NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: [0] 0: [0] -> [1] : [ j>=1 && k>=1 ], cost: 1 1: [1] -> [2] : [ i>=0 ], cost: 1 2: [2] -> [1] : j'=1+j, k'=1+k, i'=j*k, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: [0] -> [1] : [ j>=1 && k>=1 ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: [0] 0: [0] -> [1] : [ j>=1 && k>=1 ], cost: 1 3: [1] -> [1] : j'=1+j, k'=1+k, i'=j*k, [ i>=0 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 3: [1] -> [1] : j'=1+j, k'=1+k, i'=j*k, [ i>=0 ], cost: 2 Accelerated rule 3 with non-termination, yielding the new rule 4. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 3. Accelerated all simple loops using metering functions (where possible): Start location: [0] 0: [0] -> [1] : [ j>=1 && k>=1 ], cost: 1 4: [1] -> [3] : [ i>=0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: [0] 0: [0] -> [1] : [ j>=1 && k>=1 ], cost: 1 5: [0] -> [3] : [ j>=1 && k>=1 && i>=0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: [0] 5: [0] -> [3] : [ j>=1 && k>=1 && i>=0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: [0] 5: [0] -> [3] : [ j>=1 && k>=1 && i>=0 ], cost: NONTERM Computing asymptotic complexity for rule 5 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: [ j>=1 && k>=1 && i>=0 ] NO