NO Initial ITS Start location: l6 0: l0 -> l1 : Result_4^0'=Result_4^post0, d_6^0'=d_6^post0, ___cil_tmp4_8^0'=___cil_tmp4_8^post0, ___retres3_7^0'=___retres3_7^post0, ___cil_tmp2_10^0'=___cil_tmp2_10^post0, i_5^0'=i_5^post0, ___retres1_9^0'=___retres1_9^post0, (d_6^0-d_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -i_5^post0+i_5^0 == 0 /\ -___cil_tmp4_8^post0+___cil_tmp4_8^0 == 0 /\ -___retres1_9^post0+___retres1_9^0 == 0 /\ ___cil_tmp2_10^0-___cil_tmp2_10^post0 == 0 /\ -___retres3_7^post0+___retres3_7^0 == 0), cost: 1 4: l1 -> l3 : Result_4^0'=Result_4^post4, d_6^0'=d_6^post4, ___cil_tmp4_8^0'=___cil_tmp4_8^post4, ___retres3_7^0'=___retres3_7^post4, ___cil_tmp2_10^0'=___cil_tmp2_10^post4, i_5^0'=i_5^post4, ___retres1_9^0'=___retres1_9^post4, (-___cil_tmp2_10^post4+___cil_tmp2_10^0 == 0 /\ -___retres1_9^post4+___retres1_9^0 == 0 /\ ___cil_tmp4_8^post4-___retres3_7^post4 == 0 /\ d_6^0-d_6^post4 == 0 /\ -d_6^0 <= 0 /\ ___retres3_7^post4 == 0 /\ -i_5^post4+i_5^0 == 0 /\ Result_4^post4-___cil_tmp4_8^post4 == 0), cost: 1 5: l1 -> l2 : Result_4^0'=Result_4^post5, d_6^0'=d_6^post5, ___cil_tmp4_8^0'=___cil_tmp4_8^post5, ___retres3_7^0'=___retres3_7^post5, ___cil_tmp2_10^0'=___cil_tmp2_10^post5, i_5^0'=i_5^post5, ___retres1_9^0'=___retres1_9^post5, (-___retres1_9^post5+___retres1_9^0 == 0 /\ -i_5^post5+i_5^0 == 0 /\ d_6^0-d_6^post5 == 0 /\ -___retres3_7^post5+___retres3_7^0 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post5 == 0 /\ 1+d_6^0 <= 0 /\ Result_4^0-Result_4^post5 == 0 /\ -___cil_tmp2_10^post5+___cil_tmp2_10^0 == 0), cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post1, d_6^0'=d_6^post1, ___cil_tmp4_8^0'=___cil_tmp4_8^post1, ___retres3_7^0'=___retres3_7^post1, ___cil_tmp2_10^0'=___cil_tmp2_10^post1, i_5^0'=i_5^post1, ___retres1_9^0'=___retres1_9^post1, (___cil_tmp2_10^0-___cil_tmp2_10^post1 == 0 /\ -___retres1_9^post1+___retres1_9^0 == 0 /\ d_6^0-d_6^post1 == 0 /\ ___retres3_7^post1 == 0 /\ ___cil_tmp4_8^post1-___retres3_7^post1 == 0 /\ -___cil_tmp4_8^post1+Result_4^post1 == 0 /\ 1+i_5^0 <= 0 /\ -i_5^post1+i_5^0 == 0), cost: 1 2: l2 -> l4 : Result_4^0'=Result_4^post2, d_6^0'=d_6^post2, ___cil_tmp4_8^0'=___cil_tmp4_8^post2, ___retres3_7^0'=___retres3_7^post2, ___cil_tmp2_10^0'=___cil_tmp2_10^post2, i_5^0'=i_5^post2, ___retres1_9^0'=___retres1_9^post2, (-___retres1_9^post2+___retres1_9^0 == 0 /\ -i_5^0 <= 0 /\ Result_4^0-Result_4^post2 == 0 /\ ___retres3_7^0-___retres3_7^post2 == 0 /\ -___cil_tmp2_10^post2+___cil_tmp2_10^0 == 0 /\ d_6^0-d_6^post2 == 0 /\ d_6^0+i_5^post2-i_5^0 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post2 == 0), cost: 1 6: l3 -> l5 : Result_4^0'=Result_4^post6, d_6^0'=d_6^post6, ___cil_tmp4_8^0'=___cil_tmp4_8^post6, ___retres3_7^0'=___retres3_7^post6, ___cil_tmp2_10^0'=___cil_tmp2_10^post6, i_5^0'=i_5^post6, ___retres1_9^0'=___retres1_9^post6, (Result_4^post6-___cil_tmp2_10^post6 == 0 /\ -i_5^post6+i_5^0 == 0 /\ d_6^0-d_6^post6 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post6 == 0 /\ -___retres3_7^post6+___retres3_7^0 == 0 /\ ___retres1_9^post6 == 0 /\ ___cil_tmp2_10^post6-___retres1_9^post6 == 0), cost: 1 3: l4 -> l2 : Result_4^0'=Result_4^post3, d_6^0'=d_6^post3, ___cil_tmp4_8^0'=___cil_tmp4_8^post3, ___retres3_7^0'=___retres3_7^post3, ___cil_tmp2_10^0'=___cil_tmp2_10^post3, i_5^0'=i_5^post3, ___retres1_9^0'=___retres1_9^post3, (Result_4^0-Result_4^post3 == 0 /\ d_6^0-d_6^post3 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post3 == 0 /\ -___cil_tmp2_10^post3+___cil_tmp2_10^0 == 0 /\ -___retres1_9^post3+___retres1_9^0 == 0 /\ -i_5^post3+i_5^0 == 0 /\ ___retres3_7^0-___retres3_7^post3 == 0), cost: 1 7: l6 -> l0 : Result_4^0'=Result_4^post7, d_6^0'=d_6^post7, ___cil_tmp4_8^0'=___cil_tmp4_8^post7, ___retres3_7^0'=___retres3_7^post7, ___cil_tmp2_10^0'=___cil_tmp2_10^post7, i_5^0'=i_5^post7, ___retres1_9^0'=___retres1_9^post7, (-___retres3_7^post7+___retres3_7^0 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ -___retres1_9^post7+___retres1_9^0 == 0 /\ i_5^0-i_5^post7 == 0 /\ ___cil_tmp2_10^0-___cil_tmp2_10^post7 == 0 /\ -___cil_tmp4_8^post7+___cil_tmp4_8^0 == 0 /\ d_6^0-d_6^post7 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 0: l0 -> l1 : Result_4^0'=Result_4^post0, d_6^0'=d_6^post0, ___cil_tmp4_8^0'=___cil_tmp4_8^post0, ___retres3_7^0'=___retres3_7^post0, ___cil_tmp2_10^0'=___cil_tmp2_10^post0, i_5^0'=i_5^post0, ___retres1_9^0'=___retres1_9^post0, (d_6^0-d_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -i_5^post0+i_5^0 == 0 /\ -___cil_tmp4_8^post0+___cil_tmp4_8^0 == 0 /\ -___retres1_9^post0+___retres1_9^0 == 0 /\ ___cil_tmp2_10^0-___cil_tmp2_10^post0 == 0 /\ -___retres3_7^post0+___retres3_7^0 == 0), cost: 1 5: l1 -> l2 : Result_4^0'=Result_4^post5, d_6^0'=d_6^post5, ___cil_tmp4_8^0'=___cil_tmp4_8^post5, ___retres3_7^0'=___retres3_7^post5, ___cil_tmp2_10^0'=___cil_tmp2_10^post5, i_5^0'=i_5^post5, ___retres1_9^0'=___retres1_9^post5, (-___retres1_9^post5+___retres1_9^0 == 0 /\ -i_5^post5+i_5^0 == 0 /\ d_6^0-d_6^post5 == 0 /\ -___retres3_7^post5+___retres3_7^0 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post5 == 0 /\ 1+d_6^0 <= 0 /\ Result_4^0-Result_4^post5 == 0 /\ -___cil_tmp2_10^post5+___cil_tmp2_10^0 == 0), cost: 1 2: l2 -> l4 : Result_4^0'=Result_4^post2, d_6^0'=d_6^post2, ___cil_tmp4_8^0'=___cil_tmp4_8^post2, ___retres3_7^0'=___retres3_7^post2, ___cil_tmp2_10^0'=___cil_tmp2_10^post2, i_5^0'=i_5^post2, ___retres1_9^0'=___retres1_9^post2, (-___retres1_9^post2+___retres1_9^0 == 0 /\ -i_5^0 <= 0 /\ Result_4^0-Result_4^post2 == 0 /\ ___retres3_7^0-___retres3_7^post2 == 0 /\ -___cil_tmp2_10^post2+___cil_tmp2_10^0 == 0 /\ d_6^0-d_6^post2 == 0 /\ d_6^0+i_5^post2-i_5^0 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post2 == 0), cost: 1 3: l4 -> l2 : Result_4^0'=Result_4^post3, d_6^0'=d_6^post3, ___cil_tmp4_8^0'=___cil_tmp4_8^post3, ___retres3_7^0'=___retres3_7^post3, ___cil_tmp2_10^0'=___cil_tmp2_10^post3, i_5^0'=i_5^post3, ___retres1_9^0'=___retres1_9^post3, (Result_4^0-Result_4^post3 == 0 /\ d_6^0-d_6^post3 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post3 == 0 /\ -___cil_tmp2_10^post3+___cil_tmp2_10^0 == 0 /\ -___retres1_9^post3+___retres1_9^0 == 0 /\ -i_5^post3+i_5^0 == 0 /\ ___retres3_7^0-___retres3_7^post3 == 0), cost: 1 7: l6 -> l0 : Result_4^0'=Result_4^post7, d_6^0'=d_6^post7, ___cil_tmp4_8^0'=___cil_tmp4_8^post7, ___retres3_7^0'=___retres3_7^post7, ___cil_tmp2_10^0'=___cil_tmp2_10^post7, i_5^0'=i_5^post7, ___retres1_9^0'=___retres1_9^post7, (-___retres3_7^post7+___retres3_7^0 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ -___retres1_9^post7+___retres1_9^0 == 0 /\ i_5^0-i_5^post7 == 0 /\ ___cil_tmp2_10^0-___cil_tmp2_10^post7 == 0 /\ -___cil_tmp4_8^post7+___cil_tmp4_8^0 == 0 /\ d_6^0-d_6^post7 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : Result_4^0'=Result_4^post0, d_6^0'=d_6^post0, ___cil_tmp4_8^0'=___cil_tmp4_8^post0, ___retres3_7^0'=___retres3_7^post0, ___cil_tmp2_10^0'=___cil_tmp2_10^post0, i_5^0'=i_5^post0, ___retres1_9^0'=___retres1_9^post0, (d_6^0-d_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -i_5^post0+i_5^0 == 0 /\ -___cil_tmp4_8^post0+___cil_tmp4_8^0 == 0 /\ -___retres1_9^post0+___retres1_9^0 == 0 /\ ___cil_tmp2_10^0-___cil_tmp2_10^post0 == 0 /\ -___retres3_7^post0+___retres3_7^0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l4 : Result_4^0'=Result_4^post2, d_6^0'=d_6^post2, ___cil_tmp4_8^0'=___cil_tmp4_8^post2, ___retres3_7^0'=___retres3_7^post2, ___cil_tmp2_10^0'=___cil_tmp2_10^post2, i_5^0'=i_5^post2, ___retres1_9^0'=___retres1_9^post2, (-___retres1_9^post2+___retres1_9^0 == 0 /\ -i_5^0 <= 0 /\ Result_4^0-Result_4^post2 == 0 /\ ___retres3_7^0-___retres3_7^post2 == 0 /\ -___cil_tmp2_10^post2+___cil_tmp2_10^0 == 0 /\ d_6^0-d_6^post2 == 0 /\ d_6^0+i_5^post2-i_5^0 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post2 == 0), cost: 1 New rule: l2 -> l4 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l4 -> l2 : Result_4^0'=Result_4^post3, d_6^0'=d_6^post3, ___cil_tmp4_8^0'=___cil_tmp4_8^post3, ___retres3_7^0'=___retres3_7^post3, ___cil_tmp2_10^0'=___cil_tmp2_10^post3, i_5^0'=i_5^post3, ___retres1_9^0'=___retres1_9^post3, (Result_4^0-Result_4^post3 == 0 /\ d_6^0-d_6^post3 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post3 == 0 /\ -___cil_tmp2_10^post3+___cil_tmp2_10^0 == 0 /\ -___retres1_9^post3+___retres1_9^0 == 0 /\ -i_5^post3+i_5^0 == 0 /\ ___retres3_7^0-___retres3_7^post3 == 0), cost: 1 New rule: l4 -> l2 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l2 : Result_4^0'=Result_4^post5, d_6^0'=d_6^post5, ___cil_tmp4_8^0'=___cil_tmp4_8^post5, ___retres3_7^0'=___retres3_7^post5, ___cil_tmp2_10^0'=___cil_tmp2_10^post5, i_5^0'=i_5^post5, ___retres1_9^0'=___retres1_9^post5, (-___retres1_9^post5+___retres1_9^0 == 0 /\ -i_5^post5+i_5^0 == 0 /\ d_6^0-d_6^post5 == 0 /\ -___retres3_7^post5+___retres3_7^0 == 0 /\ ___cil_tmp4_8^0-___cil_tmp4_8^post5 == 0 /\ 1+d_6^0 <= 0 /\ Result_4^0-Result_4^post5 == 0 /\ -___cil_tmp2_10^post5+___cil_tmp2_10^0 == 0), cost: 1 New rule: l1 -> l2 : 1+d_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l6 -> l0 : Result_4^0'=Result_4^post7, d_6^0'=d_6^post7, ___cil_tmp4_8^0'=___cil_tmp4_8^post7, ___retres3_7^0'=___retres3_7^post7, ___cil_tmp2_10^0'=___cil_tmp2_10^post7, i_5^0'=i_5^post7, ___retres1_9^0'=___retres1_9^post7, (-___retres3_7^post7+___retres3_7^0 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ -___retres1_9^post7+___retres1_9^0 == 0 /\ i_5^0-i_5^post7 == 0 /\ ___cil_tmp2_10^0-___cil_tmp2_10^post7 == 0 /\ -___cil_tmp4_8^post7+___cil_tmp4_8^0 == 0 /\ d_6^0-d_6^post7 == 0), cost: 1 New rule: l6 -> l0 : TRUE, cost: 1 Simplified rules Start location: l6 8: l0 -> l1 : TRUE, cost: 1 11: l1 -> l2 : 1+d_6^0 <= 0, cost: 1 9: l2 -> l4 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 1 10: l4 -> l2 : TRUE, cost: 1 12: l6 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l6 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l6 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 8 12 Eliminating location l1 by chaining: Applied chaining First rule: l6 -> l1 : TRUE, cost: 2 Second rule: l1 -> l2 : 1+d_6^0 <= 0, cost: 1 New rule: l6 -> l2 : 1+d_6^0 <= 0, cost: 3 Applied deletion Removed the following rules: 11 13 Eliminating location l4 by chaining: Applied chaining First rule: l2 -> l4 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 1 Second rule: l4 -> l2 : TRUE, cost: 1 New rule: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 9 10 Eliminated locations on linear paths Start location: l6 15: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 2 14: l6 -> l2 : 1+d_6^0 <= 0, cost: 3 Applied acceleration Original rule: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 2 New rule: l2 -> l2 : i_5^0'=-d_6^0*n0+i_5^0, (-d_6^0*(-1+n0)+i_5^0 >= 0 /\ i_5^0 >= 0 /\ n0 >= 0), cost: 2*n0 Applied recurrent set Original rule: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 2 New rule: l2 -> [7] : (i_5^0 >= 0 /\ 1+d_6^0 <= 0), cost: NONTERM Applied fixed-point processor Original rule: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, i_5^0 >= 0, cost: 2 New rule: l2 -> [7] : (d_6^0 == 0 /\ i_5^0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 15 Accelerated simple loops Start location: l6 16: l2 -> l2 : i_5^0'=-d_6^0*n0+i_5^0, (-d_6^0*(-1+n0)+i_5^0 >= 0 /\ i_5^0 >= 0 /\ n0 >= 0), cost: 2*n0 17: l2 -> [7] : (i_5^0 >= 0 /\ 1+d_6^0 <= 0), cost: NONTERM 18: l2 -> [7] : (d_6^0 == 0 /\ i_5^0 >= 0), cost: NONTERM 14: l6 -> l2 : 1+d_6^0 <= 0, cost: 3 Applied chaining First rule: l6 -> l2 : 1+d_6^0 <= 0, cost: 3 Second rule: l2 -> l2 : i_5^0'=-d_6^0*n0+i_5^0, (-d_6^0*(-1+n0)+i_5^0 >= 0 /\ i_5^0 >= 0 /\ n0 >= 0), cost: 2*n0 New rule: l6 -> l2 : i_5^0'=-d_6^0*n0+i_5^0, (-d_6^0*(-1+n0)+i_5^0 >= 0 /\ i_5^0 >= 0 /\ 1+d_6^0 <= 0 /\ n0 >= 0), cost: 3+2*n0 Applied chaining First rule: l6 -> l2 : 1+d_6^0 <= 0, cost: 3 Second rule: l2 -> [7] : (i_5^0 >= 0 /\ 1+d_6^0 <= 0), cost: NONTERM New rule: l6 -> [7] : (i_5^0 >= 0 /\ 1+d_6^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 16 17 18 Chained accelerated rules with incoming rules Start location: l6 14: l6 -> l2 : 1+d_6^0 <= 0, cost: 3 19: l6 -> l2 : i_5^0'=-d_6^0*n0+i_5^0, (-d_6^0*(-1+n0)+i_5^0 >= 0 /\ i_5^0 >= 0 /\ 1+d_6^0 <= 0 /\ n0 >= 0), cost: 3+2*n0 20: l6 -> [7] : (i_5^0 >= 0 /\ 1+d_6^0 <= 0), cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l6 20: l6 -> [7] : (i_5^0 >= 0 /\ 1+d_6^0 <= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 20 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (i_5^0 >= 0 /\ 1+d_6^0 <= 0)