l3 : tmp^0'=tmp^post14, i^0'=i^post14, k^0'=k^post14, __const_100^0'=__const_100^post14, tmp___0^0'=tmp___0^post14, j^0'=j^post14, (0 == 0 /\ i^0-i^post14 == 0 /\ k^post14-tmp^post14 == 0 /\ tmp___0^0-tmp___0^post14 == 0 /\ j^0-j^post14 == 0 /\ -__const_100^post14+__const_100^0 == 0), cost: 1 15: l10 -> l9 : tmp^0'=tmp^post15, i^0'=i^post15, k^0'=k^post15, __const_100^0'=__const_100^post15, tmp___0^0'=tmp___0^post15, j^0'=j^post15, (j^0-j^post15 == 0 /\ -__const_100^post15+__const_100^0 == 0 /\ -tmp___0^post15+tmp___0^0 == 0 /\ i^0-i^post15 == 0 /\ tmp^0-tmp^post15 == 0 /\ k^0-k^post15 == 0), cost: 1 Removed unreachable rules and leafs Start location: l10 0: l0 -> l1 : tmp^0'=tmp^post0, i^0'=i^post0, k^0'=k^post0, __const_100^0'=__const_100^post0, tmp___0^0'=tmp___0^post0, j^0'=j^post0, (0 == 0 /\ k^0-__const_100^0 <= 0 /\ -k^post0+k^0 == 0 /\ -__const_100^post0+__const_100^0 == 0 /\ -j^post0+j^0 == 0 /\ i^post0 == 0 /\ tmp^0-tmp^post0 == 0), cost: 1 4: l1 -> l4 : tmp^0'=tmp^post4, i^0'=i^post4, k^0'=k^post4, __const_100^0'=__const_100^post4, tmp___0^0'=tmp___0^post4, j^0'=j^post4, (k^0-k^post4 == 0 /\ __const_100^0-__const_100^post4 == 0 /\ -i^post4+i^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ -j^post4+j^0 == 0 /\ -tmp___0^post4+tmp___0^0 == 0), cost: 1 2: l3 -> l0 : tmp^0'=tmp^post2, i^0'=i^post2, k^0'=k^post2, __const_100^0'=__const_100^post2, tmp___0^0'=tmp___0^post2, j^0'=j^post2, (-j^post2+j^0 == 0 /\ 1-k^0 <= 0 /\ __const_100^0-__const_100^post2 == 0 /\ i^0-i^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ k^0-k^post2 == 0 /\ -tmp___0^post2+tmp___0^0 == 0), cost: 1 11: l4 -> l7 : tmp^0'=tmp^post11, i^0'=i^post11, k^0'=k^post11, __const_100^0'=__const_100^post11, tmp___0^0'=tmp___0^post11, j^0'=j^post11, (__const_100^0-__const_100^post11 == 0 /\ -j^post11+j^0 == 0 /\ tmp^0-tmp^post11 == 0 /\ -i^0+k^0 <= 0 /\ k^0-k^post11 == 0 /\ i^0-k^0 <= 0 /\ i^0-i^post11 == 0 /\ tmp___0^0-tmp___0^post11 == 0), cost: 1 12: l4 -> l8 : tmp^0'=tmp^post12, i^0'=i^post12, k^0'=k^post12, __const_100^0'=__const_100^post12, tmp___0^0'=tmp___0^post12, j^0'=j^post12, (tmp^0-tmp^post12 == 0 /\ tmp___0^0-tmp___0^post12 == 0 /\ 1-i^0+k^0 <= 0 /\ i^0-i^post12 == 0 /\ -j^post12+j^0 == 0 /\ -k^post12+k^0 == 0 /\ -__const_100^post12+__const_100^0 == 0), cost: 1 13: l4 -> l8 : tmp^0'=tmp^post13, i^0'=i^post13, k^0'=k^post13, __const_100^0'=__const_100^post13, tmp___0^0'=tmp___0^post13, j^0'=j^post13, (tmp^0-tmp^post13 == 0 /\ i^0-i^post13 == 0 /\ -k^post13+k^0 == 0 /\ -j^post13+j^0 == 0 /\ -__const_100^post13+__const_100^0 == 0 /\ tmp___0^0-tmp___0^post13 == 0 /\ 1+i^0-k^0 <= 0), cost: 1 6: l5 -> l6 : tmp^0'=tmp^post6, i^0'=i^post6, k^0'=k^post6, __const_100^0'=__const_100^post6, tmp___0^0'=tmp___0^post6, j^0'=j^post6, (tmp^0-tmp^post6 == 0 /\ -k^post6+k^0 == 0 /\ tmp___0^0-tmp___0^post6 == 0 /\ -__const_100^post6+__const_100^0 == 0 /\ i^0-i^post6 == 0 /\ -1+j^post6-j^0 == 0 /\ 1-i^0+j^0 <= 0), cost: 1 8: l6 -> l5 : tmp^0'=tmp^post8, i^0'=i^post8, k^0'=k^post8, __const_100^0'=__const_100^post8, tmp___0^0'=tmp___0^post8, j^0'=j^post8, (-tmp___0^post8+tmp___0^0 == 0 /\ -j^post8+j^0 == 0 /\ -__const_100^post8+__const_100^0 == 0 /\ k^0-k^post8 == 0 /\ i^0-i^post8 == 0 /\ tmp^0-tmp^post8 == 0), cost: 1 7: l7 -> l6 : tmp^0'=tmp^post7, i^0'=i^post7, k^0'=k^post7, __const_100^0'=__const_100^post7, tmp___0^0'=tmp___0^post7, j^0'=j^post7, (1-i^0+i^post7 == 0 /\ -tmp___0^post7+tmp___0^0 == 0 /\ tmp^0-tmp^post7 == 0 /\ k^0-k^post7 == 0 /\ -__const_100^post7+__const_100^0 == 0 /\ j^post7 == 0), cost: 1 9: l8 -> l1 : tmp^0'=tmp^post9, i^0'=i^post9, k^0'=k^post9, __const_100^0'=__const_100^post9, tmp___0^0'=tmp___0^post9, j^0'=j^post9, (-1-i^0+i^post9 == 0 /\ -tmp___0^post9+tmp___0^0 == 0 /\ -__const_100^post9+__const_100^0 == 0 /\ -j^post9+j^0 == 0 /\ k^0-k^post9 == 0 /\ -tmp^post9+tmp^0 == 0), cost: 1 10: l8 -> l7 : tmp^0'=tmp^post10, i^0'=i^post10, k^0'=k^post10, __const_100^0'=__const_100^post10, tmp___0^0'=tmp___0^post10, j^0'=j^post10, (tmp^0-tmp^post10 == 0 /\ -i^post10+i^0 == 0 /\ k^0-k^post10 == 0 /\ __const_100^0-__const_100^post10 == 0 /\ -j^post10+j^0 == 0 /\ -tmp___0^post10+tmp___0^0 == 0), cost: 1 14: l9 -> l3 : tmp^0'=tmp^post14, i^0'=i^post14, k^0'=k^post14, __const_100^0'=__const_100^post14, tmp___0^0'=tmp___0^post14, j^0'=j^post14, (0 == 0 /\ i^0-i^post14 == 0 /\ k^post14-tmp^post14 == 0 /\ tmp___0^0-tmp___0^post14 == 0 /\ j^0-j^post14 == 0 /\ -__const_100^post14+__const_100^0 == 0), cost: 1 15: l10 -> l9 : tmp^0'=tmp^post15, i^0'=i^post15, k^0'=k^post15, __const_100^0'=__const_100^post15, tmp___0^0'=tmp___0^post15, j^0'=j^post15, (j^0-j^post15 == 0 /\ -__const_100^post15+__const_100^0 == 0 /\ -tmp___0^post15+tmp___0^0 == 0 /\ i^0-i^post15 == 0 /\ tmp^0-tmp^post15 == 0 /\ k^0-k^post15 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : tmp^0'=tmp^post0, i^0'=i^post0, k^0'=k^post0, __const_100^0'=__const_100^post0, tmp___0^0'=tmp___0^post0, j^0'=j^post0, (0 == 0 /\ k^0-__const_100^0 <= 0 /\ -k^post0+k^0 == 0 /\ -__const_100^post0+__const_100^0 == 0 /\ -j^post0+j^0 == 0 /\ i^post0 == 0 /\ tmp^0-tmp^post0 == 0), cost: 1 New rule: l0 -> l1 : i^0'=0, tmp___0^0'=tmp___0^post0, k^0-__const_100^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : tmp^0'=tmp^post2, i^0'=i^post2, k^0'=k^post2, __const_100^0'=__const_100^post2, tmp___0^0'=tmp___0^post2, j^0'=j^post2, (-j^post2+j^0 == 0 /\ 1-k^0 <= 0 /\ __const_100^0-__const_100^post2 == 0 /\ i^0-i^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ k^0-k^post2 == 0 /\ -tmp___0^post2+tmp___0^0 == 0), cost: 1 New rule: l3 -> l0 : -1+k^0 >= 0, cost: 1 Applied preprocessing Original rule: l1 -> l4 : tmp^0'=tmp^post4, i^0'=i^post4, k^0'=k^post4, __const_100^0'=__const_100^post4, tmp___0^0'=tmp___0^post4, j^0'=j^post4, (k^0-k^post4 == 0 /\ __const_100^0-__const_100^post4 == 0 /\ -i^post4+i^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ -j^post4+j^0 == 0 /\ -tmp___0^post4+tmp___0^0 == 0), cost: 1 New rule: l1 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l6 : tmp^0'=tmp^post6, i^0'=i^post6, k^0'=k^post6, __const_100^0'=__const_100^post6, tmp___0^0'=tmp___0^post6, j^0'=j^post6, (tmp^0-tmp^post6 == 0 /\ -k^post6+k^0 == 0 /\ tmp___0^0-tmp___0^post6 == 0 /\ -__const_100^post6+__const_100^0 == 0 /\ i^0-i^post6 == 0 /\ -1+j^post6-j^0 == 0 /\ 1-i^0+j^0 <= 0), cost: 1 New rule: l5 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 1 Applied preprocessing Original rule: l7 -> l6 : tmp^0'=tmp^post7, i^0'=i^post7, k^0'=k^post7, __const_100^0'=__const_100^post7, tmp___0^0'=tmp___0^post7, j^0'=j^post7, (1-i^0+i^post7 == 0 /\ -tmp___0^post7+tmp___0^0 == 0 /\ tmp^0-tmp^post7 == 0 /\ k^0-k^post7 == 0 /\ -__const_100^post7+__const_100^0 == 0 /\ j^post7 == 0), cost: 1 New rule: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : tmp^0'=tmp^post8, i^0'=i^post8, k^0'=k^post8, __const_100^0'=__const_100^post8, tmp___0^0'=tmp___0^post8, j^0'=j^post8, (-tmp___0^post8+tmp___0^0 == 0 /\ -j^post8+j^0 == 0 /\ -__const_100^post8+__const_100^0 == 0 /\ k^0-k^post8 == 0 /\ i^0-i^post8 == 0 /\ tmp^0-tmp^post8 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Applied preprocessing Original rule: l8 -> l1 : tmp^0'=tmp^post9, i^0'=i^post9, k^0'=k^post9, __const_100^0'=__const_100^post9, tmp___0^0'=tmp___0^post9, j^0'=j^post9, (-1-i^0+i^post9 == 0 /\ -tmp___0^post9+tmp___0^0 == 0 /\ -__const_100^post9+__const_100^0 == 0 /\ -j^post9+j^0 == 0 /\ k^0-k^post9 == 0 /\ -tmp^post9+tmp^0 == 0), cost: 1 New rule: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 Applied preprocessing Original rule: l8 -> l7 : tmp^0'=tmp^post10, i^0'=i^post10, k^0'=k^post10, __const_100^0'=__const_100^post10, tmp___0^0'=tmp___0^post10, j^0'=j^post10, (tmp^0-tmp^post10 == 0 /\ -i^post10+i^0 == 0 /\ k^0-k^post10 == 0 /\ __const_100^0-__const_100^post10 == 0 /\ -j^post10+j^0 == 0 /\ -tmp___0^post10+tmp___0^0 == 0), cost: 1 New rule: l8 -> l7 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l7 : tmp^0'=tmp^post11, i^0'=i^post11, k^0'=k^post11, __const_100^0'=__const_100^post11, tmp___0^0'=tmp___0^post11, j^0'=j^post11, (__const_100^0-__const_100^post11 == 0 /\ -j^post11+j^0 == 0 /\ tmp^0-tmp^post11 == 0 /\ -i^0+k^0 <= 0 /\ k^0-k^post11 == 0 /\ i^0-k^0 <= 0 /\ i^0-i^post11 == 0 /\ tmp___0^0-tmp___0^post11 == 0), cost: 1 New rule: l4 -> l7 : -i^0+k^0 == 0, cost: 1 Applied preprocessing Original rule: l4 -> l8 : tmp^0'=tmp^post12, i^0'=i^post12, k^0'=k^post12, __const_100^0'=__const_100^post12, tmp___0^0'=tmp___0^post12, j^0'=j^post12, (tmp^0-tmp^post12 == 0 /\ tmp___0^0-tmp___0^post12 == 0 /\ 1-i^0+k^0 <= 0 /\ i^0-i^post12 == 0 /\ -j^post12+j^0 == 0 /\ -k^post12+k^0 == 0 /\ -__const_100^post12+__const_100^0 == 0), cost: 1 New rule: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l8 : tmp^0'=tmp^post13, i^0'=i^post13, k^0'=k^post13, __const_100^0'=__const_100^post13, tmp___0^0'=tmp___0^post13, j^0'=j^post13, (tmp^0-tmp^post13 == 0 /\ i^0-i^post13 == 0 /\ -k^post13+k^0 == 0 /\ -j^post13+j^0 == 0 /\ -__const_100^post13+__const_100^0 == 0 /\ tmp___0^0-tmp___0^post13 == 0 /\ 1+i^0-k^0 <= 0), cost: 1 New rule: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 Applied preprocessing Original rule: l9 -> l3 : tmp^0'=tmp^post14, i^0'=i^post14, k^0'=k^post14, __const_100^0'=__const_100^post14, tmp___0^0'=tmp___0^post14, j^0'=j^post14, (0 == 0 /\ i^0-i^post14 == 0 /\ k^post14-tmp^post14 == 0 /\ tmp___0^0-tmp___0^post14 == 0 /\ j^0-j^post14 == 0 /\ -__const_100^post14+__const_100^0 == 0), cost: 1 New rule: l9 -> l3 : tmp^0'=tmp^post14, k^0'=tmp^post14, 0 == 0, cost: 1 Applied preprocessing Original rule: l10 -> l9 : tmp^0'=tmp^post15, i^0'=i^post15, k^0'=k^post15, __const_100^0'=__const_100^post15, tmp___0^0'=tmp___0^post15, j^0'=j^post15, (j^0-j^post15 == 0 /\ -__const_100^post15+__const_100^0 == 0 /\ -tmp___0^post15+tmp___0^0 == 0 /\ i^0-i^post15 == 0 /\ tmp^0-tmp^post15 == 0 /\ k^0-k^post15 == 0), cost: 1 New rule: l10 -> l9 : TRUE, cost: 1 Simplified rules Start location: l10 16: l0 -> l1 : i^0'=0, tmp___0^0'=tmp___0^post0, k^0-__const_100^0 <= 0, cost: 1 18: l1 -> l4 : TRUE, cost: 1 17: l3 -> l0 : -1+k^0 >= 0, cost: 1 24: l4 -> l7 : -i^0+k^0 == 0, cost: 1 25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 19: l5 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 1 21: l6 -> l5 : TRUE, cost: 1 20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1 22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 23: l8 -> l7 : TRUE, cost: 1 27: l9 -> l3 : tmp^0'=tmp^post14, k^0'=tmp^post14, 0 == 0, cost: 1 28: l10 -> l9 : TRUE, cost: 1 Eliminating location l9 by chaining: Applied chaining First rule: l10 -> l9 : TRUE, cost: 1 Second rule: l9 -> l3 : tmp^0'=tmp^post14, k^0'=tmp^post14, 0 == 0, cost: 1 New rule: l10 -> l3 : tmp^0'=tmp^post14, k^0'=tmp^post14, 0 == 0, cost: 2 Applied deletion Removed the following rules: 27 28 Eliminating location l3 by chaining: Applied chaining First rule: l10 -> l3 : tmp^0'=tmp^post14, k^0'=tmp^post14, 0 == 0, cost: 2 Second rule: l3 -> l0 : -1+k^0 >= 0, cost: 1 New rule: l10 -> l0 : tmp^0'=tmp^post14, k^0'=tmp^post14, (0 == 0 /\ -1+tmp^post14 >= 0), cost: 3 Applied simplification Original rule: l10 -> l0 : tmp^0'=tmp^post14, k^0'=tmp^post14, (0 == 0 /\ -1+tmp^post14 >= 0), cost: 3 New rule: l10 -> l0 : tmp^0'=tmp^post14, k^0'=tmp^post14, -1+tmp^post14 >= 0, cost: 3 Applied deletion Removed the following rules: 17 29 Eliminating location l0 by chaining: Applied chaining First rule: l10 -> l0 : tmp^0'=tmp^post14, k^0'=tmp^post14, -1+tmp^post14 >= 0, cost: 3 Second rule: l0 -> l1 : i^0'=0, tmp___0^0'=tmp___0^post0, k^0-__const_100^0 <= 0, cost: 1 New rule: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Applied deletion Removed the following rules: 16 30 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 1 New rule: l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 2 Applied deletion Removed the following rules: 19 21 Eliminated locations on linear paths Start location: l10 18: l1 -> l4 : TRUE, cost: 1 24: l4 -> l7 : -i^0+k^0 == 0, cost: 1 25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 32: l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 2 20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1 22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 23: l8 -> l7 : TRUE, cost: 1 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Applied acceleration Original rule: l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 2 New rule: l6 -> l6 : j^0'=n+j^0, (i^0-n-j^0 >= 0 /\ n >= 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_lmppHP.txt Applied instantiation Original rule: l6 -> l6 : j^0'=n+j^0, (i^0-n-j^0 >= 0 /\ n >= 0), cost: 2*n New rule: l6 -> l6 : j^0'=i^0, (0 >= 0 /\ i^0-j^0 >= 0), cost: 2*i^0-2*j^0 Applied simplification Original rule: l6 -> l6 : j^0'=i^0, (0 >= 0 /\ i^0-j^0 >= 0), cost: 2*i^0-2*j^0 New rule: l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 2*i^0-2*j^0 Applied deletion Removed the following rules: 32 Accelerated simple loops Start location: l10 18: l1 -> l4 : TRUE, cost: 1 24: l4 -> l7 : -i^0+k^0 == 0, cost: 1 25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 34: l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 2*i^0-2*j^0 20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1 22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 23: l8 -> l7 : TRUE, cost: 1 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Applied chaining First rule: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1 Second rule: l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 2*i^0-2*j^0 New rule: l7 -> l6 : i^0'=-1+i^0, j^0'=-1+i^0, -1+i^0 >= 0, cost: -1+2*i^0 Applied deletion Removed the following rules: 34 Chained accelerated rules with incoming rules Start location: l10 18: l1 -> l4 : TRUE, cost: 1 24: l4 -> l7 : -i^0+k^0 == 0, cost: 1 25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1 35: l7 -> l6 : i^0'=-1+i^0, j^0'=-1+i^0, -1+i^0 >= 0, cost: -1+2*i^0 22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 23: l8 -> l7 : TRUE, cost: 1 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Removed unreachable locations and irrelevant leafs Start location: l10 18: l1 -> l4 : TRUE, cost: 1 25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Eliminating location l4 by chaining: Applied chaining First rule: l1 -> l4 : TRUE, cost: 1 Second rule: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1 New rule: l1 -> l8 : 1-i^0+k^0 <= 0, cost: 2 Applied chaining First rule: l1 -> l4 : TRUE, cost: 1 Second rule: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1 New rule: l1 -> l8 : 1+i^0-k^0 <= 0, cost: 2 Applied deletion Removed the following rules: 18 25 26 Eliminated locations on tree-shaped paths Start location: l10 36: l1 -> l8 : 1-i^0+k^0 <= 0, cost: 2 37: l1 -> l8 : 1+i^0-k^0 <= 0, cost: 2 22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Eliminating location l8 by chaining: Applied chaining First rule: l1 -> l8 : 1-i^0+k^0 <= 0, cost: 2 Second rule: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 New rule: l1 -> l1 : i^0'=1+i^0, 1-i^0+k^0 <= 0, cost: 3 Applied chaining First rule: l1 -> l8 : 1+i^0-k^0 <= 0, cost: 2 Second rule: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1 New rule: l1 -> l1 : i^0'=1+i^0, 1+i^0-k^0 <= 0, cost: 3 Applied deletion Removed the following rules: 22 36 37 Eliminated locations on tree-shaped paths Start location: l10 38: l1 -> l1 : i^0'=1+i^0, 1-i^0+k^0 <= 0, cost: 3 39: l1 -> l1 : i^0'=1+i^0, 1+i^0-k^0 <= 0, cost: 3 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Applied nonterm Original rule: l1 -> l1 : i^0'=1+i^0, 1-i^0+k^0 <= 0, cost: 3 New rule: l1 -> [12] : (-1+i^0-k^0 >= 0 /\ n0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_MAljJH.txt Applied acceleration Original rule: l1 -> l1 : i^0'=1+i^0, 1+i^0-k^0 <= 0, cost: 3 New rule: l1 -> l1 : i^0'=i^0+n1, (-i^0+k^0-n1 >= 0 /\ n1 >= 0), cost: 3*n1 Sub-proof via acceration calculus written to file:///tmp/tmpnam_EnbHPd.txt Applied instantiation Original rule: l1 -> l1 : i^0'=i^0+n1, (-i^0+k^0-n1 >= 0 /\ n1 >= 0), cost: 3*n1 New rule: l1 -> l1 : i^0'=k^0, (0 >= 0 /\ -i^0+k^0 >= 0), cost: -3*i^0+3*k^0 Applied simplification Original rule: l1 -> l1 : i^0'=k^0, (0 >= 0 /\ -i^0+k^0 >= 0), cost: -3*i^0+3*k^0 New rule: l1 -> l1 : i^0'=k^0, -i^0+k^0 >= 0, cost: -3*i^0+3*k^0 Applied deletion Removed the following rules: 38 39 Accelerated simple loops Start location: l10 40: l1 -> [12] : (-1+i^0-k^0 >= 0 /\ n0 >= 0), cost: NONTERM 42: l1 -> l1 : i^0'=k^0, -i^0+k^0 >= 0, cost: -3*i^0+3*k^0 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Applied chaining First rule: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 Second rule: l1 -> l1 : i^0'=k^0, -i^0+k^0 >= 0, cost: -3*i^0+3*k^0 New rule: l10 -> l1 : tmp^0'=tmp^post14, i^0'=tmp^post14, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4+3*tmp^post14 Applied deletion Removed the following rules: 40 42 Chained accelerated rules with incoming rules Start location: l10 31: l10 -> l1 : tmp^0'=tmp^post14, i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4 43: l10 -> l1 : tmp^0'=tmp^post14, i^0'=tmp^post14, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, (-1+tmp^post14 >= 0 /\ tmp^post14-__const_100^0 <= 0), cost: 4+3*tmp^post14 Removed unreachable locations and irrelevant leafs Start location: l10 Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0