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