NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: [0] 0: [0] -> [1] : [ z>=3 ], cost: 1 1: [1] -> [2] : [ z>=3 ], cost: 1 2: [2] -> [1] : z'=nondet, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: [0] -> [1] : [ z>=3 ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: [0] 0: [0] -> [1] : [ z>=3 ], cost: 1 3: [1] -> [1] : z'=nondet, [ z>=3 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 3: [1] -> [1] : z'=nondet, [ z>=3 ], cost: 2 [test] deduced pseudo-invariant z-nondet<=0, also trying -z+nondet<=-1 Accelerated rule 3 with non-termination, yielding the new rule 4. Accelerated rule 3 with non-termination, yielding the new rule 5. Accelerated rule 3 with backward acceleration, yielding the new rule 6. [accelerate] Nesting with 0 inner and 1 outer candidates Also removing duplicate rules: 5. Accelerated all simple loops using metering functions (where possible): Start location: [0] 0: [0] -> [1] : [ z>=3 ], cost: 1 3: [1] -> [1] : z'=nondet, [ z>=3 ], cost: 2 4: [1] -> [3] : [ z>=3 && nondet>=3 ], cost: NONTERM 6: [1] -> [3] : [ z>=3 && z-nondet<=0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: [0] 0: [0] -> [1] : [ z>=3 ], cost: 1 7: [0] -> [1] : z'=nondet, [ z>=3 && z>=3 ], cost: 3 8: [0] -> [3] : [ z>=3 && z>=3 ], cost: NONTERM 9: [0] -> [3] : [ z>=3 && z>=3 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: [0] 8: [0] -> [3] : [ z>=3 && z>=3 ], cost: NONTERM 9: [0] -> [3] : [ z>=3 && z>=3 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: [0] 9: [0] -> [3] : [ z>=3 && z>=3 ], cost: NONTERM Computing asymptotic complexity for rule 9 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: [ z>=3 && z>=3 ] NO