NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : Result_4^0'=Result_4^post_1, cnt_33^0'=cnt_33^post_1, cnt_40^0'=cnt_40^post_1, lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, px_8^0'=px_8^post_1, py_6^0'=py_6^post_1, q_9^0'=q_9^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ px_8^post_1==px_8^post_1 && x_7^post_1==x_7^post_1 && py_6^post_1==py_6^post_1 && y_5^post_1==y_5^post_1 && q_9^post_1==py_6^post_1 && Result_4^0==Result_4^post_1 && cnt_33^0==cnt_33^post_1 && cnt_40^0==cnt_40^post_1 && lt_10^0==lt_10^post_1 && lt_11^0==lt_11^post_1 && lt_12^0==lt_12^post_1 ], cost: 1 1: l1 -> l2 : Result_4^0'=Result_4^post_2, cnt_33^0'=cnt_33^post_2, cnt_40^0'=cnt_40^post_2, lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_12^0'=lt_12^post_2, px_8^0'=px_8^post_2, py_6^0'=py_6^post_2, q_9^0'=q_9^post_2, x_7^0'=x_7^post_2, y_5^0'=y_5^post_2, [ lt_11^1_1==y_5^0 && lt_12^1_1==cnt_33^0 && lt_12^1_1<=0 && lt_11^post_2==lt_11^post_2 && lt_12^post_2==lt_12^post_2 && Result_4^post_2==Result_4^post_2 && cnt_33^0==cnt_33^post_2 && cnt_40^0==cnt_40^post_2 && lt_10^0==lt_10^post_2 && px_8^0==px_8^post_2 && py_6^0==py_6^post_2 && q_9^0==q_9^post_2 && x_7^0==x_7^post_2 && y_5^0==y_5^post_2 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, cnt_33^0'=cnt_33^post_3, cnt_40^0'=cnt_40^post_3, lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, px_8^0'=px_8^post_3, py_6^0'=py_6^post_3, q_9^0'=q_9^post_3, x_7^0'=x_7^post_3, y_5^0'=y_5^post_3, [ lt_11^1_2_1==y_5^0 && lt_12^1_2_1==cnt_33^0 && 0<=-1+lt_12^1_2_1 && lt_11^post_3==lt_11^post_3 && lt_12^post_3==lt_12^post_3 && lt_10^1_1==cnt_40^0 && lt_10^post_3==lt_10^post_3 && q_9^post_3==px_8^0 && Result_4^0==Result_4^post_3 && cnt_33^0==cnt_33^post_3 && cnt_40^0==cnt_40^post_3 && px_8^0==px_8^post_3 && py_6^0==py_6^post_3 && x_7^0==x_7^post_3 && y_5^0==y_5^post_3 ], cost: 1 3: l3 -> l2 : Result_4^0'=Result_4^post_4, cnt_33^0'=cnt_33^post_4, cnt_40^0'=cnt_40^post_4, lt_10^0'=lt_10^post_4, lt_11^0'=lt_11^post_4, lt_12^0'=lt_12^post_4, px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=q_9^post_4, x_7^0'=x_7^post_4, y_5^0'=y_5^post_4, [ lt_11^1_2_2==x_7^0 && lt_12^1_3_1==-1+cnt_40^0 && lt_12^1_3_1<=0 && lt_11^post_4==lt_11^post_4 && lt_12^post_4==lt_12^post_4 && Result_4^post_4==Result_4^post_4 && cnt_33^0==cnt_33^post_4 && cnt_40^0==cnt_40^post_4 && lt_10^0==lt_10^post_4 && px_8^0==px_8^post_4 && py_6^0==py_6^post_4 && q_9^0==q_9^post_4 && x_7^0==x_7^post_4 && y_5^0==y_5^post_4 ], cost: 1 4: l3 -> l4 : Result_4^0'=Result_4^post_5, cnt_33^0'=cnt_33^post_5, cnt_40^0'=cnt_40^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, px_8^0'=px_8^post_5, py_6^0'=py_6^post_5, q_9^0'=q_9^post_5, x_7^0'=x_7^post_5, y_5^0'=y_5^post_5, [ lt_11^1_3_1==x_7^0 && lt_12^1_4_1==-1+cnt_40^0 && 0<=-1+lt_12^1_4_1 && lt_11^post_5==lt_11^post_5 && lt_12^post_5==lt_12^post_5 && lt_10^1_2==-1+cnt_40^0 && lt_10^post_5==lt_10^post_5 && q_9^post_5==px_8^0 && Result_4^0==Result_4^post_5 && cnt_33^0==cnt_33^post_5 && cnt_40^0==cnt_40^post_5 && px_8^0==px_8^post_5 && py_6^0==py_6^post_5 && x_7^0==x_7^post_5 && y_5^0==y_5^post_5 ], cost: 1 5: l4 -> l3 : Result_4^0'=Result_4^post_6, cnt_33^0'=cnt_33^post_6, cnt_40^0'=cnt_40^post_6, lt_10^0'=lt_10^post_6, lt_11^0'=lt_11^post_6, lt_12^0'=lt_12^post_6, px_8^0'=px_8^post_6, py_6^0'=py_6^post_6, q_9^0'=q_9^post_6, x_7^0'=x_7^post_6, y_5^0'=y_5^post_6, [ Result_4^0==Result_4^post_6 && cnt_33^0==cnt_33^post_6 && cnt_40^0==cnt_40^post_6 && lt_10^0==lt_10^post_6 && lt_11^0==lt_11^post_6 && lt_12^0==lt_12^post_6 && px_8^0==px_8^post_6 && py_6^0==py_6^post_6 && q_9^0==q_9^post_6 && x_7^0==x_7^post_6 && y_5^0==y_5^post_6 ], cost: 1 6: l5 -> l0 : Result_4^0'=Result_4^post_7, cnt_33^0'=cnt_33^post_7, cnt_40^0'=cnt_40^post_7, lt_10^0'=lt_10^post_7, lt_11^0'=lt_11^post_7, lt_12^0'=lt_12^post_7, px_8^0'=px_8^post_7, py_6^0'=py_6^post_7, q_9^0'=q_9^post_7, x_7^0'=x_7^post_7, y_5^0'=y_5^post_7, [ Result_4^0==Result_4^post_7 && cnt_33^0==cnt_33^post_7 && cnt_40^0==cnt_40^post_7 && lt_10^0==lt_10^post_7 && lt_11^0==lt_11^post_7 && lt_12^0==lt_12^post_7 && px_8^0==px_8^post_7 && py_6^0==py_6^post_7 && q_9^0==q_9^post_7 && x_7^0==x_7^post_7 && y_5^0==y_5^post_7 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: l5 -> l0 : Result_4^0'=Result_4^post_7, cnt_33^0'=cnt_33^post_7, cnt_40^0'=cnt_40^post_7, lt_10^0'=lt_10^post_7, lt_11^0'=lt_11^post_7, lt_12^0'=lt_12^post_7, px_8^0'=px_8^post_7, py_6^0'=py_6^post_7, q_9^0'=q_9^post_7, x_7^0'=x_7^post_7, y_5^0'=y_5^post_7, [ Result_4^0==Result_4^post_7 && cnt_33^0==cnt_33^post_7 && cnt_40^0==cnt_40^post_7 && lt_10^0==lt_10^post_7 && lt_11^0==lt_11^post_7 && lt_12^0==lt_12^post_7 && px_8^0==px_8^post_7 && py_6^0==py_6^post_7 && q_9^0==q_9^post_7 && x_7^0==x_7^post_7 && y_5^0==y_5^post_7 ], cost: 1 Removed unreachable and leaf rules: Start location: l5 0: l0 -> l1 : Result_4^0'=Result_4^post_1, cnt_33^0'=cnt_33^post_1, cnt_40^0'=cnt_40^post_1, lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, px_8^0'=px_8^post_1, py_6^0'=py_6^post_1, q_9^0'=q_9^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ px_8^post_1==px_8^post_1 && x_7^post_1==x_7^post_1 && py_6^post_1==py_6^post_1 && y_5^post_1==y_5^post_1 && q_9^post_1==py_6^post_1 && Result_4^0==Result_4^post_1 && cnt_33^0==cnt_33^post_1 && cnt_40^0==cnt_40^post_1 && lt_10^0==lt_10^post_1 && lt_11^0==lt_11^post_1 && lt_12^0==lt_12^post_1 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, cnt_33^0'=cnt_33^post_3, cnt_40^0'=cnt_40^post_3, lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, px_8^0'=px_8^post_3, py_6^0'=py_6^post_3, q_9^0'=q_9^post_3, x_7^0'=x_7^post_3, y_5^0'=y_5^post_3, [ lt_11^1_2_1==y_5^0 && lt_12^1_2_1==cnt_33^0 && 0<=-1+lt_12^1_2_1 && lt_11^post_3==lt_11^post_3 && lt_12^post_3==lt_12^post_3 && lt_10^1_1==cnt_40^0 && lt_10^post_3==lt_10^post_3 && q_9^post_3==px_8^0 && Result_4^0==Result_4^post_3 && cnt_33^0==cnt_33^post_3 && cnt_40^0==cnt_40^post_3 && px_8^0==px_8^post_3 && py_6^0==py_6^post_3 && x_7^0==x_7^post_3 && y_5^0==y_5^post_3 ], cost: 1 4: l3 -> l4 : Result_4^0'=Result_4^post_5, cnt_33^0'=cnt_33^post_5, cnt_40^0'=cnt_40^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, px_8^0'=px_8^post_5, py_6^0'=py_6^post_5, q_9^0'=q_9^post_5, x_7^0'=x_7^post_5, y_5^0'=y_5^post_5, [ lt_11^1_3_1==x_7^0 && lt_12^1_4_1==-1+cnt_40^0 && 0<=-1+lt_12^1_4_1 && lt_11^post_5==lt_11^post_5 && lt_12^post_5==lt_12^post_5 && lt_10^1_2==-1+cnt_40^0 && lt_10^post_5==lt_10^post_5 && q_9^post_5==px_8^0 && Result_4^0==Result_4^post_5 && cnt_33^0==cnt_33^post_5 && cnt_40^0==cnt_40^post_5 && px_8^0==px_8^post_5 && py_6^0==py_6^post_5 && x_7^0==x_7^post_5 && y_5^0==y_5^post_5 ], cost: 1 5: l4 -> l3 : Result_4^0'=Result_4^post_6, cnt_33^0'=cnt_33^post_6, cnt_40^0'=cnt_40^post_6, lt_10^0'=lt_10^post_6, lt_11^0'=lt_11^post_6, lt_12^0'=lt_12^post_6, px_8^0'=px_8^post_6, py_6^0'=py_6^post_6, q_9^0'=q_9^post_6, x_7^0'=x_7^post_6, y_5^0'=y_5^post_6, [ Result_4^0==Result_4^post_6 && cnt_33^0==cnt_33^post_6 && cnt_40^0==cnt_40^post_6 && lt_10^0==lt_10^post_6 && lt_11^0==lt_11^post_6 && lt_12^0==lt_12^post_6 && px_8^0==px_8^post_6 && py_6^0==py_6^post_6 && q_9^0==q_9^post_6 && x_7^0==x_7^post_6 && y_5^0==y_5^post_6 ], cost: 1 6: l5 -> l0 : Result_4^0'=Result_4^post_7, cnt_33^0'=cnt_33^post_7, cnt_40^0'=cnt_40^post_7, lt_10^0'=lt_10^post_7, lt_11^0'=lt_11^post_7, lt_12^0'=lt_12^post_7, px_8^0'=px_8^post_7, py_6^0'=py_6^post_7, q_9^0'=q_9^post_7, x_7^0'=x_7^post_7, y_5^0'=y_5^post_7, [ Result_4^0==Result_4^post_7 && cnt_33^0==cnt_33^post_7 && cnt_40^0==cnt_40^post_7 && lt_10^0==lt_10^post_7 && lt_11^0==lt_11^post_7 && lt_12^0==lt_12^post_7 && px_8^0==px_8^post_7 && py_6^0==py_6^post_7 && q_9^0==q_9^post_7 && x_7^0==x_7^post_7 && y_5^0==y_5^post_7 ], cost: 1 Simplified all rules, resulting in: Start location: l5 0: l0 -> l1 : px_8^0'=px_8^post_1, py_6^0'=q_9^post_1, q_9^0'=q_9^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [], cost: 1 2: l1 -> l3 : lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, q_9^0'=px_8^0, [ 0<=-1+cnt_33^0 ], cost: 1 4: l3 -> l4 : lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, q_9^0'=px_8^0, [ 0<=-2+cnt_40^0 ], cost: 1 5: l4 -> l3 : [], cost: 1 6: l5 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 9: l3 -> l3 : lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, q_9^0'=px_8^0, [ 0<=-2+cnt_40^0 ], cost: 2 8: l5 -> l3 : lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, px_8^0'=px_8^post_1, py_6^0'=q_9^post_1, q_9^0'=px_8^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ 0<=-1+cnt_33^0 ], cost: 3 Accelerating simple loops of location 3. Accelerating the following rules: 9: l3 -> l3 : lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, q_9^0'=px_8^0, [ 0<=-2+cnt_40^0 ], cost: 2 Accelerated rule 9 with non-termination, yielding the new rule 10. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 9. Accelerated all simple loops using metering functions (where possible): Start location: l5 10: l3 -> [6] : [ 0<=-2+cnt_40^0 ], cost: NONTERM 8: l5 -> l3 : lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, px_8^0'=px_8^post_1, py_6^0'=q_9^post_1, q_9^0'=px_8^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ 0<=-1+cnt_33^0 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: l5 8: l5 -> l3 : lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, px_8^0'=px_8^post_1, py_6^0'=q_9^post_1, q_9^0'=px_8^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ 0<=-1+cnt_33^0 ], cost: 3 11: l5 -> [6] : [ 0<=-1+cnt_33^0 && 0<=-2+cnt_40^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l5 11: l5 -> [6] : [ 0<=-1+cnt_33^0 && 0<=-2+cnt_40^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 11: l5 -> [6] : [ 0<=-1+cnt_33^0 && 0<=-2+cnt_40^0 ], cost: NONTERM Computing asymptotic complexity for rule 11 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ 0<=-1+cnt_33^0 && 0<=-2+cnt_40^0 ] NO