NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l7 0: l0 -> l1 : __const_1024^0'=__const_1024^post_1, i5^0'=i5^post_1, n_promoted_1^0'=n_promoted_1^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 && tmp___0^post_1==tmp___0^post_1 && __const_1024^0==__const_1024^post_1 && i5^0==i5^post_1 && n_promoted_1^0==n_promoted_1^post_1 && tmp^0==tmp^post_1 ], cost: 1 1: l0 -> l1 : __const_1024^0'=__const_1024^post_2, i5^0'=i5^post_2, n_promoted_1^0'=n_promoted_1^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ __const_1024^0<=n_promoted_1^0 && __const_1024^0==__const_1024^post_2 && i5^0==i5^post_2 && n_promoted_1^0==n_promoted_1^post_2 && tmp^0==tmp^post_2 && tmp___0^0==tmp___0^post_2 ], cost: 1 2: l1 -> l2 : __const_1024^0'=__const_1024^post_3, i5^0'=i5^post_3, n_promoted_1^0'=n_promoted_1^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, [ i5^post_3==0 && __const_1024^0==__const_1024^post_3 && n_promoted_1^0==n_promoted_1^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 ], cost: 1 5: l2 -> l4 : __const_1024^0'=__const_1024^post_6, i5^0'=i5^post_6, n_promoted_1^0'=n_promoted_1^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, [ __const_1024^0==__const_1024^post_6 && i5^0==i5^post_6 && n_promoted_1^0==n_promoted_1^post_6 && tmp^0==tmp^post_6 && tmp___0^0==tmp___0^post_6 ], cost: 1 3: l3 -> l0 : __const_1024^0'=__const_1024^post_4, i5^0'=i5^post_4, n_promoted_1^0'=n_promoted_1^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, [ 1<=n_promoted_1^0 && __const_1024^0==__const_1024^post_4 && i5^0==i5^post_4 && n_promoted_1^0==n_promoted_1^post_4 && tmp^0==tmp^post_4 && tmp___0^0==tmp___0^post_4 ], cost: 1 4: l3 -> l1 : __const_1024^0'=__const_1024^post_5, i5^0'=i5^post_5, n_promoted_1^0'=n_promoted_1^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, [ n_promoted_1^0<=0 && __const_1024^0==__const_1024^post_5 && i5^0==i5^post_5 && n_promoted_1^0==n_promoted_1^post_5 && tmp^0==tmp^post_5 && tmp___0^0==tmp___0^post_5 ], cost: 1 6: l4 -> l5 : __const_1024^0'=__const_1024^post_7, i5^0'=i5^post_7, n_promoted_1^0'=n_promoted_1^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, [ __const_1024^0==__const_1024^post_7 && i5^0==i5^post_7 && n_promoted_1^0==n_promoted_1^post_7 && tmp^0==tmp^post_7 && tmp___0^0==tmp___0^post_7 ], cost: 1 7: l4 -> l2 : __const_1024^0'=__const_1024^post_8, i5^0'=i5^post_8, n_promoted_1^0'=n_promoted_1^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ i5^post_8==1+i5^0 && __const_1024^0==__const_1024^post_8 && n_promoted_1^0==n_promoted_1^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1 8: l6 -> l3 : __const_1024^0'=__const_1024^post_9, i5^0'=i5^post_9, n_promoted_1^0'=n_promoted_1^post_9, tmp^0'=tmp^post_9, tmp___0^0'=tmp___0^post_9, [ tmp^post_9==tmp^post_9 && n_promoted_1^post_9==tmp^post_9 && __const_1024^0==__const_1024^post_9 && i5^0==i5^post_9 && tmp___0^0==tmp___0^post_9 ], cost: 1 9: l7 -> l6 : __const_1024^0'=__const_1024^post_10, i5^0'=i5^post_10, n_promoted_1^0'=n_promoted_1^post_10, tmp^0'=tmp^post_10, tmp___0^0'=tmp___0^post_10, [ __const_1024^0==__const_1024^post_10 && i5^0==i5^post_10 && n_promoted_1^0==n_promoted_1^post_10 && tmp^0==tmp^post_10 && tmp___0^0==tmp___0^post_10 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 9: l7 -> l6 : __const_1024^0'=__const_1024^post_10, i5^0'=i5^post_10, n_promoted_1^0'=n_promoted_1^post_10, tmp^0'=tmp^post_10, tmp___0^0'=tmp___0^post_10, [ __const_1024^0==__const_1024^post_10 && i5^0==i5^post_10 && n_promoted_1^0==n_promoted_1^post_10 && tmp^0==tmp^post_10 && tmp___0^0==tmp___0^post_10 ], cost: 1 Removed unreachable and leaf rules: Start location: l7 0: l0 -> l1 : __const_1024^0'=__const_1024^post_1, i5^0'=i5^post_1, n_promoted_1^0'=n_promoted_1^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 && tmp___0^post_1==tmp___0^post_1 && __const_1024^0==__const_1024^post_1 && i5^0==i5^post_1 && n_promoted_1^0==n_promoted_1^post_1 && tmp^0==tmp^post_1 ], cost: 1 1: l0 -> l1 : __const_1024^0'=__const_1024^post_2, i5^0'=i5^post_2, n_promoted_1^0'=n_promoted_1^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ __const_1024^0<=n_promoted_1^0 && __const_1024^0==__const_1024^post_2 && i5^0==i5^post_2 && n_promoted_1^0==n_promoted_1^post_2 && tmp^0==tmp^post_2 && tmp___0^0==tmp___0^post_2 ], cost: 1 2: l1 -> l2 : __const_1024^0'=__const_1024^post_3, i5^0'=i5^post_3, n_promoted_1^0'=n_promoted_1^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, [ i5^post_3==0 && __const_1024^0==__const_1024^post_3 && n_promoted_1^0==n_promoted_1^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 ], cost: 1 5: l2 -> l4 : __const_1024^0'=__const_1024^post_6, i5^0'=i5^post_6, n_promoted_1^0'=n_promoted_1^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, [ __const_1024^0==__const_1024^post_6 && i5^0==i5^post_6 && n_promoted_1^0==n_promoted_1^post_6 && tmp^0==tmp^post_6 && tmp___0^0==tmp___0^post_6 ], cost: 1 3: l3 -> l0 : __const_1024^0'=__const_1024^post_4, i5^0'=i5^post_4, n_promoted_1^0'=n_promoted_1^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, [ 1<=n_promoted_1^0 && __const_1024^0==__const_1024^post_4 && i5^0==i5^post_4 && n_promoted_1^0==n_promoted_1^post_4 && tmp^0==tmp^post_4 && tmp___0^0==tmp___0^post_4 ], cost: 1 4: l3 -> l1 : __const_1024^0'=__const_1024^post_5, i5^0'=i5^post_5, n_promoted_1^0'=n_promoted_1^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, [ n_promoted_1^0<=0 && __const_1024^0==__const_1024^post_5 && i5^0==i5^post_5 && n_promoted_1^0==n_promoted_1^post_5 && tmp^0==tmp^post_5 && tmp___0^0==tmp___0^post_5 ], cost: 1 7: l4 -> l2 : __const_1024^0'=__const_1024^post_8, i5^0'=i5^post_8, n_promoted_1^0'=n_promoted_1^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ i5^post_8==1+i5^0 && __const_1024^0==__const_1024^post_8 && n_promoted_1^0==n_promoted_1^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1 8: l6 -> l3 : __const_1024^0'=__const_1024^post_9, i5^0'=i5^post_9, n_promoted_1^0'=n_promoted_1^post_9, tmp^0'=tmp^post_9, tmp___0^0'=tmp___0^post_9, [ tmp^post_9==tmp^post_9 && n_promoted_1^post_9==tmp^post_9 && __const_1024^0==__const_1024^post_9 && i5^0==i5^post_9 && tmp___0^0==tmp___0^post_9 ], cost: 1 9: l7 -> l6 : __const_1024^0'=__const_1024^post_10, i5^0'=i5^post_10, n_promoted_1^0'=n_promoted_1^post_10, tmp^0'=tmp^post_10, tmp___0^0'=tmp___0^post_10, [ __const_1024^0==__const_1024^post_10 && i5^0==i5^post_10 && n_promoted_1^0==n_promoted_1^post_10 && tmp^0==tmp^post_10 && tmp___0^0==tmp___0^post_10 ], cost: 1 Simplified all rules, resulting in: Start location: l7 0: l0 -> l1 : tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 ], cost: 1 1: l0 -> l1 : [ __const_1024^0<=n_promoted_1^0 ], cost: 1 2: l1 -> l2 : i5^0'=0, [], cost: 1 5: l2 -> l4 : [], cost: 1 3: l3 -> l0 : [ 1<=n_promoted_1^0 ], cost: 1 4: l3 -> l1 : [ n_promoted_1^0<=0 ], cost: 1 7: l4 -> l2 : i5^0'=1+i5^0, [], cost: 1 8: l6 -> l3 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [], cost: 1 9: l7 -> l6 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l7 0: l0 -> l1 : tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 ], cost: 1 1: l0 -> l1 : [ __const_1024^0<=n_promoted_1^0 ], cost: 1 2: l1 -> l2 : i5^0'=0, [], cost: 1 11: l2 -> l2 : i5^0'=1+i5^0, [], cost: 2 3: l3 -> l0 : [ 1<=n_promoted_1^0 ], cost: 1 4: l3 -> l1 : [ n_promoted_1^0<=0 ], cost: 1 10: l7 -> l3 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 11: l2 -> l2 : i5^0'=1+i5^0, [], cost: 2 Accelerated rule 11 with non-termination, yielding the new rule 12. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: l7 0: l0 -> l1 : tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 ], cost: 1 1: l0 -> l1 : [ __const_1024^0<=n_promoted_1^0 ], cost: 1 2: l1 -> l2 : i5^0'=0, [], cost: 1 12: l2 -> [8] : [], cost: NONTERM 3: l3 -> l0 : [ 1<=n_promoted_1^0 ], cost: 1 4: l3 -> l1 : [ n_promoted_1^0<=0 ], cost: 1 10: l7 -> l3 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l7 0: l0 -> l1 : tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 ], cost: 1 1: l0 -> l1 : [ __const_1024^0<=n_promoted_1^0 ], cost: 1 2: l1 -> l2 : i5^0'=0, [], cost: 1 13: l1 -> [8] : [], cost: NONTERM 3: l3 -> l0 : [ 1<=n_promoted_1^0 ], cost: 1 4: l3 -> l1 : [ n_promoted_1^0<=0 ], cost: 1 10: l7 -> l3 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [], cost: 2 Removed unreachable locations (and leaf rules with constant cost): Start location: l7 0: l0 -> l1 : tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 ], cost: 1 1: l0 -> l1 : [ __const_1024^0<=n_promoted_1^0 ], cost: 1 13: l1 -> [8] : [], cost: NONTERM 3: l3 -> l0 : [ 1<=n_promoted_1^0 ], cost: 1 4: l3 -> l1 : [ n_promoted_1^0<=0 ], cost: 1 10: l7 -> l3 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l7 0: l0 -> l1 : tmp___0^0'=tmp___0^post_1, [ 1+n_promoted_1^0<=__const_1024^0 ], cost: 1 1: l0 -> l1 : [ __const_1024^0<=n_promoted_1^0 ], cost: 1 13: l1 -> [8] : [], cost: NONTERM 14: l7 -> l0 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [ 1<=tmp^post_9 ], cost: 3 15: l7 -> l1 : n_promoted_1^0'=tmp^post_9, tmp^0'=tmp^post_9, [ tmp^post_9<=0 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: l7 18: l7 -> [8] : [ tmp^post_9<=0 ], cost: NONTERM 19: l7 -> [8] : [ 1<=tmp^post_9 && 1+tmp^post_9<=__const_1024^0 ], cost: NONTERM 20: l7 -> [8] : [ 1<=tmp^post_9 && __const_1024^0<=tmp^post_9 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l7 18: l7 -> [8] : [ tmp^post_9<=0 ], cost: NONTERM 19: l7 -> [8] : [ 1<=tmp^post_9 && 1+tmp^post_9<=__const_1024^0 ], cost: NONTERM 20: l7 -> [8] : [ 1<=tmp^post_9 && __const_1024^0<=tmp^post_9 ], cost: NONTERM Computing asymptotic complexity for rule 18 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: [ tmp^post_9<=0 ] NO