NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : p^0'=p^post_1, y_1^0'=y_1^post_1, [ p^0==p^post_1 && y_1^0==y_1^post_1 ], cost: 1 1: l1 -> l0 : p^0'=p^post_2, y_1^0'=y_1^post_2, [ p^0==p^post_2 && y_1^0==y_1^post_2 ], cost: 1 2: l2 -> l3 : p^0'=p^post_3, y_1^0'=y_1^post_3, [ p^post_3==0 && y_1^0==y_1^post_3 ], cost: 1 3: l3 -> l4 : p^0'=p^post_4, y_1^0'=y_1^post_4, [ 1<=y_1^0 && y_1^post_4==-1+y_1^0 && p^0==p^post_4 ], cost: 1 5: l3 -> l0 : p^0'=p^post_6, y_1^0'=y_1^post_6, [ y_1^0<=0 && p^post_6==-1 && y_1^0==y_1^post_6 ], cost: 1 4: l4 -> l3 : p^0'=p^post_5, y_1^0'=y_1^post_5, [ p^0==p^post_5 && y_1^0==y_1^post_5 ], cost: 1 6: l5 -> l2 : p^0'=p^post_7, y_1^0'=y_1^post_7, [ p^0==p^post_7 && y_1^0==y_1^post_7 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: l5 -> l2 : p^0'=p^post_7, y_1^0'=y_1^post_7, [ p^0==p^post_7 && y_1^0==y_1^post_7 ], cost: 1 Simplified all rules, resulting in: Start location: l5 0: l0 -> l1 : [], cost: 1 1: l1 -> l0 : [], cost: 1 2: l2 -> l3 : p^0'=0, [], cost: 1 3: l3 -> l4 : y_1^0'=-1+y_1^0, [ 1<=y_1^0 ], cost: 1 5: l3 -> l0 : p^0'=-1, [ y_1^0<=0 ], cost: 1 4: l4 -> l3 : [], cost: 1 6: l5 -> l2 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 9: l0 -> l0 : [], cost: 2 5: l3 -> l0 : p^0'=-1, [ y_1^0<=0 ], cost: 1 8: l3 -> l3 : y_1^0'=-1+y_1^0, [ 1<=y_1^0 ], cost: 2 7: l5 -> l3 : p^0'=0, [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 9: l0 -> l0 : [], 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. Accelerating simple loops of location 3. Accelerating the following rules: 8: l3 -> l3 : y_1^0'=-1+y_1^0, [ 1<=y_1^0 ], cost: 2 Accelerated rule 8 with backward acceleration, yielding the new rule 11. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: l5 10: l0 -> [6] : [], cost: NONTERM 5: l3 -> l0 : p^0'=-1, [ y_1^0<=0 ], cost: 1 11: l3 -> l3 : y_1^0'=0, [ y_1^0>=0 ], cost: 2*y_1^0 7: l5 -> l3 : p^0'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l5 5: l3 -> l0 : p^0'=-1, [ y_1^0<=0 ], cost: 1 12: l3 -> [6] : [ y_1^0<=0 ], cost: NONTERM 7: l5 -> l3 : p^0'=0, [], cost: 2 13: l5 -> l3 : p^0'=0, y_1^0'=0, [ y_1^0>=0 ], cost: 2+2*y_1^0 Removed unreachable locations (and leaf rules with constant cost): Start location: l5 12: l3 -> [6] : [ y_1^0<=0 ], cost: NONTERM 7: l5 -> l3 : p^0'=0, [], cost: 2 13: l5 -> l3 : p^0'=0, y_1^0'=0, [ y_1^0>=0 ], cost: 2+2*y_1^0 Eliminated locations (on tree-shaped paths): Start location: l5 14: l5 -> [6] : [ y_1^0<=0 ], cost: NONTERM 15: l5 -> [6] : [ y_1^0>=0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 14: l5 -> [6] : [ y_1^0<=0 ], cost: NONTERM 15: l5 -> [6] : [ y_1^0>=0 ], cost: NONTERM Computing asymptotic complexity for rule 14 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: [ y_1^0<=0 ] NO