WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l10 0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, [ n^0<=i^0 && i^0==i^post_1 && j^0==j^post_1 && n^0==n^post_1 && tmp^0==tmp^post_1 ], cost: 1 1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && tmp^post_2==tmp^post_2 && i^0==i^post_2 && j^0==j^post_2 && n^0==n^post_2 ], cost: 1 6: l1 -> l7 : i^0'=i^post_7, j^0'=j^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ i^0==i^post_7 && j^0==j^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 ], cost: 1 10: l2 -> l1 : i^0'=i^post_11, j^0'=j^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, [ tmp^0<=0 && 0<=tmp^0 && i^0==i^post_11 && j^0==j^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 ], cost: 1 11: l2 -> l8 : i^0'=i^post_12, j^0'=j^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, [ 1<=tmp^0 && i^0==i^post_12 && j^0==j^post_12 && n^0==n^post_12 && tmp^0==tmp^post_12 ], cost: 1 12: l2 -> l8 : i^0'=i^post_13, j^0'=j^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, [ 1+tmp^0<=0 && i^0==i^post_13 && j^0==j^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 ], cost: 1 2: l3 -> l4 : i^0'=i^post_3, j^0'=j^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, [ n^0<=i^0 && i^0==i^post_3 && j^0==j^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 ], cost: 1 3: l3 -> l5 : i^0'=i^post_4, j^0'=j^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, [ 1+i^0<=n^0 && i^post_4==1+i^0 && j^post_4==0 && n^0==n^post_4 && tmp^0==tmp^post_4 ], cost: 1 5: l5 -> l0 : i^0'=i^post_6, j^0'=j^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, [ i^0==i^post_6 && j^0==j^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 ], cost: 1 4: l6 -> l3 : i^0'=i^post_5, j^0'=j^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, [ i^0==i^post_5 && j^0==j^post_5 && n^0==n^post_5 && tmp^0==tmp^post_5 ], cost: 1 7: l7 -> l6 : i^0'=i^post_8, j^0'=j^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, [ j^0<=0 && i^0==i^post_8 && j^0==j^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 ], cost: 1 8: l7 -> l6 : i^0'=i^post_9, j^0'=j^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, [ 1<=j^0 && i^post_9==-1+i^0 && j^0==j^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 ], cost: 1 9: l8 -> l5 : i^0'=i^post_10, j^0'=j^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, [ i^post_10==1+i^0 && j^post_10==1+j^0 && n^0==n^post_10 && tmp^0==tmp^post_10 ], cost: 1 13: l9 -> l6 : i^0'=i^post_14, j^0'=j^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, [ i^post_14==0 && j^0==j^post_14 && n^0==n^post_14 && tmp^0==tmp^post_14 ], cost: 1 14: l10 -> l9 : i^0'=i^post_15, j^0'=j^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 14: l10 -> l9 : i^0'=i^post_15, j^0'=j^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1 Removed unreachable and leaf rules: Start location: l10 0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, [ n^0<=i^0 && i^0==i^post_1 && j^0==j^post_1 && n^0==n^post_1 && tmp^0==tmp^post_1 ], cost: 1 1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && tmp^post_2==tmp^post_2 && i^0==i^post_2 && j^0==j^post_2 && n^0==n^post_2 ], cost: 1 6: l1 -> l7 : i^0'=i^post_7, j^0'=j^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ i^0==i^post_7 && j^0==j^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 ], cost: 1 10: l2 -> l1 : i^0'=i^post_11, j^0'=j^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, [ tmp^0<=0 && 0<=tmp^0 && i^0==i^post_11 && j^0==j^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 ], cost: 1 11: l2 -> l8 : i^0'=i^post_12, j^0'=j^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, [ 1<=tmp^0 && i^0==i^post_12 && j^0==j^post_12 && n^0==n^post_12 && tmp^0==tmp^post_12 ], cost: 1 12: l2 -> l8 : i^0'=i^post_13, j^0'=j^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, [ 1+tmp^0<=0 && i^0==i^post_13 && j^0==j^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 ], cost: 1 3: l3 -> l5 : i^0'=i^post_4, j^0'=j^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, [ 1+i^0<=n^0 && i^post_4==1+i^0 && j^post_4==0 && n^0==n^post_4 && tmp^0==tmp^post_4 ], cost: 1 5: l5 -> l0 : i^0'=i^post_6, j^0'=j^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, [ i^0==i^post_6 && j^0==j^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 ], cost: 1 4: l6 -> l3 : i^0'=i^post_5, j^0'=j^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, [ i^0==i^post_5 && j^0==j^post_5 && n^0==n^post_5 && tmp^0==tmp^post_5 ], cost: 1 7: l7 -> l6 : i^0'=i^post_8, j^0'=j^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, [ j^0<=0 && i^0==i^post_8 && j^0==j^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 ], cost: 1 8: l7 -> l6 : i^0'=i^post_9, j^0'=j^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, [ 1<=j^0 && i^post_9==-1+i^0 && j^0==j^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 ], cost: 1 9: l8 -> l5 : i^0'=i^post_10, j^0'=j^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, [ i^post_10==1+i^0 && j^post_10==1+j^0 && n^0==n^post_10 && tmp^0==tmp^post_10 ], cost: 1 13: l9 -> l6 : i^0'=i^post_14, j^0'=j^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, [ i^post_14==0 && j^0==j^post_14 && n^0==n^post_14 && tmp^0==tmp^post_14 ], cost: 1 14: l10 -> l9 : i^0'=i^post_15, j^0'=j^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1 Simplified all rules, resulting in: Start location: l10 0: l0 -> l1 : [ n^0<=i^0 ], cost: 1 1: l0 -> l2 : tmp^0'=tmp^post_2, [ 1+i^0<=n^0 ], cost: 1 6: l1 -> l7 : [], cost: 1 10: l2 -> l1 : [ tmp^0==0 ], cost: 1 11: l2 -> l8 : [ 1<=tmp^0 ], cost: 1 12: l2 -> l8 : [ 1+tmp^0<=0 ], cost: 1 3: l3 -> l5 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 ], cost: 1 5: l5 -> l0 : [], cost: 1 4: l6 -> l3 : [], cost: 1 7: l7 -> l6 : [ j^0<=0 ], cost: 1 8: l7 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 1 9: l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, [], cost: 1 13: l9 -> l6 : i^0'=0, [], cost: 1 14: l10 -> l9 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l10 0: l0 -> l1 : [ n^0<=i^0 ], cost: 1 1: l0 -> l2 : tmp^0'=tmp^post_2, [ 1+i^0<=n^0 ], cost: 1 6: l1 -> l7 : [], cost: 1 10: l2 -> l1 : [ tmp^0==0 ], cost: 1 11: l2 -> l8 : [ 1<=tmp^0 ], cost: 1 12: l2 -> l8 : [ 1+tmp^0<=0 ], cost: 1 5: l5 -> l0 : [], cost: 1 16: l6 -> l5 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 ], cost: 2 7: l7 -> l6 : [ j^0<=0 ], cost: 1 8: l7 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 1 9: l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, [], cost: 1 15: l10 -> l6 : i^0'=0, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 19: l1 -> l6 : [ j^0<=0 ], cost: 2 20: l1 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 2 10: l2 -> l1 : [ tmp^0==0 ], cost: 1 21: l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, [ 1<=tmp^0 ], cost: 2 22: l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, [ 1+tmp^0<=0 ], cost: 2 17: l5 -> l1 : [ n^0<=i^0 ], cost: 2 18: l5 -> l2 : tmp^0'=tmp^post_2, [ 1+i^0<=n^0 ], cost: 2 16: l6 -> l5 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 ], cost: 2 15: l10 -> l6 : i^0'=0, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 19: l1 -> l6 : [ j^0<=0 ], cost: 2 20: l1 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 2 17: l5 -> l1 : [ n^0<=i^0 ], cost: 2 23: l5 -> l1 : tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && tmp^post_2==0 ], cost: 3 24: l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && 1<=tmp^post_2 ], cost: 4 25: l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && 1+tmp^post_2<=0 ], cost: 4 16: l6 -> l5 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 ], cost: 2 15: l10 -> l6 : i^0'=0, [], cost: 2 Accelerating simple loops of location 5. Accelerating the following rules: 24: l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && 1<=tmp^post_2 ], cost: 4 25: l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && 1+tmp^post_2<=0 ], cost: 4 Accelerated rule 24 with backward acceleration, yielding the new rule 26. Accelerated rule 25 with backward acceleration, yielding the new rule 27. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 24 25. Accelerated all simple loops using metering functions (where possible): Start location: l10 19: l1 -> l6 : [ j^0<=0 ], cost: 2 20: l1 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 2 17: l5 -> l1 : [ n^0<=i^0 ], cost: 2 23: l5 -> l1 : tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && tmp^post_2==0 ], cost: 3 26: l5 -> l5 : i^0'=n^0, j^0'=j^0+n^0-i^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && n^0-i^0>=1 ], cost: 4*n^0-4*i^0 27: l5 -> l5 : i^0'=n^0, j^0'=j^0+n^0-i^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && n^0-i^0>=1 ], cost: 4*n^0-4*i^0 16: l6 -> l5 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 ], cost: 2 15: l10 -> l6 : i^0'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l10 19: l1 -> l6 : [ j^0<=0 ], cost: 2 20: l1 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 2 17: l5 -> l1 : [ n^0<=i^0 ], cost: 2 23: l5 -> l1 : tmp^0'=tmp^post_2, [ 1+i^0<=n^0 && tmp^post_2==0 ], cost: 3 16: l6 -> l5 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 ], cost: 2 28: l6 -> l5 : i^0'=n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 29: l6 -> l5 : i^0'=n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 15: l10 -> l6 : i^0'=0, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 19: l1 -> l6 : [ j^0<=0 ], cost: 2 20: l1 -> l6 : i^0'=-1+i^0, [ 1<=j^0 ], cost: 2 30: l6 -> l1 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 && n^0<=1+i^0 ], cost: 4 31: l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post_2, [ 2+i^0<=n^0 && tmp^post_2==0 ], cost: 5 32: l6 -> l1 : i^0'=n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 33: l6 -> l1 : i^0'=n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 34: l6 -> [12] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 35: l6 -> [12] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 15: l10 -> l6 : i^0'=0, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 34: l6 -> [12] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 35: l6 -> [12] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 36: l6 -> l6 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 && n^0<=1+i^0 ], cost: 6 37: l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post_2, [ 2+i^0<=n^0 && tmp^post_2==0 ], cost: 7 38: l6 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 2+4*n^0-4*i^0 39: l6 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 2+4*n^0-4*i^0 40: l6 -> [13] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 41: l6 -> [13] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 15: l10 -> l6 : i^0'=0, [], cost: 2 Accelerating simple loops of location 6. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 36: l6 -> l6 : i^0'=1+i^0, j^0'=0, [ 1-n^0+i^0==0 ], cost: 6 37: l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=0, [ 2+i^0<=n^0 ], cost: 7 38: l6 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 2+4*n^0-4*i^0 39: l6 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 2+4*n^0-4*i^0 Failed to prove monotonicity of the guard of rule 36. Accelerated rule 37 with backward acceleration, yielding the new rule 42. Failed to prove monotonicity of the guard of rule 38. Failed to prove monotonicity of the guard of rule 39. [accelerate] Nesting with 4 inner and 4 outer candidates Removing the simple loops: 37. Accelerated all simple loops using metering functions (where possible): Start location: l10 34: l6 -> [12] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 35: l6 -> [12] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 36: l6 -> l6 : i^0'=1+i^0, j^0'=0, [ 1-n^0+i^0==0 ], cost: 6 38: l6 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 2+4*n^0-4*i^0 39: l6 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0-i^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 2+4*n^0-4*i^0 40: l6 -> [13] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 41: l6 -> [13] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 42: l6 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, [ -1+n^0-i^0>=1 ], cost: -7+7*n^0-7*i^0 15: l10 -> l6 : i^0'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l10 34: l6 -> [12] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 35: l6 -> [12] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: -2+4*n^0-4*i^0 40: l6 -> [13] : [ 1<=tmp^post_2 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 41: l6 -> [13] : [ 1+tmp^post_2<=0 && -1+n^0-i^0>=1 ], cost: 4*n^0-4*i^0 15: l10 -> l6 : i^0'=0, [], cost: 2 43: l10 -> l6 : i^0'=1, j^0'=0, [ 1-n^0==0 ], cost: 8 44: l10 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0, tmp^0'=tmp^post_2, [ 1<=tmp^post_2 && -1+n^0>=1 ], cost: 4+4*n^0 45: l10 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0, tmp^0'=tmp^post_2, [ 1+tmp^post_2<=0 && -1+n^0>=1 ], cost: 4+4*n^0 46: l10 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, [ -1+n^0>=1 ], cost: -5+7*n^0 Eliminated locations (on tree-shaped paths): Start location: l10 47: l10 -> [12] : i^0'=0, [ 1<=tmp^post_2 && -1+n^0>=1 ], cost: 4*n^0 48: l10 -> [12] : i^0'=0, [ 1+tmp^post_2<=0 && -1+n^0>=1 ], cost: 4*n^0 49: l10 -> [13] : i^0'=0, [ 1<=tmp^post_2 && -1+n^0>=1 ], cost: 2+4*n^0 50: l10 -> [13] : i^0'=0, [ 1+tmp^post_2<=0 && -1+n^0>=1 ], cost: 2+4*n^0 51: l10 -> [15] : [ 1<=tmp^post_2 && -1+n^0>=1 ], cost: 4+4*n^0 52: l10 -> [15] : [ 1+tmp^post_2<=0 && -1+n^0>=1 ], cost: 4+4*n^0 53: l10 -> [15] : [ -1+n^0>=1 ], cost: -5+7*n^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l10 51: l10 -> [15] : [ 1<=tmp^post_2 && -1+n^0>=1 ], cost: 4+4*n^0 52: l10 -> [15] : [ 1+tmp^post_2<=0 && -1+n^0>=1 ], cost: 4+4*n^0 53: l10 -> [15] : [ -1+n^0>=1 ], cost: -5+7*n^0 Computing asymptotic complexity for rule 53 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 51 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 52 Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ] WORST_CASE(Omega(1),?)