WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l7 0: l0 -> l1 : nd_12^0'=nd_12^post_1, rt_11^0'=rt_11^post_1, rv_15^0'=rv_15^post_1, st_14^0'=st_14^post_1, st_16^0'=st_16^post_1, x_13^0'=x_13^post_1, y_17^0'=y_17^post_1, [ nd_12^0==nd_12^post_1 && rt_11^0==rt_11^post_1 && rv_15^0==rv_15^post_1 && st_14^0==st_14^post_1 && st_16^0==st_16^post_1 && x_13^0==x_13^post_1 && y_17^0==y_17^post_1 ], cost: 1 1: l1 -> l2 : nd_12^0'=nd_12^post_2, rt_11^0'=rt_11^post_2, rv_15^0'=rv_15^post_2, st_14^0'=st_14^post_2, st_16^0'=st_16^post_2, x_13^0'=x_13^post_2, y_17^0'=y_17^post_2, [ x_13^0<=0 && rt_11^post_2==st_14^0 && nd_12^0==nd_12^post_2 && rv_15^0==rv_15^post_2 && st_14^0==st_14^post_2 && st_16^0==st_16^post_2 && x_13^0==x_13^post_2 && y_17^0==y_17^post_2 ], cost: 1 2: l1 -> l3 : nd_12^0'=nd_12^post_3, rt_11^0'=rt_11^post_3, rv_15^0'=rv_15^post_3, st_14^0'=st_14^post_3, st_16^0'=st_16^post_3, x_13^0'=x_13^post_3, y_17^0'=y_17^post_3, [ 1<=x_13^0 && nd_12^1_1==nd_12^1_1 && rv_15^post_3==nd_12^1_1 && nd_12^post_3==nd_12^post_3 && 0<=rv_15^post_3 && rv_15^post_3<=0 && y_17^post_3==-1+y_17^0 && st_16^post_3==st_16^post_3 && 2<=y_17^post_3 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 && x_13^0==x_13^post_3 ], cost: 1 4: l1 -> l5 : nd_12^0'=nd_12^post_5, rt_11^0'=rt_11^post_5, rv_15^0'=rv_15^post_5, st_14^0'=st_14^post_5, st_16^0'=st_16^post_5, x_13^0'=x_13^post_5, y_17^0'=y_17^post_5, [ 1<=x_13^0 && nd_12^1_2==nd_12^1_2 && rv_15^post_5==nd_12^1_2 && nd_12^post_5==nd_12^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && st_16^0==st_16^post_5 && x_13^0==x_13^post_5 && y_17^0==y_17^post_5 ], cost: 1 3: l3 -> l1 : nd_12^0'=nd_12^post_4, rt_11^0'=rt_11^post_4, rv_15^0'=rv_15^post_4, st_14^0'=st_14^post_4, st_16^0'=st_16^post_4, x_13^0'=x_13^post_4, y_17^0'=y_17^post_4, [ nd_12^0==nd_12^post_4 && rt_11^0==rt_11^post_4 && rv_15^0==rv_15^post_4 && st_14^0==st_14^post_4 && st_16^0==st_16^post_4 && x_13^0==x_13^post_4 && y_17^0==y_17^post_4 ], cost: 1 5: l5 -> l6 : nd_12^0'=nd_12^post_6, rt_11^0'=rt_11^post_6, rv_15^0'=rv_15^post_6, st_14^0'=st_14^post_6, st_16^0'=st_16^post_6, x_13^0'=x_13^post_6, y_17^0'=y_17^post_6, [ 1<=rv_15^0 && nd_12^0==nd_12^post_6 && rt_11^0==rt_11^post_6 && rv_15^0==rv_15^post_6 && st_14^0==st_14^post_6 && st_16^0==st_16^post_6 && x_13^0==x_13^post_6 && y_17^0==y_17^post_6 ], cost: 1 6: l5 -> l6 : nd_12^0'=nd_12^post_7, rt_11^0'=rt_11^post_7, rv_15^0'=rv_15^post_7, st_14^0'=st_14^post_7, st_16^0'=st_16^post_7, x_13^0'=x_13^post_7, y_17^0'=y_17^post_7, [ 1+rv_15^0<=0 && nd_12^0==nd_12^post_7 && rt_11^0==rt_11^post_7 && rv_15^0==rv_15^post_7 && st_14^0==st_14^post_7 && st_16^0==st_16^post_7 && x_13^0==x_13^post_7 && y_17^0==y_17^post_7 ], cost: 1 7: l6 -> l4 : nd_12^0'=nd_12^post_8, rt_11^0'=rt_11^post_8, rv_15^0'=rv_15^post_8, st_14^0'=st_14^post_8, st_16^0'=st_16^post_8, x_13^0'=x_13^post_8, y_17^0'=y_17^post_8, [ x_13^post_8==-1+x_13^0 && nd_12^1_3==nd_12^1_3 && y_17^post_8==nd_12^1_3 && nd_12^post_8==nd_12^post_8 && rt_11^0==rt_11^post_8 && rv_15^0==rv_15^post_8 && st_14^0==st_14^post_8 && st_16^0==st_16^post_8 ], cost: 1 8: l4 -> l1 : nd_12^0'=nd_12^post_9, rt_11^0'=rt_11^post_9, rv_15^0'=rv_15^post_9, st_14^0'=st_14^post_9, st_16^0'=st_16^post_9, x_13^0'=x_13^post_9, y_17^0'=y_17^post_9, [ nd_12^0==nd_12^post_9 && rt_11^0==rt_11^post_9 && rv_15^0==rv_15^post_9 && st_14^0==st_14^post_9 && st_16^0==st_16^post_9 && x_13^0==x_13^post_9 && y_17^0==y_17^post_9 ], cost: 1 9: l7 -> l0 : nd_12^0'=nd_12^post_10, rt_11^0'=rt_11^post_10, rv_15^0'=rv_15^post_10, st_14^0'=st_14^post_10, st_16^0'=st_16^post_10, x_13^0'=x_13^post_10, y_17^0'=y_17^post_10, [ nd_12^0==nd_12^post_10 && rt_11^0==rt_11^post_10 && rv_15^0==rv_15^post_10 && st_14^0==st_14^post_10 && st_16^0==st_16^post_10 && x_13^0==x_13^post_10 && y_17^0==y_17^post_10 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 9: l7 -> l0 : nd_12^0'=nd_12^post_10, rt_11^0'=rt_11^post_10, rv_15^0'=rv_15^post_10, st_14^0'=st_14^post_10, st_16^0'=st_16^post_10, x_13^0'=x_13^post_10, y_17^0'=y_17^post_10, [ nd_12^0==nd_12^post_10 && rt_11^0==rt_11^post_10 && rv_15^0==rv_15^post_10 && st_14^0==st_14^post_10 && st_16^0==st_16^post_10 && x_13^0==x_13^post_10 && y_17^0==y_17^post_10 ], cost: 1 Removed unreachable and leaf rules: Start location: l7 0: l0 -> l1 : nd_12^0'=nd_12^post_1, rt_11^0'=rt_11^post_1, rv_15^0'=rv_15^post_1, st_14^0'=st_14^post_1, st_16^0'=st_16^post_1, x_13^0'=x_13^post_1, y_17^0'=y_17^post_1, [ nd_12^0==nd_12^post_1 && rt_11^0==rt_11^post_1 && rv_15^0==rv_15^post_1 && st_14^0==st_14^post_1 && st_16^0==st_16^post_1 && x_13^0==x_13^post_1 && y_17^0==y_17^post_1 ], cost: 1 2: l1 -> l3 : nd_12^0'=nd_12^post_3, rt_11^0'=rt_11^post_3, rv_15^0'=rv_15^post_3, st_14^0'=st_14^post_3, st_16^0'=st_16^post_3, x_13^0'=x_13^post_3, y_17^0'=y_17^post_3, [ 1<=x_13^0 && nd_12^1_1==nd_12^1_1 && rv_15^post_3==nd_12^1_1 && nd_12^post_3==nd_12^post_3 && 0<=rv_15^post_3 && rv_15^post_3<=0 && y_17^post_3==-1+y_17^0 && st_16^post_3==st_16^post_3 && 2<=y_17^post_3 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 && x_13^0==x_13^post_3 ], cost: 1 4: l1 -> l5 : nd_12^0'=nd_12^post_5, rt_11^0'=rt_11^post_5, rv_15^0'=rv_15^post_5, st_14^0'=st_14^post_5, st_16^0'=st_16^post_5, x_13^0'=x_13^post_5, y_17^0'=y_17^post_5, [ 1<=x_13^0 && nd_12^1_2==nd_12^1_2 && rv_15^post_5==nd_12^1_2 && nd_12^post_5==nd_12^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && st_16^0==st_16^post_5 && x_13^0==x_13^post_5 && y_17^0==y_17^post_5 ], cost: 1 3: l3 -> l1 : nd_12^0'=nd_12^post_4, rt_11^0'=rt_11^post_4, rv_15^0'=rv_15^post_4, st_14^0'=st_14^post_4, st_16^0'=st_16^post_4, x_13^0'=x_13^post_4, y_17^0'=y_17^post_4, [ nd_12^0==nd_12^post_4 && rt_11^0==rt_11^post_4 && rv_15^0==rv_15^post_4 && st_14^0==st_14^post_4 && st_16^0==st_16^post_4 && x_13^0==x_13^post_4 && y_17^0==y_17^post_4 ], cost: 1 5: l5 -> l6 : nd_12^0'=nd_12^post_6, rt_11^0'=rt_11^post_6, rv_15^0'=rv_15^post_6, st_14^0'=st_14^post_6, st_16^0'=st_16^post_6, x_13^0'=x_13^post_6, y_17^0'=y_17^post_6, [ 1<=rv_15^0 && nd_12^0==nd_12^post_6 && rt_11^0==rt_11^post_6 && rv_15^0==rv_15^post_6 && st_14^0==st_14^post_6 && st_16^0==st_16^post_6 && x_13^0==x_13^post_6 && y_17^0==y_17^post_6 ], cost: 1 6: l5 -> l6 : nd_12^0'=nd_12^post_7, rt_11^0'=rt_11^post_7, rv_15^0'=rv_15^post_7, st_14^0'=st_14^post_7, st_16^0'=st_16^post_7, x_13^0'=x_13^post_7, y_17^0'=y_17^post_7, [ 1+rv_15^0<=0 && nd_12^0==nd_12^post_7 && rt_11^0==rt_11^post_7 && rv_15^0==rv_15^post_7 && st_14^0==st_14^post_7 && st_16^0==st_16^post_7 && x_13^0==x_13^post_7 && y_17^0==y_17^post_7 ], cost: 1 7: l6 -> l4 : nd_12^0'=nd_12^post_8, rt_11^0'=rt_11^post_8, rv_15^0'=rv_15^post_8, st_14^0'=st_14^post_8, st_16^0'=st_16^post_8, x_13^0'=x_13^post_8, y_17^0'=y_17^post_8, [ x_13^post_8==-1+x_13^0 && nd_12^1_3==nd_12^1_3 && y_17^post_8==nd_12^1_3 && nd_12^post_8==nd_12^post_8 && rt_11^0==rt_11^post_8 && rv_15^0==rv_15^post_8 && st_14^0==st_14^post_8 && st_16^0==st_16^post_8 ], cost: 1 8: l4 -> l1 : nd_12^0'=nd_12^post_9, rt_11^0'=rt_11^post_9, rv_15^0'=rv_15^post_9, st_14^0'=st_14^post_9, st_16^0'=st_16^post_9, x_13^0'=x_13^post_9, y_17^0'=y_17^post_9, [ nd_12^0==nd_12^post_9 && rt_11^0==rt_11^post_9 && rv_15^0==rv_15^post_9 && st_14^0==st_14^post_9 && st_16^0==st_16^post_9 && x_13^0==x_13^post_9 && y_17^0==y_17^post_9 ], cost: 1 9: l7 -> l0 : nd_12^0'=nd_12^post_10, rt_11^0'=rt_11^post_10, rv_15^0'=rv_15^post_10, st_14^0'=st_14^post_10, st_16^0'=st_16^post_10, x_13^0'=x_13^post_10, y_17^0'=y_17^post_10, [ nd_12^0==nd_12^post_10 && rt_11^0==rt_11^post_10 && rv_15^0==rv_15^post_10 && st_14^0==st_14^post_10 && st_16^0==st_16^post_10 && x_13^0==x_13^post_10 && y_17^0==y_17^post_10 ], cost: 1 Simplified all rules, resulting in: Start location: l7 0: l0 -> l1 : [], cost: 1 2: l1 -> l3 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=-1+y_17^0, [ 1<=x_13^0 && 2<=-1+y_17^0 ], cost: 1 4: l1 -> l5 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 ], cost: 1 3: l3 -> l1 : [], cost: 1 5: l5 -> l6 : [ 1<=rv_15^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_15^0<=0 ], cost: 1 7: l6 -> l4 : nd_12^0'=nd_12^post_8, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [], cost: 1 8: l4 -> l1 : [], cost: 1 9: l7 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l7 4: l1 -> l5 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 ], cost: 1 11: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=-1+y_17^0, [ 1<=x_13^0 && 2<=-1+y_17^0 ], cost: 2 5: l5 -> l6 : [ 1<=rv_15^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_15^0<=0 ], cost: 1 12: l6 -> l1 : nd_12^0'=nd_12^post_8, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [], cost: 2 10: l7 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 11: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=-1+y_17^0, [ 1<=x_13^0 && 2<=-1+y_17^0 ], cost: 2 Accelerated rule 11 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: l7 4: l1 -> l5 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 ], cost: 1 13: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -4+2*y_17^0 5: l5 -> l6 : [ 1<=rv_15^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_15^0<=0 ], cost: 1 12: l6 -> l1 : nd_12^0'=nd_12^post_8, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [], cost: 2 10: l7 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l7 4: l1 -> l5 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 ], cost: 1 5: l5 -> l6 : [ 1<=rv_15^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_15^0<=0 ], cost: 1 12: l6 -> l1 : nd_12^0'=nd_12^post_8, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [], cost: 2 15: l6 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=-1+x_13^0, y_17^0'=2, [ 1<=-1+x_13^0 && -2+nd_12^1_3>=1 ], cost: -2+2*nd_12^1_3 10: l7 -> l1 : [], cost: 2 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 Eliminated locations (on tree-shaped paths): Start location: l7 16: l1 -> l6 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 && 1<=nd_12^1_2 ], cost: 2 17: l1 -> l6 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 && 1+nd_12^1_2<=0 ], cost: 2 12: l6 -> l1 : nd_12^0'=nd_12^post_8, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [], cost: 2 15: l6 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=-1+x_13^0, y_17^0'=2, [ 1<=-1+x_13^0 && -2+nd_12^1_3>=1 ], cost: -2+2*nd_12^1_3 10: l7 -> l1 : [], cost: 2 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 Eliminated locations (on tree-shaped paths): Start location: l7 18: l1 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && 1<=nd_12^1_2 ], cost: 4 19: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=-1+x_13^0, y_17^0'=2, [ 1<=nd_12^1_2 && 1<=-1+x_13^0 && -2+nd_12^1_3>=1 ], cost: 2*nd_12^1_3 20: l1 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && 1+nd_12^1_2<=0 ], cost: 4 21: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=-1+x_13^0, y_17^0'=2, [ 1+nd_12^1_2<=0 && 1<=-1+x_13^0 && -2+nd_12^1_3>=1 ], cost: 2*nd_12^1_3 10: l7 -> l1 : [], cost: 2 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 Accelerating simple loops of location 1. [accelerate] Removed some duplicate simple loops Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 18: l1 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && 1<=nd_12^1_2 ], cost: 4 20: l1 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && 1+nd_12^1_2<=0 ], cost: 4 21: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=-1+x_13^0, y_17^0'=2, [ 1<=-1+x_13^0 && -2+nd_12^1_3>=1 ], cost: 2*nd_12^1_3 Accelerated rule 18 with backward acceleration, yielding the new rule 22. Accelerated rule 20 with backward acceleration, yielding the new rule 23. Accelerated rule 21 with backward acceleration, yielding the new rule 24. [accelerate] Nesting with 3 inner and 3 outer candidates Removing the simple loops: 18 20 21. Accelerated all simple loops using metering functions (where possible): Start location: l7 22: l1 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=nd_12^1_2 && x_13^0>=1 ], cost: 4*x_13^0 23: l1 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1+nd_12^1_2<=0 && x_13^0>=1 ], cost: 4*x_13^0 24: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2*(-1+x_13^0)*nd_12^1_3 10: l7 -> l1 : [], cost: 2 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 Chained accelerated rules (with incoming rules): Start location: l7 10: l7 -> l1 : [], cost: 2 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 25: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=nd_12^1_2 && x_13^0>=1 ], cost: 2+4*x_13^0 26: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, st_16^0'=st_16^post_3, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && -2+y_17^0>=1 && 1<=nd_12^1_2 ], cost: -2+4*x_13^0+2*y_17^0 27: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1+nd_12^1_2<=0 && x_13^0>=1 ], cost: 2+4*x_13^0 28: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, st_16^0'=st_16^post_3, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && -2+y_17^0>=1 && 1+nd_12^1_2<=0 ], cost: -2+4*x_13^0+2*y_17^0 29: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2+2*(-1+x_13^0)*nd_12^1_3 30: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -2+2*y_17^0+2*(-1+x_13^0)*nd_12^1_3 Removed unreachable locations (and leaf rules with constant cost): Start location: l7 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 25: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=nd_12^1_2 && x_13^0>=1 ], cost: 2+4*x_13^0 26: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, st_16^0'=st_16^post_3, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && -2+y_17^0>=1 && 1<=nd_12^1_2 ], cost: -2+4*x_13^0+2*y_17^0 27: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1+nd_12^1_2<=0 && x_13^0>=1 ], cost: 2+4*x_13^0 28: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, st_16^0'=st_16^post_3, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && -2+y_17^0>=1 && 1+nd_12^1_2<=0 ], cost: -2+4*x_13^0+2*y_17^0 29: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2+2*(-1+x_13^0)*nd_12^1_3 30: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -2+2*y_17^0+2*(-1+x_13^0)*nd_12^1_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l7 14: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0 25: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=nd_12^1_2 && x_13^0>=1 ], cost: 2+4*x_13^0 26: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, st_16^0'=st_16^post_3, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && -2+y_17^0>=1 && 1<=nd_12^1_2 ], cost: -2+4*x_13^0+2*y_17^0 27: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1+nd_12^1_2<=0 && x_13^0>=1 ], cost: 2+4*x_13^0 28: l7 -> l1 : nd_12^0'=nd_12^post_8, rv_15^0'=nd_12^1_2, st_16^0'=st_16^post_3, x_13^0'=0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 && -2+y_17^0>=1 && 1+nd_12^1_2<=0 ], cost: -2+4*x_13^0+2*y_17^0 29: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2+2*(-1+x_13^0)*nd_12^1_3 30: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -2+2*y_17^0+2*(-1+x_13^0)*nd_12^1_3 Computing asymptotic complexity for rule 29 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 30 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 14 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 25 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 27 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 26 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 28 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: [ nd_12^0==nd_12^post_10 && rt_11^0==rt_11^post_10 && rv_15^0==rv_15^post_10 && st_14^0==st_14^post_10 && st_16^0==st_16^post_10 && x_13^0==x_13^post_10 && y_17^0==y_17^post_10 ] WORST_CASE(Omega(1),?)