NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l13 0: l0 -> l1 : WItemsNum^0'=WItemsNum^post_1, __const_5^0'=__const_5^post_1, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==tmp1^post_1 && WItemsNum^0==WItemsNum^post_1 && __const_5^0==__const_5^post_1 ], cost: 1 1: l0 -> l2 : WItemsNum^0'=WItemsNum^post_2, __const_5^0'=__const_5^post_2, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && WItemsNum^0==WItemsNum^post_2 && __const_5^0==__const_5^post_2 && tmp1^0==tmp1^post_2 ], cost: 1 11: l1 -> l5 : WItemsNum^0'=WItemsNum^post_12, __const_5^0'=__const_5^post_12, tmp1^0'=tmp1^post_12, [ tmp1^0<=0 && 0<=tmp1^0 && WItemsNum^0==WItemsNum^post_12 && __const_5^0==__const_5^post_12 && tmp1^0==tmp1^post_12 ], cost: 1 12: l1 -> l2 : WItemsNum^0'=WItemsNum^post_13, __const_5^0'=__const_5^post_13, tmp1^0'=tmp1^post_13, [ 1<=tmp1^0 && WItemsNum^0==WItemsNum^post_13 && __const_5^0==__const_5^post_13 && tmp1^0==tmp1^post_13 ], cost: 1 13: l1 -> l2 : WItemsNum^0'=WItemsNum^post_14, __const_5^0'=__const_5^post_14, tmp1^0'=tmp1^post_14, [ 1+tmp1^0<=0 && WItemsNum^0==WItemsNum^post_14 && __const_5^0==__const_5^post_14 && tmp1^0==tmp1^post_14 ], cost: 1 14: l2 -> l4 : WItemsNum^0'=WItemsNum^post_15, __const_5^0'=__const_5^post_15, tmp1^0'=tmp1^post_15, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^post_15==1+WItemsNum^0 && __const_5^0==__const_5^post_15 && tmp1^0==tmp1^post_15 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=WItemsNum^post_16, __const_5^0'=__const_5^post_16, tmp1^0'=tmp1^post_16, [ WItemsNum^0<=__const_5^0 && WItemsNum^post_16==1+WItemsNum^0 && __const_5^0==__const_5^post_16 && tmp1^0==tmp1^post_16 ], cost: 1 2: l3 -> l4 : WItemsNum^0'=WItemsNum^post_3, __const_5^0'=__const_5^post_3, tmp1^0'=tmp1^post_3, [ WItemsNum^0==WItemsNum^post_3 && __const_5^0==__const_5^post_3 && tmp1^0==tmp1^post_3 ], cost: 1 3: l4 -> l0 : WItemsNum^0'=WItemsNum^post_4, __const_5^0'=__const_5^post_4, tmp1^0'=tmp1^post_4, [ WItemsNum^0==WItemsNum^post_4 && __const_5^0==__const_5^post_4 && tmp1^0==tmp1^post_4 ], cost: 1 4: l5 -> l6 : WItemsNum^0'=WItemsNum^post_5, __const_5^0'=__const_5^post_5, tmp1^0'=tmp1^post_5, [ WItemsNum^0==WItemsNum^post_5 && __const_5^0==__const_5^post_5 && tmp1^0==tmp1^post_5 ], cost: 1 9: l6 -> l3 : WItemsNum^0'=WItemsNum^post_10, __const_5^0'=__const_5^post_10, tmp1^0'=tmp1^post_10, [ WItemsNum^0<=2 && WItemsNum^0==WItemsNum^post_10 && __const_5^0==__const_5^post_10 && tmp1^0==tmp1^post_10 ], cost: 1 10: l6 -> l5 : WItemsNum^0'=WItemsNum^post_11, __const_5^0'=__const_5^post_11, tmp1^0'=tmp1^post_11, [ 3<=WItemsNum^0 && WItemsNum^post_11==-1+WItemsNum^0 && __const_5^0==__const_5^post_11 && tmp1^0==tmp1^post_11 ], cost: 1 5: l7 -> l8 : WItemsNum^0'=WItemsNum^post_6, __const_5^0'=__const_5^post_6, tmp1^0'=tmp1^post_6, [ WItemsNum^0==WItemsNum^post_6 && __const_5^0==__const_5^post_6 && tmp1^0==tmp1^post_6 ], cost: 1 6: l9 -> l10 : WItemsNum^0'=WItemsNum^post_7, __const_5^0'=__const_5^post_7, tmp1^0'=tmp1^post_7, [ WItemsNum^0==WItemsNum^post_7 && __const_5^0==__const_5^post_7 && tmp1^0==tmp1^post_7 ], cost: 1 7: l10 -> l11 : WItemsNum^0'=WItemsNum^post_8, __const_5^0'=__const_5^post_8, tmp1^0'=tmp1^post_8, [ WItemsNum^0==WItemsNum^post_8 && __const_5^0==__const_5^post_8 && tmp1^0==tmp1^post_8 ], cost: 1 8: l11 -> l10 : WItemsNum^0'=WItemsNum^post_9, __const_5^0'=__const_5^post_9, tmp1^0'=tmp1^post_9, [ WItemsNum^0==WItemsNum^post_9 && __const_5^0==__const_5^post_9 && tmp1^0==tmp1^post_9 ], cost: 1 16: l12 -> l3 : WItemsNum^0'=WItemsNum^post_17, __const_5^0'=__const_5^post_17, tmp1^0'=tmp1^post_17, [ WItemsNum^1_1==WItemsNum^1_1 && WItemsNum^post_17==WItemsNum^post_17 && __const_5^0==__const_5^post_17 && tmp1^0==tmp1^post_17 ], cost: 1 17: l13 -> l12 : WItemsNum^0'=WItemsNum^post_18, __const_5^0'=__const_5^post_18, tmp1^0'=tmp1^post_18, [ WItemsNum^0==WItemsNum^post_18 && __const_5^0==__const_5^post_18 && tmp1^0==tmp1^post_18 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 17: l13 -> l12 : WItemsNum^0'=WItemsNum^post_18, __const_5^0'=__const_5^post_18, tmp1^0'=tmp1^post_18, [ WItemsNum^0==WItemsNum^post_18 && __const_5^0==__const_5^post_18 && tmp1^0==tmp1^post_18 ], cost: 1 Removed unreachable and leaf rules: Start location: l13 0: l0 -> l1 : WItemsNum^0'=WItemsNum^post_1, __const_5^0'=__const_5^post_1, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==tmp1^post_1 && WItemsNum^0==WItemsNum^post_1 && __const_5^0==__const_5^post_1 ], cost: 1 1: l0 -> l2 : WItemsNum^0'=WItemsNum^post_2, __const_5^0'=__const_5^post_2, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && WItemsNum^0==WItemsNum^post_2 && __const_5^0==__const_5^post_2 && tmp1^0==tmp1^post_2 ], cost: 1 11: l1 -> l5 : WItemsNum^0'=WItemsNum^post_12, __const_5^0'=__const_5^post_12, tmp1^0'=tmp1^post_12, [ tmp1^0<=0 && 0<=tmp1^0 && WItemsNum^0==WItemsNum^post_12 && __const_5^0==__const_5^post_12 && tmp1^0==tmp1^post_12 ], cost: 1 12: l1 -> l2 : WItemsNum^0'=WItemsNum^post_13, __const_5^0'=__const_5^post_13, tmp1^0'=tmp1^post_13, [ 1<=tmp1^0 && WItemsNum^0==WItemsNum^post_13 && __const_5^0==__const_5^post_13 && tmp1^0==tmp1^post_13 ], cost: 1 13: l1 -> l2 : WItemsNum^0'=WItemsNum^post_14, __const_5^0'=__const_5^post_14, tmp1^0'=tmp1^post_14, [ 1+tmp1^0<=0 && WItemsNum^0==WItemsNum^post_14 && __const_5^0==__const_5^post_14 && tmp1^0==tmp1^post_14 ], cost: 1 14: l2 -> l4 : WItemsNum^0'=WItemsNum^post_15, __const_5^0'=__const_5^post_15, tmp1^0'=tmp1^post_15, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^post_15==1+WItemsNum^0 && __const_5^0==__const_5^post_15 && tmp1^0==tmp1^post_15 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=WItemsNum^post_16, __const_5^0'=__const_5^post_16, tmp1^0'=tmp1^post_16, [ WItemsNum^0<=__const_5^0 && WItemsNum^post_16==1+WItemsNum^0 && __const_5^0==__const_5^post_16 && tmp1^0==tmp1^post_16 ], cost: 1 2: l3 -> l4 : WItemsNum^0'=WItemsNum^post_3, __const_5^0'=__const_5^post_3, tmp1^0'=tmp1^post_3, [ WItemsNum^0==WItemsNum^post_3 && __const_5^0==__const_5^post_3 && tmp1^0==tmp1^post_3 ], cost: 1 3: l4 -> l0 : WItemsNum^0'=WItemsNum^post_4, __const_5^0'=__const_5^post_4, tmp1^0'=tmp1^post_4, [ WItemsNum^0==WItemsNum^post_4 && __const_5^0==__const_5^post_4 && tmp1^0==tmp1^post_4 ], cost: 1 4: l5 -> l6 : WItemsNum^0'=WItemsNum^post_5, __const_5^0'=__const_5^post_5, tmp1^0'=tmp1^post_5, [ WItemsNum^0==WItemsNum^post_5 && __const_5^0==__const_5^post_5 && tmp1^0==tmp1^post_5 ], cost: 1 9: l6 -> l3 : WItemsNum^0'=WItemsNum^post_10, __const_5^0'=__const_5^post_10, tmp1^0'=tmp1^post_10, [ WItemsNum^0<=2 && WItemsNum^0==WItemsNum^post_10 && __const_5^0==__const_5^post_10 && tmp1^0==tmp1^post_10 ], cost: 1 10: l6 -> l5 : WItemsNum^0'=WItemsNum^post_11, __const_5^0'=__const_5^post_11, tmp1^0'=tmp1^post_11, [ 3<=WItemsNum^0 && WItemsNum^post_11==-1+WItemsNum^0 && __const_5^0==__const_5^post_11 && tmp1^0==tmp1^post_11 ], cost: 1 16: l12 -> l3 : WItemsNum^0'=WItemsNum^post_17, __const_5^0'=__const_5^post_17, tmp1^0'=tmp1^post_17, [ WItemsNum^1_1==WItemsNum^1_1 && WItemsNum^post_17==WItemsNum^post_17 && __const_5^0==__const_5^post_17 && tmp1^0==tmp1^post_17 ], cost: 1 17: l13 -> l12 : WItemsNum^0'=WItemsNum^post_18, __const_5^0'=__const_5^post_18, tmp1^0'=tmp1^post_18, [ WItemsNum^0==WItemsNum^post_18 && __const_5^0==__const_5^post_18 && tmp1^0==tmp1^post_18 ], cost: 1 Simplified all rules, resulting in: Start location: l13 0: l0 -> l1 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 1: l0 -> l2 : [ WItemsNum^0<=__const_5^0 ], cost: 1 11: l1 -> l5 : [ tmp1^0==0 ], cost: 1 12: l1 -> l2 : [ 1<=tmp1^0 ], cost: 1 13: l1 -> l2 : [ 1+tmp1^0<=0 ], cost: 1 14: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 2: l3 -> l4 : [], cost: 1 3: l4 -> l0 : [], cost: 1 4: l5 -> l6 : [], cost: 1 9: l6 -> l3 : [ WItemsNum^0<=2 ], cost: 1 10: l6 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 16: l12 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 1 17: l13 -> l12 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l13 0: l0 -> l1 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 1: l0 -> l2 : [ WItemsNum^0<=__const_5^0 ], cost: 1 11: l1 -> l5 : [ tmp1^0==0 ], cost: 1 12: l1 -> l2 : [ 1<=tmp1^0 ], cost: 1 13: l1 -> l2 : [ 1+tmp1^0<=0 ], cost: 1 14: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 2: l3 -> l4 : [], cost: 1 3: l4 -> l0 : [], cost: 1 4: l5 -> l6 : [], cost: 1 9: l6 -> l3 : [ WItemsNum^0<=2 ], cost: 1 10: l6 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l13 11: l1 -> l5 : [ tmp1^0==0 ], cost: 1 12: l1 -> l2 : [ 1<=tmp1^0 ], cost: 1 13: l1 -> l2 : [ 1+tmp1^0<=0 ], cost: 1 14: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 2: l3 -> l4 : [], cost: 1 19: l4 -> l1 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 20: l4 -> l2 : [ WItemsNum^0<=__const_5^0 ], cost: 2 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 22: l5 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Accelerating simple loops of location 5. Accelerating the following rules: 22: l5 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 Accelerated rule 22 with metering function -2+WItemsNum^0, yielding the new rule 23. Removing the simple loops: 22. Accelerated all simple loops using metering functions (where possible): Start location: l13 11: l1 -> l5 : [ tmp1^0==0 ], cost: 1 12: l1 -> l2 : [ 1<=tmp1^0 ], cost: 1 13: l1 -> l2 : [ 1+tmp1^0<=0 ], cost: 1 14: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 2: l3 -> l4 : [], cost: 1 19: l4 -> l1 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 20: l4 -> l2 : [ WItemsNum^0<=__const_5^0 ], cost: 2 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 23: l5 -> l5 : WItemsNum^0'=2, [ 3<=WItemsNum^0 ], cost: -4+2*WItemsNum^0 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l13 11: l1 -> l5 : [ tmp1^0==0 ], cost: 1 12: l1 -> l2 : [ 1<=tmp1^0 ], cost: 1 13: l1 -> l2 : [ 1+tmp1^0<=0 ], cost: 1 24: l1 -> l5 : WItemsNum^0'=2, [ tmp1^0==0 && 3<=WItemsNum^0 ], cost: -3+2*WItemsNum^0 14: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 15: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 2: l3 -> l4 : [], cost: 1 19: l4 -> l1 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 20: l4 -> l2 : [ WItemsNum^0<=__const_5^0 ], cost: 2 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l13 2: l3 -> l4 : [], cost: 1 25: l4 -> l5 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 ], cost: 3 28: l4 -> l5 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 && 3<=WItemsNum^0 ], cost: -1+2*WItemsNum^0 29: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 3 30: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && 1<=tmp1^post_1 ], cost: 4 31: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && 1+tmp1^post_1<=0 ], cost: 4 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Accelerating simple loops of location 4. Accelerating the following rules: 29: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 3 30: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && 1<=tmp1^post_1 ], cost: 4 31: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && 1+tmp1^post_1<=0 ], cost: 4 Accelerated rule 29 with metering function 1-WItemsNum^0+__const_5^0, yielding the new rule 32. Accelerated rule 30 with NONTERM, yielding the new rule 33. Accelerated rule 31 with NONTERM, yielding the new rule 34. Removing the simple loops: 29 30 31. Accelerated all simple loops using metering functions (where possible): Start location: l13 2: l3 -> l4 : [], cost: 1 25: l4 -> l5 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 ], cost: 3 28: l4 -> l5 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 && 3<=WItemsNum^0 ], cost: -1+2*WItemsNum^0 32: l4 -> l4 : WItemsNum^0'=1+__const_5^0, [ WItemsNum^0<=__const_5^0 ], cost: 3-3*WItemsNum^0+3*__const_5^0 33: l4 -> [15] : [ 1+__const_5^0<=WItemsNum^0 && 1<=tmp1^post_1 ], cost: NONTERM 34: l4 -> [15] : [ 1+__const_5^0<=WItemsNum^0 && 1+tmp1^post_1<=0 ], cost: NONTERM 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l13 2: l3 -> l4 : [], cost: 1 35: l3 -> l4 : WItemsNum^0'=1+__const_5^0, [ WItemsNum^0<=__const_5^0 ], cost: 4-3*WItemsNum^0+3*__const_5^0 36: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 37: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 25: l4 -> l5 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 ], cost: 3 28: l4 -> l5 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 && 3<=WItemsNum^0 ], cost: -1+2*WItemsNum^0 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l13 36: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 37: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 38: l3 -> l5 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 ], cost: 4 39: l3 -> l5 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 && 3<=WItemsNum^0 ], cost: 2*WItemsNum^0 40: l3 -> l5 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_1, [ WItemsNum^0<=__const_5^0 && tmp1^post_1==0 ], cost: 7-3*WItemsNum^0+3*__const_5^0 41: l3 -> l5 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ WItemsNum^0<=__const_5^0 && tmp1^post_1==0 && 3<=1+__const_5^0 ], cost: 5-3*WItemsNum^0+5*__const_5^0 21: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l13 37: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 42: l3 -> l3 : tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 && WItemsNum^0<=2 ], cost: 6 43: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ 1+__const_5^0<=WItemsNum^0 && tmp1^post_1==0 && 3<=WItemsNum^0 ], cost: 2+2*WItemsNum^0 44: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_1, [ WItemsNum^0<=__const_5^0 && tmp1^post_1==0 && 1+__const_5^0<=2 ], cost: 9-3*WItemsNum^0+3*__const_5^0 45: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_1, [ WItemsNum^0<=__const_5^0 && tmp1^post_1==0 && 3<=1+__const_5^0 ], cost: 7-3*WItemsNum^0+5*__const_5^0 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 42: l3 -> l3 : tmp1^0'=0, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^0<=2 ], cost: 6 43: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=0, [ 1+__const_5^0<=WItemsNum^0 && 3<=WItemsNum^0 ], cost: 2+2*WItemsNum^0 44: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=0, [ WItemsNum^0<=__const_5^0 && 1+__const_5^0<=2 ], cost: 9-3*WItemsNum^0+3*__const_5^0 45: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=0, [ WItemsNum^0<=__const_5^0 && 3<=1+__const_5^0 ], cost: 7-3*WItemsNum^0+5*__const_5^0 Accelerated rule 42 with NONTERM, yielding the new rule 46. Found no metering function for rule 43. Found no metering function for rule 44. Accelerated rule 45 with NONTERM, yielding the new rule 47. Removing the simple loops: 42 45. Accelerated all simple loops using metering functions (where possible): Start location: l13 37: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 43: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=0, [ 1+__const_5^0<=WItemsNum^0 && 3<=WItemsNum^0 ], cost: 2+2*WItemsNum^0 44: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=0, [ WItemsNum^0<=__const_5^0 && 1+__const_5^0<=2 ], cost: 9-3*WItemsNum^0+3*__const_5^0 46: l3 -> [16] : [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^0<=2 ], cost: NONTERM 47: l3 -> [16] : [ WItemsNum^0<=__const_5^0 && 3<=1+__const_5^0 && 7-3*WItemsNum^0+5*__const_5^0>=1 ], cost: NONTERM 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l13 37: l3 -> [15] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 18: l13 -> l3 : WItemsNum^0'=WItemsNum^post_17, [], cost: 2 48: l13 -> l3 : WItemsNum^0'=2, tmp1^0'=0, [ 1+__const_5^0<=WItemsNum^post_17 && 3<=WItemsNum^post_17 ], cost: 4+2*WItemsNum^post_17 49: l13 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=0, [ WItemsNum^post_17<=__const_5^0 && 1+__const_5^0<=2 ], cost: 11-3*WItemsNum^post_17+3*__const_5^0 50: l13 -> [16] : WItemsNum^0'=WItemsNum^post_17, [ 1+__const_5^0<=WItemsNum^post_17 && WItemsNum^post_17<=2 ], cost: NONTERM 51: l13 -> [16] : WItemsNum^0'=WItemsNum^post_17, [ WItemsNum^post_17<=__const_5^0 && 3<=1+__const_5^0 && 7-3*WItemsNum^post_17+5*__const_5^0>=1 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l13 50: l13 -> [16] : WItemsNum^0'=WItemsNum^post_17, [ 1+__const_5^0<=WItemsNum^post_17 && WItemsNum^post_17<=2 ], cost: NONTERM 51: l13 -> [16] : WItemsNum^0'=WItemsNum^post_17, [ WItemsNum^post_17<=__const_5^0 && 3<=1+__const_5^0 && 7-3*WItemsNum^post_17+5*__const_5^0>=1 ], cost: NONTERM 52: l13 -> [15] : WItemsNum^0'=WItemsNum^post_17, [ 1+__const_5^0<=WItemsNum^post_17 ], cost: NONTERM 53: l13 -> [15] : WItemsNum^0'=2, tmp1^0'=0, [ 1+__const_5^0<=WItemsNum^post_17 && 3<=WItemsNum^post_17 && 1+__const_5^0<=2 ], cost: NONTERM 54: l13 -> [15] : WItemsNum^0'=1+__const_5^0, tmp1^0'=0, [ WItemsNum^post_17<=__const_5^0 && 1+__const_5^0<=2 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l13 50: l13 -> [16] : WItemsNum^0'=WItemsNum^post_17, [ 1+__const_5^0<=WItemsNum^post_17 && WItemsNum^post_17<=2 ], cost: NONTERM 51: l13 -> [16] : WItemsNum^0'=WItemsNum^post_17, [ WItemsNum^post_17<=__const_5^0 && 3<=1+__const_5^0 && 7-3*WItemsNum^post_17+5*__const_5^0>=1 ], cost: NONTERM 52: l13 -> [15] : WItemsNum^0'=WItemsNum^post_17, [ 1+__const_5^0<=WItemsNum^post_17 ], cost: NONTERM 53: l13 -> [15] : WItemsNum^0'=2, tmp1^0'=0, [ 1+__const_5^0<=WItemsNum^post_17 && 3<=WItemsNum^post_17 && 1+__const_5^0<=2 ], cost: NONTERM 54: l13 -> [15] : WItemsNum^0'=1+__const_5^0, tmp1^0'=0, [ WItemsNum^post_17<=__const_5^0 && 1+__const_5^0<=2 ], cost: NONTERM Computing asymptotic complexity for rule 50 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+__const_5^0<=WItemsNum^post_17 && WItemsNum^post_17<=2 ] NO