NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l14 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 && WItemsNum^0==WItemsNum^post_1 && __const_5^0==__const_5^post_1 && tmp1^0==tmp1^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 && tmp1^post_2==tmp1^post_2 && WItemsNum^0==WItemsNum^post_2 && __const_5^0==__const_5^post_2 ], cost: 1 11: l1 -> l5 : WItemsNum^0'=WItemsNum^post_12, __const_5^0'=__const_5^post_12, tmp1^0'=tmp1^post_12, [ WItemsNum^0==WItemsNum^post_12 && __const_5^0==__const_5^post_12 && tmp1^0==tmp1^post_12 ], cost: 1 14: l2 -> l1 : WItemsNum^0'=WItemsNum^post_15, __const_5^0'=__const_5^post_15, tmp1^0'=tmp1^post_15, [ tmp1^0<=0 && 0<=tmp1^0 && WItemsNum^0==WItemsNum^post_15 && __const_5^0==__const_5^post_15 && tmp1^0==tmp1^post_15 ], cost: 1 15: l2 -> l12 : WItemsNum^0'=WItemsNum^post_16, __const_5^0'=__const_5^post_16, tmp1^0'=tmp1^post_16, [ 1<=tmp1^0 && WItemsNum^0==WItemsNum^post_16 && __const_5^0==__const_5^post_16 && tmp1^0==tmp1^post_16 ], cost: 1 16: l2 -> l12 : WItemsNum^0'=WItemsNum^post_17, __const_5^0'=__const_5^post_17, tmp1^0'=tmp1^post_17, [ 1+tmp1^0<=0 && WItemsNum^0==WItemsNum^post_17 && __const_5^0==__const_5^post_17 && tmp1^0==tmp1^post_17 ], 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 7: l6 -> l3 : WItemsNum^0'=WItemsNum^post_8, __const_5^0'=__const_5^post_8, tmp1^0'=tmp1^post_8, [ WItemsNum^0<=2 && WItemsNum^0==WItemsNum^post_8 && __const_5^0==__const_5^post_8 && tmp1^0==tmp1^post_8 ], cost: 1 8: l6 -> l5 : WItemsNum^0'=WItemsNum^post_9, __const_5^0'=__const_5^post_9, tmp1^0'=tmp1^post_9, [ 3<=WItemsNum^0 && WItemsNum^post_9==-1+WItemsNum^0 && __const_5^0==__const_5^post_9 && tmp1^0==tmp1^post_9 ], 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 9: l10 -> l11 : WItemsNum^0'=WItemsNum^post_10, __const_5^0'=__const_5^post_10, tmp1^0'=tmp1^post_10, [ WItemsNum^0==WItemsNum^post_10 && __const_5^0==__const_5^post_10 && tmp1^0==tmp1^post_10 ], cost: 1 10: l11 -> l10 : WItemsNum^0'=WItemsNum^post_11, __const_5^0'=__const_5^post_11, tmp1^0'=tmp1^post_11, [ WItemsNum^0==WItemsNum^post_11 && __const_5^0==__const_5^post_11 && tmp1^0==tmp1^post_11 ], cost: 1 12: l12 -> l4 : WItemsNum^0'=WItemsNum^post_13, __const_5^0'=__const_5^post_13, tmp1^0'=tmp1^post_13, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^post_13==1+WItemsNum^0 && __const_5^0==__const_5^post_13 && tmp1^0==tmp1^post_13 ], cost: 1 13: l12 -> l4 : WItemsNum^0'=WItemsNum^post_14, __const_5^0'=__const_5^post_14, tmp1^0'=tmp1^post_14, [ WItemsNum^0<=__const_5^0 && WItemsNum^post_14==1+WItemsNum^0 && __const_5^0==__const_5^post_14 && tmp1^0==tmp1^post_14 ], cost: 1 17: l13 -> l3 : WItemsNum^0'=WItemsNum^post_18, __const_5^0'=__const_5^post_18, tmp1^0'=tmp1^post_18, [ WItemsNum^1_1==WItemsNum^1_1 && WItemsNum^post_18==WItemsNum^post_18 && __const_5^0==__const_5^post_18 && tmp1^0==tmp1^post_18 ], cost: 1 18: l14 -> l13 : WItemsNum^0'=WItemsNum^post_19, __const_5^0'=__const_5^post_19, tmp1^0'=tmp1^post_19, [ WItemsNum^0==WItemsNum^post_19 && __const_5^0==__const_5^post_19 && tmp1^0==tmp1^post_19 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 18: l14 -> l13 : WItemsNum^0'=WItemsNum^post_19, __const_5^0'=__const_5^post_19, tmp1^0'=tmp1^post_19, [ WItemsNum^0==WItemsNum^post_19 && __const_5^0==__const_5^post_19 && tmp1^0==tmp1^post_19 ], cost: 1 Removed unreachable and leaf rules: Start location: l14 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 && WItemsNum^0==WItemsNum^post_1 && __const_5^0==__const_5^post_1 && tmp1^0==tmp1^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 && tmp1^post_2==tmp1^post_2 && WItemsNum^0==WItemsNum^post_2 && __const_5^0==__const_5^post_2 ], cost: 1 11: l1 -> l5 : WItemsNum^0'=WItemsNum^post_12, __const_5^0'=__const_5^post_12, tmp1^0'=tmp1^post_12, [ WItemsNum^0==WItemsNum^post_12 && __const_5^0==__const_5^post_12 && tmp1^0==tmp1^post_12 ], cost: 1 14: l2 -> l1 : WItemsNum^0'=WItemsNum^post_15, __const_5^0'=__const_5^post_15, tmp1^0'=tmp1^post_15, [ tmp1^0<=0 && 0<=tmp1^0 && WItemsNum^0==WItemsNum^post_15 && __const_5^0==__const_5^post_15 && tmp1^0==tmp1^post_15 ], cost: 1 15: l2 -> l12 : WItemsNum^0'=WItemsNum^post_16, __const_5^0'=__const_5^post_16, tmp1^0'=tmp1^post_16, [ 1<=tmp1^0 && WItemsNum^0==WItemsNum^post_16 && __const_5^0==__const_5^post_16 && tmp1^0==tmp1^post_16 ], cost: 1 16: l2 -> l12 : WItemsNum^0'=WItemsNum^post_17, __const_5^0'=__const_5^post_17, tmp1^0'=tmp1^post_17, [ 1+tmp1^0<=0 && WItemsNum^0==WItemsNum^post_17 && __const_5^0==__const_5^post_17 && tmp1^0==tmp1^post_17 ], 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 7: l6 -> l3 : WItemsNum^0'=WItemsNum^post_8, __const_5^0'=__const_5^post_8, tmp1^0'=tmp1^post_8, [ WItemsNum^0<=2 && WItemsNum^0==WItemsNum^post_8 && __const_5^0==__const_5^post_8 && tmp1^0==tmp1^post_8 ], cost: 1 8: l6 -> l5 : WItemsNum^0'=WItemsNum^post_9, __const_5^0'=__const_5^post_9, tmp1^0'=tmp1^post_9, [ 3<=WItemsNum^0 && WItemsNum^post_9==-1+WItemsNum^0 && __const_5^0==__const_5^post_9 && tmp1^0==tmp1^post_9 ], cost: 1 12: l12 -> l4 : WItemsNum^0'=WItemsNum^post_13, __const_5^0'=__const_5^post_13, tmp1^0'=tmp1^post_13, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^post_13==1+WItemsNum^0 && __const_5^0==__const_5^post_13 && tmp1^0==tmp1^post_13 ], cost: 1 13: l12 -> l4 : WItemsNum^0'=WItemsNum^post_14, __const_5^0'=__const_5^post_14, tmp1^0'=tmp1^post_14, [ WItemsNum^0<=__const_5^0 && WItemsNum^post_14==1+WItemsNum^0 && __const_5^0==__const_5^post_14 && tmp1^0==tmp1^post_14 ], cost: 1 17: l13 -> l3 : WItemsNum^0'=WItemsNum^post_18, __const_5^0'=__const_5^post_18, tmp1^0'=tmp1^post_18, [ WItemsNum^1_1==WItemsNum^1_1 && WItemsNum^post_18==WItemsNum^post_18 && __const_5^0==__const_5^post_18 && tmp1^0==tmp1^post_18 ], cost: 1 18: l14 -> l13 : WItemsNum^0'=WItemsNum^post_19, __const_5^0'=__const_5^post_19, tmp1^0'=tmp1^post_19, [ WItemsNum^0==WItemsNum^post_19 && __const_5^0==__const_5^post_19 && tmp1^0==tmp1^post_19 ], cost: 1 Simplified all rules, resulting in: Start location: l14 0: l0 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 1: l0 -> l2 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 ], cost: 1 11: l1 -> l5 : [], cost: 1 14: l2 -> l1 : [ tmp1^0==0 ], cost: 1 15: l2 -> l12 : [ 1<=tmp1^0 ], cost: 1 16: l2 -> l12 : [ 1+tmp1^0<=0 ], cost: 1 2: l3 -> l4 : [], cost: 1 3: l4 -> l0 : [], cost: 1 4: l5 -> l6 : [], cost: 1 7: l6 -> l3 : [ WItemsNum^0<=2 ], cost: 1 8: l6 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 12: l12 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 13: l12 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 17: l13 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 1 18: l14 -> l13 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l14 0: l0 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 1: l0 -> l2 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 ], cost: 1 11: l1 -> l5 : [], cost: 1 14: l2 -> l1 : [ tmp1^0==0 ], cost: 1 15: l2 -> l12 : [ 1<=tmp1^0 ], cost: 1 16: l2 -> l12 : [ 1+tmp1^0<=0 ], cost: 1 2: l3 -> l4 : [], cost: 1 3: l4 -> l0 : [], cost: 1 4: l5 -> l6 : [], cost: 1 7: l6 -> l3 : [ WItemsNum^0<=2 ], cost: 1 8: l6 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 12: l12 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 13: l12 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l14 11: l1 -> l5 : [], cost: 1 14: l2 -> l1 : [ tmp1^0==0 ], cost: 1 24: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1<=tmp1^0 && 1+__const_5^0<=WItemsNum^0 ], cost: 2 25: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1<=tmp1^0 && WItemsNum^0<=__const_5^0 ], cost: 2 26: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+tmp1^0<=0 && 1+__const_5^0<=WItemsNum^0 ], cost: 2 27: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+tmp1^0<=0 && WItemsNum^0<=__const_5^0 ], cost: 2 2: l3 -> l4 : [], cost: 1 20: l4 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 21: l4 -> l2 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 ], cost: 2 22: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 23: l5 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Accelerating simple loops of location 5. Accelerating the following rules: 23: l5 -> l5 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 Accelerated rule 23 with backward acceleration, yielding the new rule 28. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 23. Accelerated all simple loops using metering functions (where possible): Start location: l14 11: l1 -> l5 : [], cost: 1 14: l2 -> l1 : [ tmp1^0==0 ], cost: 1 24: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1<=tmp1^0 && 1+__const_5^0<=WItemsNum^0 ], cost: 2 25: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1<=tmp1^0 && WItemsNum^0<=__const_5^0 ], cost: 2 26: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+tmp1^0<=0 && 1+__const_5^0<=WItemsNum^0 ], cost: 2 27: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+tmp1^0<=0 && WItemsNum^0<=__const_5^0 ], cost: 2 2: l3 -> l4 : [], cost: 1 20: l4 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 21: l4 -> l2 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 ], cost: 2 22: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 28: l5 -> l5 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -4+2*WItemsNum^0 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l14 11: l1 -> l5 : [], cost: 1 29: l1 -> l5 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -3+2*WItemsNum^0 14: l2 -> l1 : [ tmp1^0==0 ], cost: 1 24: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1<=tmp1^0 && 1+__const_5^0<=WItemsNum^0 ], cost: 2 25: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1<=tmp1^0 && WItemsNum^0<=__const_5^0 ], cost: 2 26: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+tmp1^0<=0 && 1+__const_5^0<=WItemsNum^0 ], cost: 2 27: l2 -> l4 : WItemsNum^0'=1+WItemsNum^0, [ 1+tmp1^0<=0 && WItemsNum^0<=__const_5^0 ], cost: 2 2: l3 -> l4 : [], cost: 1 20: l4 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 21: l4 -> l2 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 ], cost: 2 22: l5 -> l3 : [ WItemsNum^0<=2 ], cost: 2 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l14 33: l1 -> l3 : [ WItemsNum^0<=2 ], cost: 3 34: l1 -> l3 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -1+2*WItemsNum^0 2: l3 -> l4 : [], cost: 1 20: l4 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 30: l4 -> l1 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 ], cost: 3 31: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && 1<=tmp1^post_2 ], cost: 4 32: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && 1+tmp1^post_2<=0 ], cost: 4 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Accelerating simple loops of location 4. Accelerating the following rules: 31: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && 1<=tmp1^post_2 ], cost: 4 32: l4 -> l4 : WItemsNum^0'=1+WItemsNum^0, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && 1+tmp1^post_2<=0 ], cost: 4 Accelerated rule 31 with backward acceleration, yielding the new rule 35. Accelerated rule 32 with backward acceleration, yielding the new rule 36. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 31 32. Accelerated all simple loops using metering functions (where possible): Start location: l14 33: l1 -> l3 : [ WItemsNum^0<=2 ], cost: 3 34: l1 -> l3 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -1+2*WItemsNum^0 2: l3 -> l4 : [], cost: 1 20: l4 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 30: l4 -> l1 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 ], cost: 3 35: l4 -> l4 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 4+4*__const_5^0-4*WItemsNum^0 36: l4 -> l4 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 4+4*__const_5^0-4*WItemsNum^0 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l14 33: l1 -> l3 : [ WItemsNum^0<=2 ], cost: 3 34: l1 -> l3 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -1+2*WItemsNum^0 2: l3 -> l4 : [], cost: 1 37: l3 -> l4 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 38: l3 -> l4 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 20: l4 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 30: l4 -> l1 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 ], cost: 3 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l14 33: l1 -> l3 : [ WItemsNum^0<=2 ], cost: 3 34: l1 -> l3 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -1+2*WItemsNum^0 39: l3 -> l1 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 3 40: l3 -> l1 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 ], cost: 4 41: l3 -> l1 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 7+4*__const_5^0-4*WItemsNum^0 42: l3 -> l1 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 7+4*__const_5^0-4*WItemsNum^0 43: l3 -> [17] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 44: l3 -> [17] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l14 43: l3 -> [17] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 44: l3 -> [17] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 45: l3 -> l3 : [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^0<=2 ], cost: 6 46: l3 -> l3 : WItemsNum^0'=2, [ 1+__const_5^0<=WItemsNum^0 && -2+WItemsNum^0>=0 ], cost: 2+2*WItemsNum^0 47: l3 -> l3 : tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 && WItemsNum^0<=2 ], cost: 7 48: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 && -2+WItemsNum^0>=0 ], cost: 3+2*WItemsNum^0 49: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 50: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 51: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 52: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Applied pruning (of leafs and parallel rules): Start location: l14 43: l3 -> [17] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 44: l3 -> [17] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 48: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ WItemsNum^0<=__const_5^0 && tmp1^post_2==0 && -2+WItemsNum^0>=0 ], cost: 3+2*WItemsNum^0 49: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 50: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 51: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 52: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 48: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=0, [ WItemsNum^0<=__const_5^0 && -2+WItemsNum^0>=0 ], cost: 3+2*WItemsNum^0 49: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 50: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 51: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 52: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 Accelerated rule 48 with non-termination, yielding the new rule 53. Failed to prove monotonicity of the guard of rule 49. [test] deduced pseudo-invariant 2-WItemsNum^0<=0, also trying -2+WItemsNum^0<=-1 Accelerated rule 50 with non-termination, yielding the new rule 54. Accelerated rule 50 with non-termination, yielding the new rule 55. Accelerated rule 50 with backward acceleration, yielding the new rule 56. Failed to prove monotonicity of the guard of rule 51. [test] deduced pseudo-invariant 2-WItemsNum^0<=0, also trying -2+WItemsNum^0<=-1 Accelerated rule 52 with non-termination, yielding the new rule 57. Accelerated rule 52 with non-termination, yielding the new rule 58. Accelerated rule 52 with backward acceleration, yielding the new rule 59. [accelerate] Nesting with 2 inner and 4 outer candidates Removing the simple loops: 48. Also removing duplicate rules: 55 58. Accelerated all simple loops using metering functions (where possible): Start location: l14 43: l3 -> [17] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 44: l3 -> [17] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 49: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 50: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 51: l3 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && 1+__const_5^0<=2 ], cost: 10+4*__const_5^0-4*WItemsNum^0 52: l3 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 ], cost: 8+6*__const_5^0-4*WItemsNum^0 53: l3 -> [18] : [ WItemsNum^0<=__const_5^0 && -2+WItemsNum^0>=0 ], cost: NONTERM 54: l3 -> [18] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=1 ], cost: NONTERM 56: l3 -> [18] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 && 2-WItemsNum^0<=0 ], cost: NONTERM 57: l3 -> [18] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=1 ], cost: NONTERM 59: l3 -> [18] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 && -1+__const_5^0>=0 && 2-WItemsNum^0<=0 ], cost: NONTERM 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l14 43: l3 -> [17] : [ 1<=tmp1^post_2 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 44: l3 -> [17] : [ 1+tmp1^post_2<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 19: l14 -> l3 : WItemsNum^0'=WItemsNum^post_18, [], cost: 2 60: l14 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && 1+__const_5^0<=2 ], cost: 12-4*WItemsNum^post_18+4*__const_5^0 61: l14 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=0 ], cost: 10-4*WItemsNum^post_18+6*__const_5^0 62: l14 -> l3 : WItemsNum^0'=1+__const_5^0, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && 1+__const_5^0<=2 ], cost: 12-4*WItemsNum^post_18+4*__const_5^0 63: l14 -> l3 : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=0 ], cost: 10-4*WItemsNum^post_18+6*__const_5^0 64: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM 65: l14 -> [18] : [ -1+__const_5^0>=1 ], cost: NONTERM 66: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM 67: l14 -> [18] : [ -1+__const_5^0>=1 ], cost: NONTERM 68: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l14 64: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM 65: l14 -> [18] : [ -1+__const_5^0>=1 ], cost: NONTERM 66: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM 67: l14 -> [18] : [ -1+__const_5^0>=1 ], cost: NONTERM 68: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM 69: l14 -> [17] : WItemsNum^0'=WItemsNum^post_18, [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+4*__const_5^0 70: l14 -> [17] : WItemsNum^0'=WItemsNum^post_18, [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+4*__const_5^0 71: l14 -> [17] : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+10*__const_5^0 72: l14 -> [17] : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+10*__const_5^0 73: l14 -> [19] : [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && 1+__const_5^0<=2 ], cost: 12-4*WItemsNum^post_18+4*__const_5^0 74: l14 -> [19] : [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=0 ], cost: 10-4*WItemsNum^post_18+6*__const_5^0 75: l14 -> [19] : [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && 1+__const_5^0<=2 ], cost: 12-4*WItemsNum^post_18+4*__const_5^0 76: l14 -> [19] : [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=0 ], cost: 10-4*WItemsNum^post_18+6*__const_5^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l14 67: l14 -> [18] : [ -1+__const_5^0>=1 ], cost: NONTERM 68: l14 -> [18] : [ 2<=__const_5^0 ], cost: NONTERM 69: l14 -> [17] : WItemsNum^0'=WItemsNum^post_18, [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+4*__const_5^0 70: l14 -> [17] : WItemsNum^0'=WItemsNum^post_18, [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+4*__const_5^0 71: l14 -> [17] : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+10*__const_5^0 72: l14 -> [17] : WItemsNum^0'=2, tmp1^0'=tmp1^post_2, [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=1 ], cost: 7-4*WItemsNum^post_18+10*__const_5^0 73: l14 -> [19] : [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && 1+__const_5^0<=2 ], cost: 12-4*WItemsNum^post_18+4*__const_5^0 74: l14 -> [19] : [ 1<=tmp1^post_2 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=0 ], cost: 10-4*WItemsNum^post_18+6*__const_5^0 75: l14 -> [19] : [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && 1+__const_5^0<=2 ], cost: 12-4*WItemsNum^post_18+4*__const_5^0 76: l14 -> [19] : [ 1+tmp1^post_2<=0 && 1-WItemsNum^post_18+__const_5^0>=1 && -1+__const_5^0>=0 ], cost: 10-4*WItemsNum^post_18+6*__const_5^0 Computing asymptotic complexity for rule 67 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>=1 ] NO