WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : Result_4^0'=Result_4^post_1, __cil_tmp4_8^0'=__cil_tmp4_8^post_1, __const_100^0'=__const_100^post_1, __retres3_7^0'=__retres3_7^post_1, i_5^0'=i_5^post_1, x_6^0'=x_6^post_1, [ 1-i_5^0+__const_100^0<=0 && __retres3_7^post_1==0 && __cil_tmp4_8^post_1==__retres3_7^post_1 && Result_4^post_1==__cil_tmp4_8^post_1 && __const_100^0==__const_100^post_1 && i_5^0==i_5^post_1 && x_6^0==x_6^post_1 ], cost: 1 1: l0 -> l2 : Result_4^0'=Result_4^post_2, __cil_tmp4_8^0'=__cil_tmp4_8^post_2, __const_100^0'=__const_100^post_2, __retres3_7^0'=__retres3_7^post_2, i_5^0'=i_5^post_2, x_6^0'=x_6^post_2, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 && i_5^post_2==1+i_5^0 && Result_4^0==Result_4^post_2 && __cil_tmp4_8^0==__cil_tmp4_8^post_2 && __const_100^0==__const_100^post_2 && __retres3_7^0==__retres3_7^post_2 && x_6^0==x_6^post_2 ], cost: 1 2: l2 -> l0 : Result_4^0'=Result_4^post_3, __cil_tmp4_8^0'=__cil_tmp4_8^post_3, __const_100^0'=__const_100^post_3, __retres3_7^0'=__retres3_7^post_3, i_5^0'=i_5^post_3, x_6^0'=x_6^post_3, [ Result_4^0==Result_4^post_3 && __cil_tmp4_8^0==__cil_tmp4_8^post_3 && __const_100^0==__const_100^post_3 && __retres3_7^0==__retres3_7^post_3 && i_5^0==i_5^post_3 && x_6^0==x_6^post_3 ], cost: 1 3: l3 -> l4 : Result_4^0'=Result_4^post_4, __cil_tmp4_8^0'=__cil_tmp4_8^post_4, __const_100^0'=__const_100^post_4, __retres3_7^0'=__retres3_7^post_4, i_5^0'=i_5^post_4, x_6^0'=x_6^post_4, [ i_5^post_4==0 && Result_4^0==Result_4^post_4 && __cil_tmp4_8^0==__cil_tmp4_8^post_4 && __const_100^0==__const_100^post_4 && __retres3_7^0==__retres3_7^post_4 && x_6^0==x_6^post_4 ], cost: 1 4: l4 -> l1 : Result_4^0'=Result_4^post_5, __cil_tmp4_8^0'=__cil_tmp4_8^post_5, __const_100^0'=__const_100^post_5, __retres3_7^0'=__retres3_7^post_5, i_5^0'=i_5^post_5, x_6^0'=x_6^post_5, [ 0<=-i_5^0+__const_100^0 && x_6^0<=0 && __retres3_7^post_5==0 && __cil_tmp4_8^post_5==__retres3_7^post_5 && Result_4^post_5==__cil_tmp4_8^post_5 && __const_100^0==__const_100^post_5 && i_5^0==i_5^post_5 && x_6^0==x_6^post_5 ], cost: 1 5: l4 -> l0 : Result_4^0'=Result_4^post_6, __cil_tmp4_8^0'=__cil_tmp4_8^post_6, __const_100^0'=__const_100^post_6, __retres3_7^0'=__retres3_7^post_6, i_5^0'=i_5^post_6, x_6^0'=x_6^post_6, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 && i_5^post_6==1+i_5^0 && Result_4^0==Result_4^post_6 && __cil_tmp4_8^0==__cil_tmp4_8^post_6 && __const_100^0==__const_100^post_6 && __retres3_7^0==__retres3_7^post_6 && x_6^0==x_6^post_6 ], cost: 1 6: l5 -> l3 : Result_4^0'=Result_4^post_7, __cil_tmp4_8^0'=__cil_tmp4_8^post_7, __const_100^0'=__const_100^post_7, __retres3_7^0'=__retres3_7^post_7, i_5^0'=i_5^post_7, x_6^0'=x_6^post_7, [ Result_4^0==Result_4^post_7 && __cil_tmp4_8^0==__cil_tmp4_8^post_7 && __const_100^0==__const_100^post_7 && __retres3_7^0==__retres3_7^post_7 && i_5^0==i_5^post_7 && x_6^0==x_6^post_7 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: l5 -> l3 : Result_4^0'=Result_4^post_7, __cil_tmp4_8^0'=__cil_tmp4_8^post_7, __const_100^0'=__const_100^post_7, __retres3_7^0'=__retres3_7^post_7, i_5^0'=i_5^post_7, x_6^0'=x_6^post_7, [ Result_4^0==Result_4^post_7 && __cil_tmp4_8^0==__cil_tmp4_8^post_7 && __const_100^0==__const_100^post_7 && __retres3_7^0==__retres3_7^post_7 && i_5^0==i_5^post_7 && x_6^0==x_6^post_7 ], cost: 1 Removed unreachable and leaf rules: Start location: l5 1: l0 -> l2 : Result_4^0'=Result_4^post_2, __cil_tmp4_8^0'=__cil_tmp4_8^post_2, __const_100^0'=__const_100^post_2, __retres3_7^0'=__retres3_7^post_2, i_5^0'=i_5^post_2, x_6^0'=x_6^post_2, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 && i_5^post_2==1+i_5^0 && Result_4^0==Result_4^post_2 && __cil_tmp4_8^0==__cil_tmp4_8^post_2 && __const_100^0==__const_100^post_2 && __retres3_7^0==__retres3_7^post_2 && x_6^0==x_6^post_2 ], cost: 1 2: l2 -> l0 : Result_4^0'=Result_4^post_3, __cil_tmp4_8^0'=__cil_tmp4_8^post_3, __const_100^0'=__const_100^post_3, __retres3_7^0'=__retres3_7^post_3, i_5^0'=i_5^post_3, x_6^0'=x_6^post_3, [ Result_4^0==Result_4^post_3 && __cil_tmp4_8^0==__cil_tmp4_8^post_3 && __const_100^0==__const_100^post_3 && __retres3_7^0==__retres3_7^post_3 && i_5^0==i_5^post_3 && x_6^0==x_6^post_3 ], cost: 1 3: l3 -> l4 : Result_4^0'=Result_4^post_4, __cil_tmp4_8^0'=__cil_tmp4_8^post_4, __const_100^0'=__const_100^post_4, __retres3_7^0'=__retres3_7^post_4, i_5^0'=i_5^post_4, x_6^0'=x_6^post_4, [ i_5^post_4==0 && Result_4^0==Result_4^post_4 && __cil_tmp4_8^0==__cil_tmp4_8^post_4 && __const_100^0==__const_100^post_4 && __retres3_7^0==__retres3_7^post_4 && x_6^0==x_6^post_4 ], cost: 1 5: l4 -> l0 : Result_4^0'=Result_4^post_6, __cil_tmp4_8^0'=__cil_tmp4_8^post_6, __const_100^0'=__const_100^post_6, __retres3_7^0'=__retres3_7^post_6, i_5^0'=i_5^post_6, x_6^0'=x_6^post_6, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 && i_5^post_6==1+i_5^0 && Result_4^0==Result_4^post_6 && __cil_tmp4_8^0==__cil_tmp4_8^post_6 && __const_100^0==__const_100^post_6 && __retres3_7^0==__retres3_7^post_6 && x_6^0==x_6^post_6 ], cost: 1 6: l5 -> l3 : Result_4^0'=Result_4^post_7, __cil_tmp4_8^0'=__cil_tmp4_8^post_7, __const_100^0'=__const_100^post_7, __retres3_7^0'=__retres3_7^post_7, i_5^0'=i_5^post_7, x_6^0'=x_6^post_7, [ Result_4^0==Result_4^post_7 && __cil_tmp4_8^0==__cil_tmp4_8^post_7 && __const_100^0==__const_100^post_7 && __retres3_7^0==__retres3_7^post_7 && i_5^0==i_5^post_7 && x_6^0==x_6^post_7 ], cost: 1 Simplified all rules, resulting in: Start location: l5 1: l0 -> l2 : i_5^0'=1+i_5^0, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 ], cost: 1 2: l2 -> l0 : [], cost: 1 3: l3 -> l4 : i_5^0'=0, [], cost: 1 5: l4 -> l0 : i_5^0'=1+i_5^0, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 ], cost: 1 6: l5 -> l3 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 9: l0 -> l0 : i_5^0'=1+i_5^0, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 ], cost: 2 8: l5 -> l0 : i_5^0'=1, [ 0<=__const_100^0 && 0<=-1+x_6^0 ], cost: 3 Accelerating simple loops of location 0. Accelerating the following rules: 9: l0 -> l0 : i_5^0'=1+i_5^0, [ 0<=-i_5^0+__const_100^0 && 0<=-1+x_6^0 ], cost: 2 Accelerated rule 9 with backward acceleration, yielding the new rule 10. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 9. Accelerated all simple loops using metering functions (where possible): Start location: l5 10: l0 -> l0 : i_5^0'=1+__const_100^0, [ 0<=-1+x_6^0 && 1-i_5^0+__const_100^0>=0 ], cost: 2-2*i_5^0+2*__const_100^0 8: l5 -> l0 : i_5^0'=1, [ 0<=__const_100^0 && 0<=-1+x_6^0 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: l5 8: l5 -> l0 : i_5^0'=1, [ 0<=__const_100^0 && 0<=-1+x_6^0 ], cost: 3 11: l5 -> l0 : i_5^0'=1+__const_100^0, [ 0<=__const_100^0 && 0<=-1+x_6^0 ], cost: 3+2*__const_100^0 Removed unreachable locations (and leaf rules with constant cost): Start location: l5 11: l5 -> l0 : i_5^0'=1+__const_100^0, [ 0<=__const_100^0 && 0<=-1+x_6^0 ], cost: 3+2*__const_100^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 11: l5 -> l0 : i_5^0'=1+__const_100^0, [ 0<=__const_100^0 && 0<=-1+x_6^0 ], cost: 3+2*__const_100^0 Computing asymptotic complexity for rule 11 Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ Result_4^0==Result_4^post_7 && __cil_tmp4_8^0==__cil_tmp4_8^post_7 && __const_100^0==__const_100^post_7 && __retres3_7^0==__retres3_7^post_7 && i_5^0==i_5^post_7 && x_6^0==x_6^post_7 ] WORST_CASE(Omega(1),?)