NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l17 0: l0 -> l1 : WItemsNum^0'=WItemsNum^post_1, __const_5^0'=__const_5^post_1, __rho_1_^0'=__rho_1_^post_1, __rho_2_^0'=__rho_2_^post_1, [ WItemsNum^0==WItemsNum^post_1 && __const_5^0==__const_5^post_1 && __rho_1_^0==__rho_1_^post_1 && __rho_2_^0==__rho_2_^post_1 ], cost: 1 1: l1 -> l0 : WItemsNum^0'=WItemsNum^post_2, __const_5^0'=__const_5^post_2, __rho_1_^0'=__rho_1_^post_2, __rho_2_^0'=__rho_2_^post_2, [ WItemsNum^0==WItemsNum^post_2 && __const_5^0==__const_5^post_2 && __rho_1_^0==__rho_1_^post_2 && __rho_2_^0==__rho_2_^post_2 ], cost: 1 2: l2 -> l3 : WItemsNum^0'=WItemsNum^post_3, __const_5^0'=__const_5^post_3, __rho_1_^0'=__rho_1_^post_3, __rho_2_^0'=__rho_2_^post_3, [ WItemsNum^0==WItemsNum^post_3 && __const_5^0==__const_5^post_3 && __rho_1_^0==__rho_1_^post_3 && __rho_2_^0==__rho_2_^post_3 ], cost: 1 3: l3 -> l4 : WItemsNum^0'=WItemsNum^post_4, __const_5^0'=__const_5^post_4, __rho_1_^0'=__rho_1_^post_4, __rho_2_^0'=__rho_2_^post_4, [ __rho_2_^post_4==__rho_2_^post_4 && WItemsNum^0==WItemsNum^post_4 && __const_5^0==__const_5^post_4 && __rho_1_^0==__rho_1_^post_4 ], cost: 1 15: l4 -> l12 : WItemsNum^0'=WItemsNum^post_16, __const_5^0'=__const_5^post_16, __rho_1_^0'=__rho_1_^post_16, __rho_2_^0'=__rho_2_^post_16, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^0==WItemsNum^post_16 && __const_5^0==__const_5^post_16 && __rho_1_^0==__rho_1_^post_16 && __rho_2_^0==__rho_2_^post_16 ], cost: 1 16: l4 -> l13 : WItemsNum^0'=WItemsNum^post_17, __const_5^0'=__const_5^post_17, __rho_1_^0'=__rho_1_^post_17, __rho_2_^0'=__rho_2_^post_17, [ WItemsNum^0<=__const_5^0 && WItemsNum^0==WItemsNum^post_17 && __const_5^0==__const_5^post_17 && __rho_1_^0==__rho_1_^post_17 && __rho_2_^0==__rho_2_^post_17 ], cost: 1 4: l5 -> l6 : WItemsNum^0'=WItemsNum^post_5, __const_5^0'=__const_5^post_5, __rho_1_^0'=__rho_1_^post_5, __rho_2_^0'=__rho_2_^post_5, [ WItemsNum^0==WItemsNum^post_5 && __const_5^0==__const_5^post_5 && __rho_1_^0==__rho_1_^post_5 && __rho_2_^0==__rho_2_^post_5 ], cost: 1 5: l7 -> l8 : WItemsNum^0'=WItemsNum^post_6, __const_5^0'=__const_5^post_6, __rho_1_^0'=__rho_1_^post_6, __rho_2_^0'=__rho_2_^post_6, [ WItemsNum^0==WItemsNum^post_6 && __const_5^0==__const_5^post_6 && __rho_1_^0==__rho_1_^post_6 && __rho_2_^0==__rho_2_^post_6 ], cost: 1 9: l8 -> l11 : WItemsNum^0'=WItemsNum^post_10, __const_5^0'=__const_5^post_10, __rho_1_^0'=__rho_1_^post_10, __rho_2_^0'=__rho_2_^post_10, [ WItemsNum^0==WItemsNum^post_10 && __const_5^0==__const_5^post_10 && __rho_1_^0==__rho_1_^post_10 && __rho_2_^0==__rho_2_^post_10 ], cost: 1 6: l9 -> l10 : WItemsNum^0'=WItemsNum^post_7, __const_5^0'=__const_5^post_7, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_7, [ WItemsNum^0==WItemsNum^post_7 && __const_5^0==__const_5^post_7 && __rho_1_^0==__rho_1_^post_7 && __rho_2_^0==__rho_2_^post_7 ], cost: 1 7: l10 -> l9 : WItemsNum^0'=WItemsNum^post_8, __const_5^0'=__const_5^post_8, __rho_1_^0'=__rho_1_^post_8, __rho_2_^0'=__rho_2_^post_8, [ 3<=WItemsNum^0 && WItemsNum^post_8==-1+WItemsNum^0 && __const_5^0==__const_5^post_8 && __rho_1_^0==__rho_1_^post_8 && __rho_2_^0==__rho_2_^post_8 ], cost: 1 8: l10 -> l2 : WItemsNum^0'=WItemsNum^post_9, __const_5^0'=__const_5^post_9, __rho_1_^0'=__rho_1_^post_9, __rho_2_^0'=__rho_2_^post_9, [ WItemsNum^0<=2 && WItemsNum^0==WItemsNum^post_9 && __const_5^0==__const_5^post_9 && __rho_1_^0==__rho_1_^post_9 && __rho_2_^0==__rho_2_^post_9 ], cost: 1 10: l11 -> l8 : WItemsNum^0'=WItemsNum^post_11, __const_5^0'=__const_5^post_11, __rho_1_^0'=__rho_1_^post_11, __rho_2_^0'=__rho_2_^post_11, [ WItemsNum^0==WItemsNum^post_11 && __const_5^0==__const_5^post_11 && __rho_1_^0==__rho_1_^post_11 && __rho_2_^0==__rho_2_^post_11 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=WItemsNum^post_12, __const_5^0'=__const_5^post_12, __rho_1_^0'=__rho_1_^post_12, __rho_2_^0'=__rho_2_^post_12, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^post_12==1+WItemsNum^0 && __const_5^0==__const_5^post_12 && __rho_1_^0==__rho_1_^post_12 && __rho_2_^0==__rho_2_^post_12 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=WItemsNum^post_13, __const_5^0'=__const_5^post_13, __rho_1_^0'=__rho_1_^post_13, __rho_2_^0'=__rho_2_^post_13, [ WItemsNum^0<=__const_5^0 && WItemsNum^post_13==1+WItemsNum^0 && __const_5^0==__const_5^post_13 && __rho_1_^0==__rho_1_^post_13 && __rho_2_^0==__rho_2_^post_13 ], cost: 1 13: l13 -> l12 : WItemsNum^0'=WItemsNum^post_14, __const_5^0'=__const_5^post_14, __rho_1_^0'=__rho_1_^post_14, __rho_2_^0'=__rho_2_^post_14, [ __rho_2_^0<=0 && WItemsNum^0==WItemsNum^post_14 && __const_5^0==__const_5^post_14 && __rho_1_^0==__rho_1_^post_14 && __rho_2_^0==__rho_2_^post_14 ], cost: 1 14: l13 -> l9 : WItemsNum^0'=WItemsNum^post_15, __const_5^0'=__const_5^post_15, __rho_1_^0'=__rho_1_^post_15, __rho_2_^0'=__rho_2_^post_15, [ 1<=__rho_2_^0 && WItemsNum^0==WItemsNum^post_15 && __const_5^0==__const_5^post_15 && __rho_1_^0==__rho_1_^post_15 && __rho_2_^0==__rho_2_^post_15 ], cost: 1 17: l14 -> l2 : WItemsNum^0'=WItemsNum^post_18, __const_5^0'=__const_5^post_18, __rho_1_^0'=__rho_1_^post_18, __rho_2_^0'=__rho_2_^post_18, [ WItemsNum^0==WItemsNum^post_18 && __const_5^0==__const_5^post_18 && __rho_1_^0==__rho_1_^post_18 && __rho_2_^0==__rho_2_^post_18 ], cost: 1 18: l15 -> l2 : WItemsNum^0'=WItemsNum^post_19, __const_5^0'=__const_5^post_19, __rho_1_^0'=__rho_1_^post_19, __rho_2_^0'=__rho_2_^post_19, [ 0<=WItemsNum^0 && WItemsNum^0==WItemsNum^post_19 && __const_5^0==__const_5^post_19 && __rho_1_^0==__rho_1_^post_19 && __rho_2_^0==__rho_2_^post_19 ], cost: 1 19: l15 -> l0 : WItemsNum^0'=WItemsNum^post_20, __const_5^0'=__const_5^post_20, __rho_1_^0'=__rho_1_^post_20, __rho_2_^0'=__rho_2_^post_20, [ 1+WItemsNum^0<=0 && WItemsNum^0==WItemsNum^post_20 && __const_5^0==__const_5^post_20 && __rho_1_^0==__rho_1_^post_20 && __rho_2_^0==__rho_2_^post_20 ], cost: 1 20: l16 -> l15 : WItemsNum^0'=WItemsNum^post_21, __const_5^0'=__const_5^post_21, __rho_1_^0'=__rho_1_^post_21, __rho_2_^0'=__rho_2_^post_21, [ WItemsNum^1_1==WItemsNum^1_1 && __rho_1_^post_21==__rho_1_^post_21 && WItemsNum^post_21==__rho_1_^post_21 && __const_5^0==__const_5^post_21 && __rho_2_^0==__rho_2_^post_21 ], cost: 1 21: l17 -> l16 : WItemsNum^0'=WItemsNum^post_22, __const_5^0'=__const_5^post_22, __rho_1_^0'=__rho_1_^post_22, __rho_2_^0'=__rho_2_^post_22, [ WItemsNum^0==WItemsNum^post_22 && __const_5^0==__const_5^post_22 && __rho_1_^0==__rho_1_^post_22 && __rho_2_^0==__rho_2_^post_22 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 21: l17 -> l16 : WItemsNum^0'=WItemsNum^post_22, __const_5^0'=__const_5^post_22, __rho_1_^0'=__rho_1_^post_22, __rho_2_^0'=__rho_2_^post_22, [ WItemsNum^0==WItemsNum^post_22 && __const_5^0==__const_5^post_22 && __rho_1_^0==__rho_1_^post_22 && __rho_2_^0==__rho_2_^post_22 ], cost: 1 Removed unreachable and leaf rules: Start location: l17 0: l0 -> l1 : WItemsNum^0'=WItemsNum^post_1, __const_5^0'=__const_5^post_1, __rho_1_^0'=__rho_1_^post_1, __rho_2_^0'=__rho_2_^post_1, [ WItemsNum^0==WItemsNum^post_1 && __const_5^0==__const_5^post_1 && __rho_1_^0==__rho_1_^post_1 && __rho_2_^0==__rho_2_^post_1 ], cost: 1 1: l1 -> l0 : WItemsNum^0'=WItemsNum^post_2, __const_5^0'=__const_5^post_2, __rho_1_^0'=__rho_1_^post_2, __rho_2_^0'=__rho_2_^post_2, [ WItemsNum^0==WItemsNum^post_2 && __const_5^0==__const_5^post_2 && __rho_1_^0==__rho_1_^post_2 && __rho_2_^0==__rho_2_^post_2 ], cost: 1 2: l2 -> l3 : WItemsNum^0'=WItemsNum^post_3, __const_5^0'=__const_5^post_3, __rho_1_^0'=__rho_1_^post_3, __rho_2_^0'=__rho_2_^post_3, [ WItemsNum^0==WItemsNum^post_3 && __const_5^0==__const_5^post_3 && __rho_1_^0==__rho_1_^post_3 && __rho_2_^0==__rho_2_^post_3 ], cost: 1 3: l3 -> l4 : WItemsNum^0'=WItemsNum^post_4, __const_5^0'=__const_5^post_4, __rho_1_^0'=__rho_1_^post_4, __rho_2_^0'=__rho_2_^post_4, [ __rho_2_^post_4==__rho_2_^post_4 && WItemsNum^0==WItemsNum^post_4 && __const_5^0==__const_5^post_4 && __rho_1_^0==__rho_1_^post_4 ], cost: 1 15: l4 -> l12 : WItemsNum^0'=WItemsNum^post_16, __const_5^0'=__const_5^post_16, __rho_1_^0'=__rho_1_^post_16, __rho_2_^0'=__rho_2_^post_16, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^0==WItemsNum^post_16 && __const_5^0==__const_5^post_16 && __rho_1_^0==__rho_1_^post_16 && __rho_2_^0==__rho_2_^post_16 ], cost: 1 16: l4 -> l13 : WItemsNum^0'=WItemsNum^post_17, __const_5^0'=__const_5^post_17, __rho_1_^0'=__rho_1_^post_17, __rho_2_^0'=__rho_2_^post_17, [ WItemsNum^0<=__const_5^0 && WItemsNum^0==WItemsNum^post_17 && __const_5^0==__const_5^post_17 && __rho_1_^0==__rho_1_^post_17 && __rho_2_^0==__rho_2_^post_17 ], cost: 1 6: l9 -> l10 : WItemsNum^0'=WItemsNum^post_7, __const_5^0'=__const_5^post_7, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_7, [ WItemsNum^0==WItemsNum^post_7 && __const_5^0==__const_5^post_7 && __rho_1_^0==__rho_1_^post_7 && __rho_2_^0==__rho_2_^post_7 ], cost: 1 7: l10 -> l9 : WItemsNum^0'=WItemsNum^post_8, __const_5^0'=__const_5^post_8, __rho_1_^0'=__rho_1_^post_8, __rho_2_^0'=__rho_2_^post_8, [ 3<=WItemsNum^0 && WItemsNum^post_8==-1+WItemsNum^0 && __const_5^0==__const_5^post_8 && __rho_1_^0==__rho_1_^post_8 && __rho_2_^0==__rho_2_^post_8 ], cost: 1 8: l10 -> l2 : WItemsNum^0'=WItemsNum^post_9, __const_5^0'=__const_5^post_9, __rho_1_^0'=__rho_1_^post_9, __rho_2_^0'=__rho_2_^post_9, [ WItemsNum^0<=2 && WItemsNum^0==WItemsNum^post_9 && __const_5^0==__const_5^post_9 && __rho_1_^0==__rho_1_^post_9 && __rho_2_^0==__rho_2_^post_9 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=WItemsNum^post_12, __const_5^0'=__const_5^post_12, __rho_1_^0'=__rho_1_^post_12, __rho_2_^0'=__rho_2_^post_12, [ 1+__const_5^0<=WItemsNum^0 && WItemsNum^post_12==1+WItemsNum^0 && __const_5^0==__const_5^post_12 && __rho_1_^0==__rho_1_^post_12 && __rho_2_^0==__rho_2_^post_12 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=WItemsNum^post_13, __const_5^0'=__const_5^post_13, __rho_1_^0'=__rho_1_^post_13, __rho_2_^0'=__rho_2_^post_13, [ WItemsNum^0<=__const_5^0 && WItemsNum^post_13==1+WItemsNum^0 && __const_5^0==__const_5^post_13 && __rho_1_^0==__rho_1_^post_13 && __rho_2_^0==__rho_2_^post_13 ], cost: 1 13: l13 -> l12 : WItemsNum^0'=WItemsNum^post_14, __const_5^0'=__const_5^post_14, __rho_1_^0'=__rho_1_^post_14, __rho_2_^0'=__rho_2_^post_14, [ __rho_2_^0<=0 && WItemsNum^0==WItemsNum^post_14 && __const_5^0==__const_5^post_14 && __rho_1_^0==__rho_1_^post_14 && __rho_2_^0==__rho_2_^post_14 ], cost: 1 14: l13 -> l9 : WItemsNum^0'=WItemsNum^post_15, __const_5^0'=__const_5^post_15, __rho_1_^0'=__rho_1_^post_15, __rho_2_^0'=__rho_2_^post_15, [ 1<=__rho_2_^0 && WItemsNum^0==WItemsNum^post_15 && __const_5^0==__const_5^post_15 && __rho_1_^0==__rho_1_^post_15 && __rho_2_^0==__rho_2_^post_15 ], cost: 1 18: l15 -> l2 : WItemsNum^0'=WItemsNum^post_19, __const_5^0'=__const_5^post_19, __rho_1_^0'=__rho_1_^post_19, __rho_2_^0'=__rho_2_^post_19, [ 0<=WItemsNum^0 && WItemsNum^0==WItemsNum^post_19 && __const_5^0==__const_5^post_19 && __rho_1_^0==__rho_1_^post_19 && __rho_2_^0==__rho_2_^post_19 ], cost: 1 19: l15 -> l0 : WItemsNum^0'=WItemsNum^post_20, __const_5^0'=__const_5^post_20, __rho_1_^0'=__rho_1_^post_20, __rho_2_^0'=__rho_2_^post_20, [ 1+WItemsNum^0<=0 && WItemsNum^0==WItemsNum^post_20 && __const_5^0==__const_5^post_20 && __rho_1_^0==__rho_1_^post_20 && __rho_2_^0==__rho_2_^post_20 ], cost: 1 20: l16 -> l15 : WItemsNum^0'=WItemsNum^post_21, __const_5^0'=__const_5^post_21, __rho_1_^0'=__rho_1_^post_21, __rho_2_^0'=__rho_2_^post_21, [ WItemsNum^1_1==WItemsNum^1_1 && __rho_1_^post_21==__rho_1_^post_21 && WItemsNum^post_21==__rho_1_^post_21 && __const_5^0==__const_5^post_21 && __rho_2_^0==__rho_2_^post_21 ], cost: 1 21: l17 -> l16 : WItemsNum^0'=WItemsNum^post_22, __const_5^0'=__const_5^post_22, __rho_1_^0'=__rho_1_^post_22, __rho_2_^0'=__rho_2_^post_22, [ WItemsNum^0==WItemsNum^post_22 && __const_5^0==__const_5^post_22 && __rho_1_^0==__rho_1_^post_22 && __rho_2_^0==__rho_2_^post_22 ], cost: 1 Simplified all rules, resulting in: Start location: l17 0: l0 -> l1 : [], cost: 1 1: l1 -> l0 : [], cost: 1 2: l2 -> l3 : [], cost: 1 3: l3 -> l4 : __rho_2_^0'=__rho_2_^post_4, [], cost: 1 15: l4 -> l12 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 16: l4 -> l13 : [ WItemsNum^0<=__const_5^0 ], cost: 1 6: l9 -> l10 : [], cost: 1 7: l10 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 8: l10 -> l2 : [ WItemsNum^0<=2 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 18: l15 -> l2 : [ 0<=WItemsNum^0 ], cost: 1 19: l15 -> l0 : [ 1+WItemsNum^0<=0 ], cost: 1 20: l16 -> l15 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [], cost: 1 21: l17 -> l16 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l17 23: l0 -> l0 : [], cost: 2 2: l2 -> l3 : [], cost: 1 3: l3 -> l4 : __rho_2_^0'=__rho_2_^post_4, [], cost: 1 15: l4 -> l12 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 16: l4 -> l13 : [ WItemsNum^0<=__const_5^0 ], cost: 1 6: l9 -> l10 : [], cost: 1 7: l10 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 8: l10 -> l2 : [ WItemsNum^0<=2 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 18: l15 -> l2 : [ 0<=WItemsNum^0 ], cost: 1 19: l15 -> l0 : [ 1+WItemsNum^0<=0 ], cost: 1 22: l17 -> l15 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 23: l0 -> l0 : [], cost: 2 Accelerated rule 23 with non-termination, yielding the new rule 24. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 23. Accelerated all simple loops using metering functions (where possible): Start location: l17 24: l0 -> [18] : [], cost: NONTERM 2: l2 -> l3 : [], cost: 1 3: l3 -> l4 : __rho_2_^0'=__rho_2_^post_4, [], cost: 1 15: l4 -> l12 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 16: l4 -> l13 : [ WItemsNum^0<=__const_5^0 ], cost: 1 6: l9 -> l10 : [], cost: 1 7: l10 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 8: l10 -> l2 : [ WItemsNum^0<=2 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 18: l15 -> l2 : [ 0<=WItemsNum^0 ], cost: 1 19: l15 -> l0 : [ 1+WItemsNum^0<=0 ], cost: 1 22: l17 -> l15 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l17 2: l2 -> l3 : [], cost: 1 3: l3 -> l4 : __rho_2_^0'=__rho_2_^post_4, [], cost: 1 15: l4 -> l12 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 16: l4 -> l13 : [ WItemsNum^0<=__const_5^0 ], cost: 1 6: l9 -> l10 : [], cost: 1 7: l10 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 8: l10 -> l2 : [ WItemsNum^0<=2 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 18: l15 -> l2 : [ 0<=WItemsNum^0 ], cost: 1 19: l15 -> l0 : [ 1+WItemsNum^0<=0 ], cost: 1 25: l15 -> [18] : [ 1+WItemsNum^0<=0 ], cost: NONTERM 22: l17 -> l15 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [], cost: 2 Removed unreachable locations (and leaf rules with constant cost): Start location: l17 2: l2 -> l3 : [], cost: 1 3: l3 -> l4 : __rho_2_^0'=__rho_2_^post_4, [], cost: 1 15: l4 -> l12 : [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 16: l4 -> l13 : [ WItemsNum^0<=__const_5^0 ], cost: 1 6: l9 -> l10 : [], cost: 1 7: l10 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 1 8: l10 -> l2 : [ WItemsNum^0<=2 ], cost: 1 11: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 18: l15 -> l2 : [ 0<=WItemsNum^0 ], cost: 1 25: l15 -> [18] : [ 1+WItemsNum^0<=0 ], cost: NONTERM 22: l17 -> l15 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l17 2: l2 -> l3 : [], cost: 1 28: l3 -> l12 : __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 29: l3 -> l13 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 ], cost: 2 30: l9 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 31: l9 -> l2 : [ WItemsNum^0<=2 ], cost: 2 11: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ 1+__const_5^0<=WItemsNum^0 ], cost: 1 12: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [ WItemsNum^0<=__const_5^0 ], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Merged rules: Start location: l17 2: l2 -> l3 : [], cost: 1 28: l3 -> l12 : __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 29: l3 -> l13 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 ], cost: 2 30: l9 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 31: l9 -> l2 : [ WItemsNum^0<=2 ], cost: 2 32: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Accelerating simple loops of location 9. Accelerating the following rules: 30: l9 -> l9 : WItemsNum^0'=-1+WItemsNum^0, [ 3<=WItemsNum^0 ], cost: 2 Accelerated rule 30 with backward acceleration, yielding the new rule 33. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 30. Accelerated all simple loops using metering functions (where possible): Start location: l17 2: l2 -> l3 : [], cost: 1 28: l3 -> l12 : __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 29: l3 -> l13 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 ], cost: 2 31: l9 -> l2 : [ WItemsNum^0<=2 ], cost: 2 33: l9 -> l9 : WItemsNum^0'=2, [ -2+WItemsNum^0>=0 ], cost: -4+2*WItemsNum^0 32: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: l17 2: l2 -> l3 : [], cost: 1 28: l3 -> l12 : __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 29: l3 -> l13 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 ], cost: 2 31: l9 -> l2 : [ WItemsNum^0<=2 ], cost: 2 32: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [], cost: 1 13: l13 -> l12 : [ __rho_2_^0<=0 ], cost: 1 14: l13 -> l9 : [ 1<=__rho_2_^0 ], cost: 1 34: l13 -> l9 : WItemsNum^0'=2, [ 1<=__rho_2_^0 && -2+WItemsNum^0>=0 ], cost: -3+2*WItemsNum^0 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l17 2: l2 -> l3 : [], cost: 1 28: l3 -> l12 : __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 2 35: l3 -> l12 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && __rho_2_^post_4<=0 ], cost: 3 36: l3 -> l9 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 ], cost: 3 37: l3 -> l9 : WItemsNum^0'=2, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: -1+2*WItemsNum^0 31: l9 -> l2 : [ WItemsNum^0<=2 ], cost: 2 32: l12 -> l3 : WItemsNum^0'=1+WItemsNum^0, [], cost: 1 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l17 2: l2 -> l3 : [], cost: 1 38: l3 -> l2 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && WItemsNum^0<=2 ], cost: 5 39: l3 -> l2 : WItemsNum^0'=2, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: 1+2*WItemsNum^0 40: l3 -> l3 : WItemsNum^0'=1+WItemsNum^0, __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 3 41: l3 -> l3 : WItemsNum^0'=1+WItemsNum^0, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && __rho_2_^post_4<=0 ], cost: 4 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Accelerating simple loops of location 3. Accelerating the following rules: 40: l3 -> l3 : WItemsNum^0'=1+WItemsNum^0, __rho_2_^0'=__rho_2_^post_4, [ 1+__const_5^0<=WItemsNum^0 ], cost: 3 41: l3 -> l3 : WItemsNum^0'=1+WItemsNum^0, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && __rho_2_^post_4<=0 ], cost: 4 Accelerated rule 40 with non-termination, yielding the new rule 42. Accelerated rule 41 with backward acceleration, yielding the new rule 43. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 40 41. Accelerated all simple loops using metering functions (where possible): Start location: l17 2: l2 -> l3 : [], cost: 1 38: l3 -> l2 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && WItemsNum^0<=2 ], cost: 5 39: l3 -> l2 : WItemsNum^0'=2, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: 1+2*WItemsNum^0 42: l3 -> [20] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 43: l3 -> l3 : WItemsNum^0'=1+__const_5^0, __rho_2_^0'=__rho_2_^post_4, [ __rho_2_^post_4<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 4+4*__const_5^0-4*WItemsNum^0 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: l17 2: l2 -> l3 : [], cost: 1 44: l2 -> [20] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 45: l2 -> l3 : WItemsNum^0'=1+__const_5^0, __rho_2_^0'=__rho_2_^post_4, [ __rho_2_^post_4<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 38: l3 -> l2 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && WItemsNum^0<=2 ], cost: 5 39: l3 -> l2 : WItemsNum^0'=2, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: 1+2*WItemsNum^0 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l17 44: l2 -> [20] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 46: l2 -> l2 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && WItemsNum^0<=2 ], cost: 6 47: l2 -> l2 : WItemsNum^0'=2, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: 2+2*WItemsNum^0 48: l2 -> [21] : [ __rho_2_^post_4<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Accelerating simple loops of location 2. Accelerating the following rules: 46: l2 -> l2 : __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && WItemsNum^0<=2 ], cost: 6 47: l2 -> l2 : WItemsNum^0'=2, __rho_2_^0'=__rho_2_^post_4, [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: 2+2*WItemsNum^0 Accelerated rule 46 with non-termination, yielding the new rule 49. Accelerated rule 47 with non-termination, yielding the new rule 50. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 46 47. Accelerated all simple loops using metering functions (where possible): Start location: l17 44: l2 -> [20] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 48: l2 -> [21] : [ __rho_2_^post_4<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 49: l2 -> [22] : [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && WItemsNum^0<=2 ], cost: NONTERM 50: l2 -> [22] : [ WItemsNum^0<=__const_5^0 && 1<=__rho_2_^post_4 && -2+WItemsNum^0>=0 ], cost: NONTERM 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: l17 44: l2 -> [20] : [ 1+__const_5^0<=WItemsNum^0 ], cost: NONTERM 48: l2 -> [21] : [ __rho_2_^post_4<=0 && 1+__const_5^0-WItemsNum^0>=1 ], cost: 5+4*__const_5^0-4*WItemsNum^0 26: l17 -> l2 : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 ], cost: 3 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM 51: l17 -> [22] : [ 0<=__const_5^0 ], cost: NONTERM 52: l17 -> [22] : [ 2<=__const_5^0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l17 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM 51: l17 -> [22] : [ 0<=__const_5^0 ], cost: NONTERM 52: l17 -> [22] : [ 2<=__const_5^0 ], cost: NONTERM 53: l17 -> [20] : [ 0<=__rho_1_^post_21 && 1+__const_5^0<=__rho_1_^post_21 ], cost: NONTERM 54: l17 -> [21] : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 && __rho_2_^post_4<=0 && 1+__const_5^0-__rho_1_^post_21>=1 ], cost: 8+4*__const_5^0-4*__rho_1_^post_21 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l17 27: l17 -> [18] : [ 1+__rho_1_^post_21<=0 ], cost: NONTERM 51: l17 -> [22] : [ 0<=__const_5^0 ], cost: NONTERM 52: l17 -> [22] : [ 2<=__const_5^0 ], cost: NONTERM 53: l17 -> [20] : [ 0<=__rho_1_^post_21 && 1+__const_5^0<=__rho_1_^post_21 ], cost: NONTERM 54: l17 -> [21] : WItemsNum^0'=__rho_1_^post_21, __rho_1_^0'=__rho_1_^post_21, [ 0<=__rho_1_^post_21 && __rho_2_^post_4<=0 && 1+__const_5^0-__rho_1_^post_21>=1 ], cost: 8+4*__const_5^0-4*__rho_1_^post_21 Computing asymptotic complexity for rule 27 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+__rho_1_^post_21<=0 ] NO