NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: [0] 0: [0] -> [1] : [ z>=5 ], cost: 1 1: [1] -> [2] : [ y<=2 && w<=-5 ], cost: 1 2: [2] -> [3] : [ x>=y ], cost: 1 5: [2] -> [5] : [ x [4] : z'=1+z, w'=-1+w, x'=-z*w, [], cost: 1 4: [4] -> [2] : [ 0<=0 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: [0] -> [1] : [ z>=5 ], cost: 1 Removed unreachable and leaf rules: Start location: [0] 0: [0] -> [1] : [ z>=5 ], cost: 1 1: [1] -> [2] : [ y<=2 && w<=-5 ], cost: 1 2: [2] -> [3] : [ x>=y ], cost: 1 3: [3] -> [4] : z'=1+z, w'=-1+w, x'=-z*w, [], cost: 1 4: [4] -> [2] : [ 0<=0 ], cost: 1 Simplified all rules, resulting in: Start location: [0] 0: [0] -> [1] : [ z>=5 ], cost: 1 1: [1] -> [2] : [ y<=2 && w<=-5 ], cost: 1 2: [2] -> [3] : [ x>=y ], cost: 1 3: [3] -> [4] : z'=1+z, w'=-1+w, x'=-z*w, [], cost: 1 4: [4] -> [2] : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: [0] 6: [0] -> [2] : [ z>=5 && y<=2 && w<=-5 ], cost: 2 8: [2] -> [2] : z'=1+z, w'=-1+w, x'=-z*w, [ x>=y ], cost: 3 Accelerating simple loops of location 2. Accelerating the following rules: 8: [2] -> [2] : z'=1+z, w'=-1+w, x'=-z*w, [ x>=y ], cost: 3 Accelerated rule 8 with non-termination, yielding the new rule 9. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: [0] 6: [0] -> [2] : [ z>=5 && y<=2 && w<=-5 ], cost: 2 9: [2] -> [6] : [ x>=y ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: [0] 6: [0] -> [2] : [ z>=5 && y<=2 && w<=-5 ], cost: 2 10: [0] -> [6] : [ z>=5 && y<=2 && w<=-5 && x>=y ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: [0] 10: [0] -> [6] : [ z>=5 && y<=2 && w<=-5 && x>=y ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: [0] 10: [0] -> [6] : [ z>=5 && y<=2 && w<=-5 && x>=y ], 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: [ z>=5 && y<=2 && w<=-5 && x>=y ] NO