NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l9 0: l0 -> l1 : __const_5^0'=__const_5^post_1, __rho_1_^0'=__rho_1_^post_1, __rho_2_^0'=__rho_2_^post_1, c^0'=c^post_1, curr_serv^0'=curr_serv^post_1, resp^0'=resp^post_1, servers^0'=servers^post_1, [ __const_5^0==__const_5^post_1 && __rho_1_^0==__rho_1_^post_1 && __rho_2_^0==__rho_2_^post_1 && c^0==c^post_1 && curr_serv^0==curr_serv^post_1 && resp^0==resp^post_1 && servers^0==servers^post_1 ], cost: 1 6: l1 -> l6 : __const_5^0'=__const_5^post_7, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_7, c^0'=c^post_7, curr_serv^0'=curr_serv^post_7, resp^0'=resp^post_7, servers^0'=servers^post_7, [ 1<=curr_serv^0 && __rho_1_^post_7==__rho_1_^post_7 && __const_5^0==__const_5^post_7 && __rho_2_^0==__rho_2_^post_7 && c^0==c^post_7 && curr_serv^0==curr_serv^post_7 && resp^0==resp^post_7 && servers^0==servers^post_7 ], cost: 1 7: l1 -> l4 : __const_5^0'=__const_5^post_8, __rho_1_^0'=__rho_1_^post_8, __rho_2_^0'=__rho_2_^post_8, c^0'=c^post_8, curr_serv^0'=curr_serv^post_8, resp^0'=resp^post_8, servers^0'=servers^post_8, [ curr_serv^0<=0 && __const_5^0==__const_5^post_8 && __rho_1_^0==__rho_1_^post_8 && __rho_2_^0==__rho_2_^post_8 && c^0==c^post_8 && curr_serv^0==curr_serv^post_8 && resp^0==resp^post_8 && servers^0==servers^post_8 ], cost: 1 1: l2 -> l3 : __const_5^0'=__const_5^post_2, __rho_1_^0'=__rho_1_^post_2, __rho_2_^0'=__rho_2_^post_2, c^0'=c^post_2, curr_serv^0'=curr_serv^post_2, resp^0'=resp^post_2, servers^0'=servers^post_2, [ __const_5^0==__const_5^post_2 && __rho_1_^0==__rho_1_^post_2 && __rho_2_^0==__rho_2_^post_2 && c^0==c^post_2 && curr_serv^0==curr_serv^post_2 && resp^0==resp^post_2 && servers^0==servers^post_2 ], cost: 1 2: l4 -> l5 : __const_5^0'=__const_5^post_3, __rho_1_^0'=__rho_1_^post_3, __rho_2_^0'=__rho_2_^post_3, c^0'=c^post_3, curr_serv^0'=curr_serv^post_3, resp^0'=resp^post_3, servers^0'=servers^post_3, [ __const_5^0==__const_5^post_3 && __rho_1_^0==__rho_1_^post_3 && __rho_2_^0==__rho_2_^post_3 && c^0==c^post_3 && curr_serv^0==curr_serv^post_3 && resp^0==resp^post_3 && servers^0==servers^post_3 ], cost: 1 3: l5 -> l4 : __const_5^0'=__const_5^post_4, __rho_1_^0'=__rho_1_^post_4, __rho_2_^0'=__rho_2_^post_4, c^0'=c^post_4, curr_serv^0'=curr_serv^post_4, resp^0'=resp^post_4, servers^0'=servers^post_4, [ __const_5^0==__const_5^post_4 && __rho_1_^0==__rho_1_^post_4 && __rho_2_^0==__rho_2_^post_4 && c^0==c^post_4 && curr_serv^0==curr_serv^post_4 && resp^0==resp^post_4 && servers^0==servers^post_4 ], cost: 1 4: l6 -> l0 : __const_5^0'=__const_5^post_5, __rho_1_^0'=__rho_1_^post_5, __rho_2_^0'=__rho_2_^post_5, c^0'=c^post_5, curr_serv^0'=curr_serv^post_5, resp^0'=resp^post_5, servers^0'=servers^post_5, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 && curr_serv^post_5==-1+curr_serv^0 && __const_5^0==__const_5^post_5 && __rho_1_^0==__rho_1_^post_5 && __rho_2_^0==__rho_2_^post_5 && c^0==c^post_5 && resp^0==resp^post_5 && servers^0==servers^post_5 ], cost: 1 5: l6 -> l0 : __const_5^0'=__const_5^post_6, __rho_1_^0'=__rho_1_^post_6, __rho_2_^0'=__rho_2_^post_6, c^0'=c^post_6, curr_serv^0'=curr_serv^post_6, resp^0'=resp^post_6, servers^0'=servers^post_6, [ 1<=__rho_1_^0 && c^post_6==-1+c^0 && curr_serv^post_6==-1+curr_serv^0 && resp^post_6==1+resp^0 && __const_5^0==__const_5^post_6 && __rho_1_^0==__rho_1_^post_6 && __rho_2_^0==__rho_2_^post_6 && servers^0==servers^post_6 ], cost: 1 8: l7 -> l4 : __const_5^0'=__const_5^post_9, __rho_1_^0'=__rho_1_^post_9, __rho_2_^0'=__rho_2_^post_9, c^0'=c^post_9, curr_serv^0'=curr_serv^post_9, resp^0'=resp^post_9, servers^0'=servers^post_9, [ 1+__const_5^0<=c^0 && __const_5^0==__const_5^post_9 && __rho_1_^0==__rho_1_^post_9 && __rho_2_^0==__rho_2_^post_9 && c^0==c^post_9 && curr_serv^0==curr_serv^post_9 && resp^0==resp^post_9 && servers^0==servers^post_9 ], cost: 1 9: l7 -> l0 : __const_5^0'=__const_5^post_10, __rho_1_^0'=__rho_1_^post_10, __rho_2_^0'=__rho_2_^post_10, c^0'=c^post_10, curr_serv^0'=curr_serv^post_10, resp^0'=resp^post_10, servers^0'=servers^post_10, [ c^0<=__const_5^0 && __const_5^0==__const_5^post_10 && __rho_1_^0==__rho_1_^post_10 && __rho_2_^0==__rho_2_^post_10 && c^0==c^post_10 && curr_serv^0==curr_serv^post_10 && resp^0==resp^post_10 && servers^0==servers^post_10 ], cost: 1 10: l8 -> l7 : __const_5^0'=__const_5^post_11, __rho_1_^0'=__rho_1_^post_11, __rho_2_^0'=__rho_2_^post_11, c^0'=c^post_11, curr_serv^0'=curr_serv^post_11, resp^0'=resp^post_11, servers^0'=servers^post_11, [ __rho_2_^post_11==__rho_2_^post_11 && c^post_11==__rho_2_^post_11 && 1<=c^post_11 && servers^post_11==4 && resp^post_11==0 && curr_serv^post_11==servers^post_11 && __const_5^0==__const_5^post_11 && __rho_1_^0==__rho_1_^post_11 ], cost: 1 11: l9 -> l8 : __const_5^0'=__const_5^post_12, __rho_1_^0'=__rho_1_^post_12, __rho_2_^0'=__rho_2_^post_12, c^0'=c^post_12, curr_serv^0'=curr_serv^post_12, resp^0'=resp^post_12, servers^0'=servers^post_12, [ __const_5^0==__const_5^post_12 && __rho_1_^0==__rho_1_^post_12 && __rho_2_^0==__rho_2_^post_12 && c^0==c^post_12 && curr_serv^0==curr_serv^post_12 && resp^0==resp^post_12 && servers^0==servers^post_12 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 11: l9 -> l8 : __const_5^0'=__const_5^post_12, __rho_1_^0'=__rho_1_^post_12, __rho_2_^0'=__rho_2_^post_12, c^0'=c^post_12, curr_serv^0'=curr_serv^post_12, resp^0'=resp^post_12, servers^0'=servers^post_12, [ __const_5^0==__const_5^post_12 && __rho_1_^0==__rho_1_^post_12 && __rho_2_^0==__rho_2_^post_12 && c^0==c^post_12 && curr_serv^0==curr_serv^post_12 && resp^0==resp^post_12 && servers^0==servers^post_12 ], cost: 1 Removed unreachable and leaf rules: Start location: l9 0: l0 -> l1 : __const_5^0'=__const_5^post_1, __rho_1_^0'=__rho_1_^post_1, __rho_2_^0'=__rho_2_^post_1, c^0'=c^post_1, curr_serv^0'=curr_serv^post_1, resp^0'=resp^post_1, servers^0'=servers^post_1, [ __const_5^0==__const_5^post_1 && __rho_1_^0==__rho_1_^post_1 && __rho_2_^0==__rho_2_^post_1 && c^0==c^post_1 && curr_serv^0==curr_serv^post_1 && resp^0==resp^post_1 && servers^0==servers^post_1 ], cost: 1 6: l1 -> l6 : __const_5^0'=__const_5^post_7, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_7, c^0'=c^post_7, curr_serv^0'=curr_serv^post_7, resp^0'=resp^post_7, servers^0'=servers^post_7, [ 1<=curr_serv^0 && __rho_1_^post_7==__rho_1_^post_7 && __const_5^0==__const_5^post_7 && __rho_2_^0==__rho_2_^post_7 && c^0==c^post_7 && curr_serv^0==curr_serv^post_7 && resp^0==resp^post_7 && servers^0==servers^post_7 ], cost: 1 7: l1 -> l4 : __const_5^0'=__const_5^post_8, __rho_1_^0'=__rho_1_^post_8, __rho_2_^0'=__rho_2_^post_8, c^0'=c^post_8, curr_serv^0'=curr_serv^post_8, resp^0'=resp^post_8, servers^0'=servers^post_8, [ curr_serv^0<=0 && __const_5^0==__const_5^post_8 && __rho_1_^0==__rho_1_^post_8 && __rho_2_^0==__rho_2_^post_8 && c^0==c^post_8 && curr_serv^0==curr_serv^post_8 && resp^0==resp^post_8 && servers^0==servers^post_8 ], cost: 1 2: l4 -> l5 : __const_5^0'=__const_5^post_3, __rho_1_^0'=__rho_1_^post_3, __rho_2_^0'=__rho_2_^post_3, c^0'=c^post_3, curr_serv^0'=curr_serv^post_3, resp^0'=resp^post_3, servers^0'=servers^post_3, [ __const_5^0==__const_5^post_3 && __rho_1_^0==__rho_1_^post_3 && __rho_2_^0==__rho_2_^post_3 && c^0==c^post_3 && curr_serv^0==curr_serv^post_3 && resp^0==resp^post_3 && servers^0==servers^post_3 ], cost: 1 3: l5 -> l4 : __const_5^0'=__const_5^post_4, __rho_1_^0'=__rho_1_^post_4, __rho_2_^0'=__rho_2_^post_4, c^0'=c^post_4, curr_serv^0'=curr_serv^post_4, resp^0'=resp^post_4, servers^0'=servers^post_4, [ __const_5^0==__const_5^post_4 && __rho_1_^0==__rho_1_^post_4 && __rho_2_^0==__rho_2_^post_4 && c^0==c^post_4 && curr_serv^0==curr_serv^post_4 && resp^0==resp^post_4 && servers^0==servers^post_4 ], cost: 1 4: l6 -> l0 : __const_5^0'=__const_5^post_5, __rho_1_^0'=__rho_1_^post_5, __rho_2_^0'=__rho_2_^post_5, c^0'=c^post_5, curr_serv^0'=curr_serv^post_5, resp^0'=resp^post_5, servers^0'=servers^post_5, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 && curr_serv^post_5==-1+curr_serv^0 && __const_5^0==__const_5^post_5 && __rho_1_^0==__rho_1_^post_5 && __rho_2_^0==__rho_2_^post_5 && c^0==c^post_5 && resp^0==resp^post_5 && servers^0==servers^post_5 ], cost: 1 5: l6 -> l0 : __const_5^0'=__const_5^post_6, __rho_1_^0'=__rho_1_^post_6, __rho_2_^0'=__rho_2_^post_6, c^0'=c^post_6, curr_serv^0'=curr_serv^post_6, resp^0'=resp^post_6, servers^0'=servers^post_6, [ 1<=__rho_1_^0 && c^post_6==-1+c^0 && curr_serv^post_6==-1+curr_serv^0 && resp^post_6==1+resp^0 && __const_5^0==__const_5^post_6 && __rho_1_^0==__rho_1_^post_6 && __rho_2_^0==__rho_2_^post_6 && servers^0==servers^post_6 ], cost: 1 8: l7 -> l4 : __const_5^0'=__const_5^post_9, __rho_1_^0'=__rho_1_^post_9, __rho_2_^0'=__rho_2_^post_9, c^0'=c^post_9, curr_serv^0'=curr_serv^post_9, resp^0'=resp^post_9, servers^0'=servers^post_9, [ 1+__const_5^0<=c^0 && __const_5^0==__const_5^post_9 && __rho_1_^0==__rho_1_^post_9 && __rho_2_^0==__rho_2_^post_9 && c^0==c^post_9 && curr_serv^0==curr_serv^post_9 && resp^0==resp^post_9 && servers^0==servers^post_9 ], cost: 1 9: l7 -> l0 : __const_5^0'=__const_5^post_10, __rho_1_^0'=__rho_1_^post_10, __rho_2_^0'=__rho_2_^post_10, c^0'=c^post_10, curr_serv^0'=curr_serv^post_10, resp^0'=resp^post_10, servers^0'=servers^post_10, [ c^0<=__const_5^0 && __const_5^0==__const_5^post_10 && __rho_1_^0==__rho_1_^post_10 && __rho_2_^0==__rho_2_^post_10 && c^0==c^post_10 && curr_serv^0==curr_serv^post_10 && resp^0==resp^post_10 && servers^0==servers^post_10 ], cost: 1 10: l8 -> l7 : __const_5^0'=__const_5^post_11, __rho_1_^0'=__rho_1_^post_11, __rho_2_^0'=__rho_2_^post_11, c^0'=c^post_11, curr_serv^0'=curr_serv^post_11, resp^0'=resp^post_11, servers^0'=servers^post_11, [ __rho_2_^post_11==__rho_2_^post_11 && c^post_11==__rho_2_^post_11 && 1<=c^post_11 && servers^post_11==4 && resp^post_11==0 && curr_serv^post_11==servers^post_11 && __const_5^0==__const_5^post_11 && __rho_1_^0==__rho_1_^post_11 ], cost: 1 11: l9 -> l8 : __const_5^0'=__const_5^post_12, __rho_1_^0'=__rho_1_^post_12, __rho_2_^0'=__rho_2_^post_12, c^0'=c^post_12, curr_serv^0'=curr_serv^post_12, resp^0'=resp^post_12, servers^0'=servers^post_12, [ __const_5^0==__const_5^post_12 && __rho_1_^0==__rho_1_^post_12 && __rho_2_^0==__rho_2_^post_12 && c^0==c^post_12 && curr_serv^0==curr_serv^post_12 && resp^0==resp^post_12 && servers^0==servers^post_12 ], cost: 1 Simplified all rules, resulting in: Start location: l9 0: l0 -> l1 : [], cost: 1 6: l1 -> l6 : __rho_1_^0'=__rho_1_^post_7, [ 1<=curr_serv^0 ], cost: 1 7: l1 -> l4 : [ curr_serv^0<=0 ], cost: 1 2: l4 -> l5 : [], cost: 1 3: l5 -> l4 : [], cost: 1 4: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 ], cost: 1 5: l6 -> l0 : c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=__rho_1_^0 ], cost: 1 8: l7 -> l4 : [ 1+__const_5^0<=c^0 ], cost: 1 9: l7 -> l0 : [ c^0<=__const_5^0 ], cost: 1 10: l8 -> l7 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 ], cost: 1 11: l9 -> l8 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l9 0: l0 -> l1 : [], cost: 1 6: l1 -> l6 : __rho_1_^0'=__rho_1_^post_7, [ 1<=curr_serv^0 ], cost: 1 7: l1 -> l4 : [ curr_serv^0<=0 ], cost: 1 13: l4 -> l4 : [], cost: 2 4: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 ], cost: 1 5: l6 -> l0 : c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=__rho_1_^0 ], cost: 1 8: l7 -> l4 : [ 1+__const_5^0<=c^0 ], cost: 1 9: l7 -> l0 : [ c^0<=__const_5^0 ], cost: 1 12: l9 -> l7 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 ], cost: 2 Accelerating simple loops of location 4. Accelerating the following rules: 13: l4 -> l4 : [], cost: 2 Accelerated rule 13 with NONTERM, yielding the new rule 14. Removing the simple loops: 13. Accelerated all simple loops using metering functions (where possible): Start location: l9 0: l0 -> l1 : [], cost: 1 6: l1 -> l6 : __rho_1_^0'=__rho_1_^post_7, [ 1<=curr_serv^0 ], cost: 1 7: l1 -> l4 : [ curr_serv^0<=0 ], cost: 1 14: l4 -> [10] : [], cost: NONTERM 4: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 ], cost: 1 5: l6 -> l0 : c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=__rho_1_^0 ], cost: 1 8: l7 -> l4 : [ 1+__const_5^0<=c^0 ], cost: 1 9: l7 -> l0 : [ c^0<=__const_5^0 ], cost: 1 12: l9 -> l7 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 0: l0 -> l1 : [], cost: 1 6: l1 -> l6 : __rho_1_^0'=__rho_1_^post_7, [ 1<=curr_serv^0 ], cost: 1 7: l1 -> l4 : [ curr_serv^0<=0 ], cost: 1 15: l1 -> [10] : [ curr_serv^0<=0 ], cost: NONTERM 4: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 ], cost: 1 5: l6 -> l0 : c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=__rho_1_^0 ], cost: 1 8: l7 -> l4 : [ 1+__const_5^0<=c^0 ], cost: 1 9: l7 -> l0 : [ c^0<=__const_5^0 ], cost: 1 16: l7 -> [10] : [ 1+__const_5^0<=c^0 ], cost: NONTERM 12: l9 -> l7 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 ], cost: 2 Removed unreachable locations (and leaf rules with constant cost): Start location: l9 0: l0 -> l1 : [], cost: 1 6: l1 -> l6 : __rho_1_^0'=__rho_1_^post_7, [ 1<=curr_serv^0 ], cost: 1 15: l1 -> [10] : [ curr_serv^0<=0 ], cost: NONTERM 4: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 ], cost: 1 5: l6 -> l0 : c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=__rho_1_^0 ], cost: 1 9: l7 -> l0 : [ c^0<=__const_5^0 ], cost: 1 16: l7 -> [10] : [ 1+__const_5^0<=c^0 ], cost: NONTERM 12: l9 -> l7 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 19: l0 -> l6 : __rho_1_^0'=__rho_1_^post_7, [ 1<=curr_serv^0 ], cost: 2 20: l0 -> [10] : [ curr_serv^0<=0 ], cost: NONTERM 4: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, [ __rho_1_^0<=0 && 1+c^0<=curr_serv^0 ], cost: 1 5: l6 -> l0 : c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=__rho_1_^0 ], cost: 1 17: l9 -> l0 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 ], cost: 3 18: l9 -> [10] : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l9 20: l0 -> [10] : [ curr_serv^0<=0 ], cost: NONTERM 21: l0 -> l0 : __rho_1_^0'=__rho_1_^post_7, curr_serv^0'=-1+curr_serv^0, [ 1<=curr_serv^0 && __rho_1_^post_7<=0 && 1+c^0<=curr_serv^0 ], cost: 3 22: l0 -> l0 : __rho_1_^0'=__rho_1_^post_7, c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=curr_serv^0 && 1<=__rho_1_^post_7 ], cost: 3 17: l9 -> l0 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 ], cost: 3 18: l9 -> [10] : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ], cost: NONTERM Accelerating simple loops of location 0. Accelerating the following rules: 21: l0 -> l0 : __rho_1_^0'=__rho_1_^post_7, curr_serv^0'=-1+curr_serv^0, [ 1<=curr_serv^0 && __rho_1_^post_7<=0 && 1+c^0<=curr_serv^0 ], cost: 3 22: l0 -> l0 : __rho_1_^0'=__rho_1_^post_7, c^0'=-1+c^0, curr_serv^0'=-1+curr_serv^0, resp^0'=1+resp^0, [ 1<=curr_serv^0 && 1<=__rho_1_^post_7 ], cost: 3 Found no metering function for rule 21. Accelerated rule 22 with metering function curr_serv^0, yielding the new rule 23. Removing the simple loops: 22. Accelerated all simple loops using metering functions (where possible): Start location: l9 20: l0 -> [10] : [ curr_serv^0<=0 ], cost: NONTERM 21: l0 -> l0 : __rho_1_^0'=__rho_1_^post_7, curr_serv^0'=-1+curr_serv^0, [ 1<=curr_serv^0 && __rho_1_^post_7<=0 && 1+c^0<=curr_serv^0 ], cost: 3 23: l0 -> l0 : __rho_1_^0'=__rho_1_^post_7, c^0'=c^0-curr_serv^0, curr_serv^0'=0, resp^0'=resp^0+curr_serv^0, [ 1<=curr_serv^0 && 1<=__rho_1_^post_7 ], cost: 3*curr_serv^0 17: l9 -> l0 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 ], cost: 3 18: l9 -> [10] : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: l9 20: l0 -> [10] : [ curr_serv^0<=0 ], cost: NONTERM 17: l9 -> l0 : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 ], cost: 3 18: l9 -> [10] : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ], cost: NONTERM 24: l9 -> l0 : __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=3, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 && __rho_1_^post_7<=0 && 1+__rho_2_^post_11<=4 ], cost: 6 25: l9 -> l0 : __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_11, c^0'=-4+__rho_2_^post_11, curr_serv^0'=0, resp^0'=4, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 && 1<=__rho_1_^post_7 ], cost: 15 Eliminated locations (on tree-shaped paths): Start location: l9 18: l9 -> [10] : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ], cost: NONTERM 26: l9 -> [10] : __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_11, c^0'=-4+__rho_2_^post_11, curr_serv^0'=0, resp^0'=4, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 && 1<=__rho_1_^post_7 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l9 18: l9 -> [10] : __rho_2_^0'=__rho_2_^post_11, c^0'=__rho_2_^post_11, curr_serv^0'=4, resp^0'=0, servers^0'=4, [ 1<=__rho_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ], cost: NONTERM 26: l9 -> [10] : __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_11, c^0'=-4+__rho_2_^post_11, curr_serv^0'=0, resp^0'=4, servers^0'=4, [ 1<=__rho_2_^post_11 && __rho_2_^post_11<=__const_5^0 && 1<=__rho_1_^post_7 ], cost: NONTERM Computing asymptotic complexity for rule 18 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_2_^post_11 && 1+__const_5^0<=__rho_2_^post_11 ] NO