NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l3 0: l0 -> l1 : x^0'=x^post_1, [ x^post_1==300+x^0 && 101<=x^post_1 ], cost: 1 1: l1 -> l0 : x^0'=x^post_2, [ x^post_2==400+x^0 && 101<=x^post_2 ], cost: 1 2: l2 -> l0 : x^0'=x^post_3, [ x^post_3==200+x^0 && 101<=x^post_3 ], cost: 1 3: l2 -> l1 : x^0'=x^post_4, [ x^post_4==100+x^0 && 101<=x^post_4 ], cost: 1 4: l3 -> l2 : x^0'=x^post_5, [ x^0==x^post_5 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: l3 -> l2 : x^0'=x^post_5, [ x^0==x^post_5 ], cost: 1 Simplified all rules, resulting in: Start location: l3 0: l0 -> l1 : x^0'=300+x^0, [ 101<=300+x^0 ], cost: 1 1: l1 -> l0 : x^0'=400+x^0, [ 101<=400+x^0 ], cost: 1 2: l2 -> l0 : x^0'=200+x^0, [ 101<=200+x^0 ], cost: 1 3: l2 -> l1 : x^0'=100+x^0, [ 101<=100+x^0 ], cost: 1 4: l3 -> l2 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on tree-shaped paths): Start location: l3 0: l0 -> l1 : x^0'=300+x^0, [ 101<=300+x^0 ], cost: 1 1: l1 -> l0 : x^0'=400+x^0, [ 101<=400+x^0 ], cost: 1 5: l3 -> l0 : x^0'=200+x^0, [ 101<=200+x^0 ], cost: 2 6: l3 -> l1 : x^0'=100+x^0, [ 101<=100+x^0 ], cost: 2 Eliminated location l0 (as a last resort): Start location: l3 7: l1 -> l1 : x^0'=700+x^0, [ 101<=400+x^0 ], cost: 2 6: l3 -> l1 : x^0'=100+x^0, [ 101<=100+x^0 ], cost: 2 8: l3 -> l1 : x^0'=500+x^0, [ 101<=200+x^0 ], cost: 3 Accelerating simple loops of location 1. Accelerating the following rules: 7: l1 -> l1 : x^0'=700+x^0, [ 101<=400+x^0 ], cost: 2 Accelerated rule 7 with non-termination, yielding the new rule 9. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 7. Accelerated all simple loops using metering functions (where possible): Start location: l3 9: l1 -> [4] : [ 101<=400+x^0 ], cost: NONTERM 6: l3 -> l1 : x^0'=100+x^0, [ 101<=100+x^0 ], cost: 2 8: l3 -> l1 : x^0'=500+x^0, [ 101<=200+x^0 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: l3 6: l3 -> l1 : x^0'=100+x^0, [ 101<=100+x^0 ], cost: 2 8: l3 -> l1 : x^0'=500+x^0, [ 101<=200+x^0 ], cost: 3 10: l3 -> [4] : [ 101<=100+x^0 ], cost: NONTERM 11: l3 -> [4] : [ 101<=200+x^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l3 10: l3 -> [4] : [ 101<=100+x^0 ], cost: NONTERM 11: l3 -> [4] : [ 101<=200+x^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l3 10: l3 -> [4] : [ 101<=100+x^0 ], cost: NONTERM 11: l3 -> [4] : [ 101<=200+x^0 ], cost: NONTERM Computing asymptotic complexity for rule 10 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: [ 101<=100+x^0 ] NO