NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post_1, ct_12^0'=ct_12^post_1, ct_13^0'=ct_13^post_1, ct_21^0'=ct_21^post_1, ct_27^0'=ct_27^post_1, lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_9^0'=lt_9^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ lt_10^1_1==ct_21^0 && lt_11^1_1==ct_27^0 && lt_11^1_1-lt_10^1_1<=0 && lt_10^post_1==lt_10^post_1 && lt_11^post_1==lt_11^post_1 && Result_4^post_1==Result_4^post_1 && ct_12^0==ct_12^post_1 && ct_13^0==ct_13^post_1 && ct_21^0==ct_21^post_1 && ct_27^0==ct_27^post_1 && lt_9^0==lt_9^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1 1: l0 -> l2 : Result_4^0'=Result_4^post_2, ct_12^0'=ct_12^post_2, ct_13^0'=ct_13^post_2, ct_21^0'=ct_21^post_2, ct_27^0'=ct_27^post_2, lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_9^0'=lt_9^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ lt_10^1_2==ct_21^0 && lt_11^1_2_1==ct_27^0 && 0<=-1-lt_10^1_2+lt_11^1_2_1 && lt_10^post_2==lt_10^post_2 && lt_11^post_2==lt_11^post_2 && lt_9^1_1==ct_21^0 && lt_9^post_2==lt_9^post_2 && Result_4^0==Result_4^post_2 && ct_12^0==ct_12^post_2 && ct_13^0==ct_13^post_2 && ct_21^0==ct_21^post_2 && ct_27^0==ct_27^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 2: l2 -> l0 : Result_4^0'=Result_4^post_3, ct_12^0'=ct_12^post_3, ct_13^0'=ct_13^post_3, ct_21^0'=ct_21^post_3, ct_27^0'=ct_27^post_3, lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_9^0'=lt_9^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && ct_12^0==ct_12^post_3 && ct_13^0==ct_13^post_3 && ct_21^0==ct_21^post_3 && ct_27^0==ct_27^post_3 && lt_10^0==lt_10^post_3 && lt_11^0==lt_11^post_3 && lt_9^0==lt_9^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1 3: l3 -> l0 : Result_4^0'=Result_4^post_4, ct_12^0'=ct_12^post_4, ct_13^0'=ct_13^post_4, ct_21^0'=ct_21^post_4, ct_27^0'=ct_27^post_4, lt_10^0'=lt_10^post_4, lt_11^0'=lt_11^post_4, lt_9^0'=lt_9^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ y_6^post_4==y_6^post_4 && x_5^post_4==x_5^post_4 && ct_13^1_1==ct_13^1_1 && ct_13^post_4==ct_13^post_4 && ct_12^1_1==ct_12^1_1 && ct_12^post_4==ct_12^post_4 && Result_4^0==Result_4^post_4 && ct_21^0==ct_21^post_4 && ct_27^0==ct_27^post_4 && lt_10^0==lt_10^post_4 && lt_11^0==lt_11^post_4 && lt_9^0==lt_9^post_4 ], cost: 1 4: l4 -> l3 : Result_4^0'=Result_4^post_5, ct_12^0'=ct_12^post_5, ct_13^0'=ct_13^post_5, ct_21^0'=ct_21^post_5, ct_27^0'=ct_27^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_9^0'=lt_9^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^0==Result_4^post_5 && ct_12^0==ct_12^post_5 && ct_13^0==ct_13^post_5 && ct_21^0==ct_21^post_5 && ct_27^0==ct_27^post_5 && lt_10^0==lt_10^post_5 && lt_11^0==lt_11^post_5 && lt_9^0==lt_9^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: l4 -> l3 : Result_4^0'=Result_4^post_5, ct_12^0'=ct_12^post_5, ct_13^0'=ct_13^post_5, ct_21^0'=ct_21^post_5, ct_27^0'=ct_27^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_9^0'=lt_9^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^0==Result_4^post_5 && ct_12^0==ct_12^post_5 && ct_13^0==ct_13^post_5 && ct_21^0==ct_21^post_5 && ct_27^0==ct_27^post_5 && lt_10^0==lt_10^post_5 && lt_11^0==lt_11^post_5 && lt_9^0==lt_9^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 Removed unreachable and leaf rules: Start location: l4 1: l0 -> l2 : Result_4^0'=Result_4^post_2, ct_12^0'=ct_12^post_2, ct_13^0'=ct_13^post_2, ct_21^0'=ct_21^post_2, ct_27^0'=ct_27^post_2, lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_9^0'=lt_9^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ lt_10^1_2==ct_21^0 && lt_11^1_2_1==ct_27^0 && 0<=-1-lt_10^1_2+lt_11^1_2_1 && lt_10^post_2==lt_10^post_2 && lt_11^post_2==lt_11^post_2 && lt_9^1_1==ct_21^0 && lt_9^post_2==lt_9^post_2 && Result_4^0==Result_4^post_2 && ct_12^0==ct_12^post_2 && ct_13^0==ct_13^post_2 && ct_21^0==ct_21^post_2 && ct_27^0==ct_27^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 2: l2 -> l0 : Result_4^0'=Result_4^post_3, ct_12^0'=ct_12^post_3, ct_13^0'=ct_13^post_3, ct_21^0'=ct_21^post_3, ct_27^0'=ct_27^post_3, lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_9^0'=lt_9^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && ct_12^0==ct_12^post_3 && ct_13^0==ct_13^post_3 && ct_21^0==ct_21^post_3 && ct_27^0==ct_27^post_3 && lt_10^0==lt_10^post_3 && lt_11^0==lt_11^post_3 && lt_9^0==lt_9^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1 3: l3 -> l0 : Result_4^0'=Result_4^post_4, ct_12^0'=ct_12^post_4, ct_13^0'=ct_13^post_4, ct_21^0'=ct_21^post_4, ct_27^0'=ct_27^post_4, lt_10^0'=lt_10^post_4, lt_11^0'=lt_11^post_4, lt_9^0'=lt_9^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ y_6^post_4==y_6^post_4 && x_5^post_4==x_5^post_4 && ct_13^1_1==ct_13^1_1 && ct_13^post_4==ct_13^post_4 && ct_12^1_1==ct_12^1_1 && ct_12^post_4==ct_12^post_4 && Result_4^0==Result_4^post_4 && ct_21^0==ct_21^post_4 && ct_27^0==ct_27^post_4 && lt_10^0==lt_10^post_4 && lt_11^0==lt_11^post_4 && lt_9^0==lt_9^post_4 ], cost: 1 4: l4 -> l3 : Result_4^0'=Result_4^post_5, ct_12^0'=ct_12^post_5, ct_13^0'=ct_13^post_5, ct_21^0'=ct_21^post_5, ct_27^0'=ct_27^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_9^0'=lt_9^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^0==Result_4^post_5 && ct_12^0==ct_12^post_5 && ct_13^0==ct_13^post_5 && ct_21^0==ct_21^post_5 && ct_27^0==ct_27^post_5 && lt_10^0==lt_10^post_5 && lt_11^0==lt_11^post_5 && lt_9^0==lt_9^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 Simplified all rules, resulting in: Start location: l4 1: l0 -> l2 : lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_9^0'=lt_9^post_2, [ 0<=-1+ct_27^0-ct_21^0 ], cost: 1 2: l2 -> l0 : [], cost: 1 3: l3 -> l0 : ct_12^0'=ct_12^post_4, ct_13^0'=ct_13^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [], cost: 1 4: l4 -> l3 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l4 6: l0 -> l0 : lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_9^0'=lt_9^post_2, [ 0<=-1+ct_27^0-ct_21^0 ], cost: 2 5: l4 -> l0 : ct_12^0'=ct_12^post_4, ct_13^0'=ct_13^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 6: l0 -> l0 : lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_9^0'=lt_9^post_2, [ 0<=-1+ct_27^0-ct_21^0 ], cost: 2 Accelerated rule 6 with non-termination, yielding the new rule 7. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 6. Accelerated all simple loops using metering functions (where possible): Start location: l4 7: l0 -> [5] : [ 0<=-1+ct_27^0-ct_21^0 ], cost: NONTERM 5: l4 -> l0 : ct_12^0'=ct_12^post_4, ct_13^0'=ct_13^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l4 5: l4 -> l0 : ct_12^0'=ct_12^post_4, ct_13^0'=ct_13^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [], cost: 2 8: l4 -> [5] : [ 0<=-1+ct_27^0-ct_21^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l4 8: l4 -> [5] : [ 0<=-1+ct_27^0-ct_21^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l4 8: l4 -> [5] : [ 0<=-1+ct_27^0-ct_21^0 ], cost: NONTERM Computing asymptotic complexity for rule 8 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+ct_27^0-ct_21^0 ] NO