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