NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l7 0: l0 -> l1 : lt_15^0'=lt_15^post_1, lt_19^0'=lt_19^post_1, nd_12^0'=nd_12^post_1, p_14^0'=p_14^post_1, rt_11^0'=rt_11^post_1, rv_18^0'=rv_18^post_1, st_17^0'=st_17^post_1, x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [ p_14^post_1==x_13^0 && lt_15^0==lt_15^post_1 && lt_19^0==lt_19^post_1 && nd_12^0==nd_12^post_1 && rt_11^0==rt_11^post_1 && rv_18^0==rv_18^post_1 && st_17^0==st_17^post_1 && x_13^0==x_13^post_1 && y_16^0==y_16^post_1 ], cost: 1 1: l1 -> l2 : lt_15^0'=lt_15^post_2, lt_19^0'=lt_19^post_2, nd_12^0'=nd_12^post_2, p_14^0'=p_14^post_2, rt_11^0'=rt_11^post_2, rv_18^0'=rv_18^post_2, st_17^0'=st_17^post_2, x_13^0'=x_13^post_2, y_16^0'=y_16^post_2, [ y_16^0<=lt_15^0 && lt_15^post_2==lt_15^post_2 && rt_11^post_2==st_17^0 && lt_19^0==lt_19^post_2 && nd_12^0==nd_12^post_2 && p_14^0==p_14^post_2 && rv_18^0==rv_18^post_2 && st_17^0==st_17^post_2 && x_13^0==x_13^post_2 && y_16^0==y_16^post_2 ], cost: 1 2: l1 -> l3 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_3, nd_12^0'=nd_12^post_3, p_14^0'=p_14^post_3, rt_11^0'=rt_11^post_3, rv_18^0'=rv_18^post_3, st_17^0'=st_17^post_3, x_13^0'=x_13^post_3, y_16^0'=y_16^post_3, [ 1+lt_15^0<=y_16^0 && lt_15^post_3==lt_15^post_3 && nd_12^1_1==nd_12^1_1 && rv_18^post_3==nd_12^1_1 && nd_12^post_3==nd_12^post_3 && 0<=rv_18^post_3 && rv_18^post_3<=0 && lt_19^0==lt_19^post_3 && p_14^0==p_14^post_3 && rt_11^0==rt_11^post_3 && st_17^0==st_17^post_3 && x_13^0==x_13^post_3 && y_16^0==y_16^post_3 ], cost: 1 4: l1 -> l5 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_5, nd_12^0'=nd_12^post_5, p_14^0'=p_14^post_5, rt_11^0'=rt_11^post_5, rv_18^0'=rv_18^post_5, st_17^0'=st_17^post_5, x_13^0'=x_13^post_5, y_16^0'=y_16^post_5, [ 1+lt_15^0<=y_16^0 && lt_15^post_5==lt_15^post_5 && nd_12^1_2==nd_12^1_2 && rv_18^post_5==nd_12^1_2 && nd_12^post_5==nd_12^post_5 && lt_19^0==lt_19^post_5 && p_14^0==p_14^post_5 && rt_11^0==rt_11^post_5 && st_17^0==st_17^post_5 && x_13^0==x_13^post_5 && y_16^0==y_16^post_5 ], cost: 1 3: l3 -> l1 : lt_15^0'=lt_15^post_4, lt_19^0'=lt_19^post_4, nd_12^0'=nd_12^post_4, p_14^0'=p_14^post_4, rt_11^0'=rt_11^post_4, rv_18^0'=rv_18^post_4, st_17^0'=st_17^post_4, x_13^0'=x_13^post_4, y_16^0'=y_16^post_4, [ lt_15^0==lt_15^post_4 && lt_19^0==lt_19^post_4 && nd_12^0==nd_12^post_4 && p_14^0==p_14^post_4 && rt_11^0==rt_11^post_4 && rv_18^0==rv_18^post_4 && st_17^0==st_17^post_4 && x_13^0==x_13^post_4 && y_16^0==y_16^post_4 ], cost: 1 5: l5 -> l6 : lt_15^0'=lt_15^post_6, lt_19^0'=lt_19^post_6, nd_12^0'=nd_12^post_6, p_14^0'=p_14^post_6, rt_11^0'=rt_11^post_6, rv_18^0'=rv_18^post_6, st_17^0'=st_17^post_6, x_13^0'=x_13^post_6, y_16^0'=y_16^post_6, [ 1<=rv_18^0 && lt_15^0==lt_15^post_6 && lt_19^0==lt_19^post_6 && nd_12^0==nd_12^post_6 && p_14^0==p_14^post_6 && rt_11^0==rt_11^post_6 && rv_18^0==rv_18^post_6 && st_17^0==st_17^post_6 && x_13^0==x_13^post_6 && y_16^0==y_16^post_6 ], cost: 1 6: l5 -> l6 : lt_15^0'=lt_15^post_7, lt_19^0'=lt_19^post_7, nd_12^0'=nd_12^post_7, p_14^0'=p_14^post_7, rt_11^0'=rt_11^post_7, rv_18^0'=rv_18^post_7, st_17^0'=st_17^post_7, x_13^0'=x_13^post_7, y_16^0'=y_16^post_7, [ 1+rv_18^0<=0 && lt_15^0==lt_15^post_7 && lt_19^0==lt_19^post_7 && nd_12^0==nd_12^post_7 && p_14^0==p_14^post_7 && rt_11^0==rt_11^post_7 && rv_18^0==rv_18^post_7 && st_17^0==st_17^post_7 && x_13^0==x_13^post_7 && y_16^0==y_16^post_7 ], cost: 1 7: l6 -> l4 : lt_15^0'=lt_15^post_8, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_8, p_14^0'=p_14^post_8, rt_11^0'=rt_11^post_8, rv_18^0'=rv_18^post_8, st_17^0'=st_17^post_8, x_13^0'=x_13^post_8, y_16^0'=y_16^post_8, [ lt_19^post_8==lt_19^post_8 && lt_15^0==lt_15^post_8 && nd_12^0==nd_12^post_8 && p_14^0==p_14^post_8 && rt_11^0==rt_11^post_8 && rv_18^0==rv_18^post_8 && st_17^0==st_17^post_8 && x_13^0==x_13^post_8 && y_16^0==y_16^post_8 ], cost: 1 8: l4 -> l1 : lt_15^0'=lt_15^post_9, lt_19^0'=lt_19^post_9, nd_12^0'=nd_12^post_9, p_14^0'=p_14^post_9, rt_11^0'=rt_11^post_9, rv_18^0'=rv_18^post_9, st_17^0'=st_17^post_9, x_13^0'=x_13^post_9, y_16^0'=y_16^post_9, [ lt_15^0==lt_15^post_9 && lt_19^0==lt_19^post_9 && nd_12^0==nd_12^post_9 && p_14^0==p_14^post_9 && rt_11^0==rt_11^post_9 && rv_18^0==rv_18^post_9 && st_17^0==st_17^post_9 && x_13^0==x_13^post_9 && y_16^0==y_16^post_9 ], cost: 1 9: l7 -> l0 : lt_15^0'=lt_15^post_10, lt_19^0'=lt_19^post_10, nd_12^0'=nd_12^post_10, p_14^0'=p_14^post_10, rt_11^0'=rt_11^post_10, rv_18^0'=rv_18^post_10, st_17^0'=st_17^post_10, x_13^0'=x_13^post_10, y_16^0'=y_16^post_10, [ lt_15^0==lt_15^post_10 && lt_19^0==lt_19^post_10 && nd_12^0==nd_12^post_10 && p_14^0==p_14^post_10 && rt_11^0==rt_11^post_10 && rv_18^0==rv_18^post_10 && st_17^0==st_17^post_10 && x_13^0==x_13^post_10 && y_16^0==y_16^post_10 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 9: l7 -> l0 : lt_15^0'=lt_15^post_10, lt_19^0'=lt_19^post_10, nd_12^0'=nd_12^post_10, p_14^0'=p_14^post_10, rt_11^0'=rt_11^post_10, rv_18^0'=rv_18^post_10, st_17^0'=st_17^post_10, x_13^0'=x_13^post_10, y_16^0'=y_16^post_10, [ lt_15^0==lt_15^post_10 && lt_19^0==lt_19^post_10 && nd_12^0==nd_12^post_10 && p_14^0==p_14^post_10 && rt_11^0==rt_11^post_10 && rv_18^0==rv_18^post_10 && st_17^0==st_17^post_10 && x_13^0==x_13^post_10 && y_16^0==y_16^post_10 ], cost: 1 Removed unreachable and leaf rules: Start location: l7 0: l0 -> l1 : lt_15^0'=lt_15^post_1, lt_19^0'=lt_19^post_1, nd_12^0'=nd_12^post_1, p_14^0'=p_14^post_1, rt_11^0'=rt_11^post_1, rv_18^0'=rv_18^post_1, st_17^0'=st_17^post_1, x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [ p_14^post_1==x_13^0 && lt_15^0==lt_15^post_1 && lt_19^0==lt_19^post_1 && nd_12^0==nd_12^post_1 && rt_11^0==rt_11^post_1 && rv_18^0==rv_18^post_1 && st_17^0==st_17^post_1 && x_13^0==x_13^post_1 && y_16^0==y_16^post_1 ], cost: 1 2: l1 -> l3 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_3, nd_12^0'=nd_12^post_3, p_14^0'=p_14^post_3, rt_11^0'=rt_11^post_3, rv_18^0'=rv_18^post_3, st_17^0'=st_17^post_3, x_13^0'=x_13^post_3, y_16^0'=y_16^post_3, [ 1+lt_15^0<=y_16^0 && lt_15^post_3==lt_15^post_3 && nd_12^1_1==nd_12^1_1 && rv_18^post_3==nd_12^1_1 && nd_12^post_3==nd_12^post_3 && 0<=rv_18^post_3 && rv_18^post_3<=0 && lt_19^0==lt_19^post_3 && p_14^0==p_14^post_3 && rt_11^0==rt_11^post_3 && st_17^0==st_17^post_3 && x_13^0==x_13^post_3 && y_16^0==y_16^post_3 ], cost: 1 4: l1 -> l5 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_5, nd_12^0'=nd_12^post_5, p_14^0'=p_14^post_5, rt_11^0'=rt_11^post_5, rv_18^0'=rv_18^post_5, st_17^0'=st_17^post_5, x_13^0'=x_13^post_5, y_16^0'=y_16^post_5, [ 1+lt_15^0<=y_16^0 && lt_15^post_5==lt_15^post_5 && nd_12^1_2==nd_12^1_2 && rv_18^post_5==nd_12^1_2 && nd_12^post_5==nd_12^post_5 && lt_19^0==lt_19^post_5 && p_14^0==p_14^post_5 && rt_11^0==rt_11^post_5 && st_17^0==st_17^post_5 && x_13^0==x_13^post_5 && y_16^0==y_16^post_5 ], cost: 1 3: l3 -> l1 : lt_15^0'=lt_15^post_4, lt_19^0'=lt_19^post_4, nd_12^0'=nd_12^post_4, p_14^0'=p_14^post_4, rt_11^0'=rt_11^post_4, rv_18^0'=rv_18^post_4, st_17^0'=st_17^post_4, x_13^0'=x_13^post_4, y_16^0'=y_16^post_4, [ lt_15^0==lt_15^post_4 && lt_19^0==lt_19^post_4 && nd_12^0==nd_12^post_4 && p_14^0==p_14^post_4 && rt_11^0==rt_11^post_4 && rv_18^0==rv_18^post_4 && st_17^0==st_17^post_4 && x_13^0==x_13^post_4 && y_16^0==y_16^post_4 ], cost: 1 5: l5 -> l6 : lt_15^0'=lt_15^post_6, lt_19^0'=lt_19^post_6, nd_12^0'=nd_12^post_6, p_14^0'=p_14^post_6, rt_11^0'=rt_11^post_6, rv_18^0'=rv_18^post_6, st_17^0'=st_17^post_6, x_13^0'=x_13^post_6, y_16^0'=y_16^post_6, [ 1<=rv_18^0 && lt_15^0==lt_15^post_6 && lt_19^0==lt_19^post_6 && nd_12^0==nd_12^post_6 && p_14^0==p_14^post_6 && rt_11^0==rt_11^post_6 && rv_18^0==rv_18^post_6 && st_17^0==st_17^post_6 && x_13^0==x_13^post_6 && y_16^0==y_16^post_6 ], cost: 1 6: l5 -> l6 : lt_15^0'=lt_15^post_7, lt_19^0'=lt_19^post_7, nd_12^0'=nd_12^post_7, p_14^0'=p_14^post_7, rt_11^0'=rt_11^post_7, rv_18^0'=rv_18^post_7, st_17^0'=st_17^post_7, x_13^0'=x_13^post_7, y_16^0'=y_16^post_7, [ 1+rv_18^0<=0 && lt_15^0==lt_15^post_7 && lt_19^0==lt_19^post_7 && nd_12^0==nd_12^post_7 && p_14^0==p_14^post_7 && rt_11^0==rt_11^post_7 && rv_18^0==rv_18^post_7 && st_17^0==st_17^post_7 && x_13^0==x_13^post_7 && y_16^0==y_16^post_7 ], cost: 1 7: l6 -> l4 : lt_15^0'=lt_15^post_8, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_8, p_14^0'=p_14^post_8, rt_11^0'=rt_11^post_8, rv_18^0'=rv_18^post_8, st_17^0'=st_17^post_8, x_13^0'=x_13^post_8, y_16^0'=y_16^post_8, [ lt_19^post_8==lt_19^post_8 && lt_15^0==lt_15^post_8 && nd_12^0==nd_12^post_8 && p_14^0==p_14^post_8 && rt_11^0==rt_11^post_8 && rv_18^0==rv_18^post_8 && st_17^0==st_17^post_8 && x_13^0==x_13^post_8 && y_16^0==y_16^post_8 ], cost: 1 8: l4 -> l1 : lt_15^0'=lt_15^post_9, lt_19^0'=lt_19^post_9, nd_12^0'=nd_12^post_9, p_14^0'=p_14^post_9, rt_11^0'=rt_11^post_9, rv_18^0'=rv_18^post_9, st_17^0'=st_17^post_9, x_13^0'=x_13^post_9, y_16^0'=y_16^post_9, [ lt_15^0==lt_15^post_9 && lt_19^0==lt_19^post_9 && nd_12^0==nd_12^post_9 && p_14^0==p_14^post_9 && rt_11^0==rt_11^post_9 && rv_18^0==rv_18^post_9 && st_17^0==st_17^post_9 && x_13^0==x_13^post_9 && y_16^0==y_16^post_9 ], cost: 1 9: l7 -> l0 : lt_15^0'=lt_15^post_10, lt_19^0'=lt_19^post_10, nd_12^0'=nd_12^post_10, p_14^0'=p_14^post_10, rt_11^0'=rt_11^post_10, rv_18^0'=rv_18^post_10, st_17^0'=st_17^post_10, x_13^0'=x_13^post_10, y_16^0'=y_16^post_10, [ lt_15^0==lt_15^post_10 && lt_19^0==lt_19^post_10 && nd_12^0==nd_12^post_10 && p_14^0==p_14^post_10 && rt_11^0==rt_11^post_10 && rv_18^0==rv_18^post_10 && st_17^0==st_17^post_10 && x_13^0==x_13^post_10 && y_16^0==y_16^post_10 ], cost: 1 Simplified all rules, resulting in: Start location: l7 0: l0 -> l1 : p_14^0'=x_13^0, [], cost: 1 2: l1 -> l3 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 1 4: l1 -> l5 : lt_15^0'=lt_15^post_5, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 ], cost: 1 3: l3 -> l1 : [], cost: 1 5: l5 -> l6 : [ 1<=rv_18^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_18^0<=0 ], cost: 1 7: l6 -> l4 : lt_19^0'=lt_19^post_8, [], 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 : lt_15^0'=lt_15^post_5, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 ], cost: 1 11: l1 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 2 5: l5 -> l6 : [ 1<=rv_18^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_18^0<=0 ], cost: 1 12: l6 -> l1 : lt_19^0'=lt_19^post_8, [], cost: 2 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 11: l1 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 2 Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 13. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: l7 4: l1 -> l5 : lt_15^0'=lt_15^post_5, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 ], cost: 1 11: l1 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 2 13: l1 -> [8] : [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 5: l5 -> l6 : [ 1<=rv_18^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_18^0<=0 ], cost: 1 12: l6 -> l1 : lt_19^0'=lt_19^post_8, [], cost: 2 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l7 4: l1 -> l5 : lt_15^0'=lt_15^post_5, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 ], cost: 1 5: l5 -> l6 : [ 1<=rv_18^0 ], cost: 1 6: l5 -> l6 : [ 1+rv_18^0<=0 ], cost: 1 12: l6 -> l1 : lt_19^0'=lt_19^post_8, [], cost: 2 15: l6 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 17: l6 -> [8] : lt_19^0'=lt_19^post_8, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 14: l7 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 16: l7 -> [8] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l7 18: l1 -> l6 : lt_15^0'=lt_15^post_5, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 ], cost: 2 19: l1 -> l6 : lt_15^0'=lt_15^post_5, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 ], cost: 2 12: l6 -> l1 : lt_19^0'=lt_19^post_8, [], cost: 2 15: l6 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 17: l6 -> [8] : lt_19^0'=lt_19^post_8, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 14: l7 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 16: l7 -> [8] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l7 20: l1 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 ], cost: 4 21: l1 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: 6 22: l1 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 23: l1 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 ], cost: 4 24: l1 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: 6 25: l1 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 14: l7 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 16: l7 -> [8] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 20: l1 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 ], cost: 4 23: l1 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 ], cost: 4 24: l1 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 6 Accelerated rule 20 with NONTERM (after strengthening guard), yielding the new rule 26. Accelerated rule 23 with NONTERM (after strengthening guard), yielding the new rule 27. Accelerated rule 24 with NONTERM (after strengthening guard), yielding the new rule 28. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: l7 20: l1 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 ], cost: 4 22: l1 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 23: l1 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 ], cost: 4 24: l1 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 6 25: l1 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 26: l1 -> [9] : [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 27: l1 -> [9] : [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 28: l1 -> [9] : [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 14: l7 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 16: l7 -> [8] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: l7 22: l1 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 25: l1 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 10: l7 -> l1 : p_14^0'=x_13^0, [], cost: 2 14: l7 -> l1 : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 4 16: l7 -> [8] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 29: l7 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 ], cost: 6 30: l7 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 ], cost: 8 31: l7 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 ], cost: 6 32: l7 -> l1 : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 ], cost: 8 33: l7 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 ], cost: 8 34: l7 -> l1 : lt_15^0'=lt_15^post_3, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: 10 35: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 36: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 37: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 38: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 39: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 40: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l7 16: l7 -> [8] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 35: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 36: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 37: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 38: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 39: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 40: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 41: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 42: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 43: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 44: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 45: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 46: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 47: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 48: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 49: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 50: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 51: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 52: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l7 39: l7 -> [9] : p_14^0'=x_13^0, [ 1+lt_15^0<=y_16^0 ], cost: NONTERM 40: l7 -> [9] : lt_15^0'=lt_15^post_3, nd_12^0'=nd_12^post_3, p_14^0'=x_13^0, rv_18^0'=0, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 ], cost: NONTERM 46: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 48: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 51: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1<=nd_12^1_2 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM 52: l7 -> [8] : lt_15^0'=lt_15^post_5, lt_19^0'=lt_19^post_8, nd_12^0'=nd_12^post_5, p_14^0'=x_13^0, rv_18^0'=nd_12^1_2, [ 1+lt_15^0<=y_16^0 && 1+lt_15^post_3<=y_16^0 && 1+nd_12^1_2<=0 && 1+lt_15^post_5<=y_16^0 ], cost: NONTERM Computing asymptotic complexity for rule 39 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: [ 1+lt_15^0<=y_16^0 ] NO