WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l1 : constant22^0'=constant22^post_1, i20^0'=i20^post_1, lx2^0'=lx2^post_1, tmp03^0'=tmp03^post_1, tmp1011^0'=tmp1011^post_1, tmp1112^0'=tmp1112^post_1, tmp1213^0'=tmp1213^post_1, tmp1314^0'=tmp1314^post_1, tmp14^0'=tmp14^post_1, tmp25^0'=tmp25^post_1, tmp36^0'=tmp36^post_1, tmp47^0'=tmp47^post_1, tmp58^0'=tmp58^post_1, tmp69^0'=tmp69^post_1, tmp710^0'=tmp710^post_1, z115^0'=z115^post_1, z216^0'=z216^post_1, z317^0'=z317^post_1, z418^0'=z418^post_1, z519^0'=z519^post_1, [ 8<=i20^0 && i20^post_1==0 && constant22^0==constant22^post_1 && lx2^0==lx2^post_1 && tmp03^0==tmp03^post_1 && tmp1011^0==tmp1011^post_1 && tmp1112^0==tmp1112^post_1 && tmp1213^0==tmp1213^post_1 && tmp1314^0==tmp1314^post_1 && tmp14^0==tmp14^post_1 && tmp25^0==tmp25^post_1 && tmp36^0==tmp36^post_1 && tmp47^0==tmp47^post_1 && tmp58^0==tmp58^post_1 && tmp69^0==tmp69^post_1 && tmp710^0==tmp710^post_1 && z115^0==z115^post_1 && z216^0==z216^post_1 && z317^0==z317^post_1 && z418^0==z418^post_1 && z519^0==z519^post_1 ], cost: 1 1: l0 -> l2 : constant22^0'=constant22^post_2, i20^0'=i20^post_2, lx2^0'=lx2^post_2, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp1011^post_2, tmp1112^0'=tmp1112^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp1314^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp25^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=z418^post_2, z519^0'=z519^post_2, [ 1+i20^0<=8 && tmp03^post_2==tmp03^post_2 && tmp710^1_1==tmp710^1_1 && tmp14^post_2==tmp14^post_2 && tmp69^1_1==tmp69^1_1 && tmp25^post_2==tmp25^post_2 && tmp58^1_1==tmp58^1_1 && tmp36^post_2==tmp36^post_2 && tmp47^1_1==tmp47^1_1 && tmp1011^post_2==tmp03^post_2+tmp36^post_2 && tmp1314^post_2==tmp03^post_2-tmp36^post_2 && tmp1112^post_2==tmp25^post_2+tmp14^post_2 && tmp1213^post_2==-tmp25^post_2+tmp14^post_2 && constant22^1_1==4433 && z115^1_1==z115^1_1 && constant22^2_1==6270 && constant22^3_1==-15137 && z115^2_1==tmp47^1_1+tmp710^1_1 && z216^1_1==tmp58^1_1+tmp69^1_1 && z317^1_1==tmp47^1_1+tmp69^1_1 && z418^1_1==tmp710^1_1+tmp58^1_1 && constant22^4_1==9633 && z519^post_2==z519^post_2 && constant22^5_1==2446 && tmp47^post_2==tmp47^post_2 && constant22^6_1==16819 && tmp58^post_2==tmp58^post_2 && constant22^7_1==25172 && tmp69^post_2==tmp69^post_2 && constant22^8_1==12299 && tmp710^post_2==tmp710^post_2 && constant22^9_1==-7373 && z115^post_2==z115^post_2 && constant22^10_1==-20995 && z216^post_2==z216^post_2 && constant22^11_1==-16069 && z317^2_1==z317^2_1 && constant22^post_2==-3196 && z418^2_1==z418^2_1 && z317^post_2==z519^post_2+z317^2_1 && z418^post_2==z519^post_2+z418^2_1 && i20^post_2==1+i20^0 && lx2^0==lx2^post_2 ], cost: 1 5: l1 -> l3 : constant22^0'=constant22^post_6, i20^0'=i20^post_6, lx2^0'=lx2^post_6, tmp03^0'=tmp03^post_6, tmp1011^0'=tmp1011^post_6, tmp1112^0'=tmp1112^post_6, tmp1213^0'=tmp1213^post_6, tmp1314^0'=tmp1314^post_6, tmp14^0'=tmp14^post_6, tmp25^0'=tmp25^post_6, tmp36^0'=tmp36^post_6, tmp47^0'=tmp47^post_6, tmp58^0'=tmp58^post_6, tmp69^0'=tmp69^post_6, tmp710^0'=tmp710^post_6, z115^0'=z115^post_6, z216^0'=z216^post_6, z317^0'=z317^post_6, z418^0'=z418^post_6, z519^0'=z519^post_6, [ constant22^0==constant22^post_6 && i20^0==i20^post_6 && lx2^0==lx2^post_6 && tmp03^0==tmp03^post_6 && tmp1011^0==tmp1011^post_6 && tmp1112^0==tmp1112^post_6 && tmp1213^0==tmp1213^post_6 && tmp1314^0==tmp1314^post_6 && tmp14^0==tmp14^post_6 && tmp25^0==tmp25^post_6 && tmp36^0==tmp36^post_6 && tmp47^0==tmp47^post_6 && tmp58^0==tmp58^post_6 && tmp69^0==tmp69^post_6 && tmp710^0==tmp710^post_6 && z115^0==z115^post_6 && z216^0==z216^post_6 && z317^0==z317^post_6 && z418^0==z418^post_6 && z519^0==z519^post_6 ], cost: 1 4: l2 -> l0 : constant22^0'=constant22^post_5, i20^0'=i20^post_5, lx2^0'=lx2^post_5, tmp03^0'=tmp03^post_5, tmp1011^0'=tmp1011^post_5, tmp1112^0'=tmp1112^post_5, tmp1213^0'=tmp1213^post_5, tmp1314^0'=tmp1314^post_5, tmp14^0'=tmp14^post_5, tmp25^0'=tmp25^post_5, tmp36^0'=tmp36^post_5, tmp47^0'=tmp47^post_5, tmp58^0'=tmp58^post_5, tmp69^0'=tmp69^post_5, tmp710^0'=tmp710^post_5, z115^0'=z115^post_5, z216^0'=z216^post_5, z317^0'=z317^post_5, z418^0'=z418^post_5, z519^0'=z519^post_5, [ constant22^0==constant22^post_5 && i20^0==i20^post_5 && lx2^0==lx2^post_5 && tmp03^0==tmp03^post_5 && tmp1011^0==tmp1011^post_5 && tmp1112^0==tmp1112^post_5 && tmp1213^0==tmp1213^post_5 && tmp1314^0==tmp1314^post_5 && tmp14^0==tmp14^post_5 && tmp25^0==tmp25^post_5 && tmp36^0==tmp36^post_5 && tmp47^0==tmp47^post_5 && tmp58^0==tmp58^post_5 && tmp69^0==tmp69^post_5 && tmp710^0==tmp710^post_5 && z115^0==z115^post_5 && z216^0==z216^post_5 && z317^0==z317^post_5 && z418^0==z418^post_5 && z519^0==z519^post_5 ], cost: 1 2: l3 -> l4 : constant22^0'=constant22^post_3, i20^0'=i20^post_3, lx2^0'=lx2^post_3, tmp03^0'=tmp03^post_3, tmp1011^0'=tmp1011^post_3, tmp1112^0'=tmp1112^post_3, tmp1213^0'=tmp1213^post_3, tmp1314^0'=tmp1314^post_3, tmp14^0'=tmp14^post_3, tmp25^0'=tmp25^post_3, tmp36^0'=tmp36^post_3, tmp47^0'=tmp47^post_3, tmp58^0'=tmp58^post_3, tmp69^0'=tmp69^post_3, tmp710^0'=tmp710^post_3, z115^0'=z115^post_3, z216^0'=z216^post_3, z317^0'=z317^post_3, z418^0'=z418^post_3, z519^0'=z519^post_3, [ 8<=i20^0 && constant22^0==constant22^post_3 && i20^0==i20^post_3 && lx2^0==lx2^post_3 && tmp03^0==tmp03^post_3 && tmp1011^0==tmp1011^post_3 && tmp1112^0==tmp1112^post_3 && tmp1213^0==tmp1213^post_3 && tmp1314^0==tmp1314^post_3 && tmp14^0==tmp14^post_3 && tmp25^0==tmp25^post_3 && tmp36^0==tmp36^post_3 && tmp47^0==tmp47^post_3 && tmp58^0==tmp58^post_3 && tmp69^0==tmp69^post_3 && tmp710^0==tmp710^post_3 && z115^0==z115^post_3 && z216^0==z216^post_3 && z317^0==z317^post_3 && z418^0==z418^post_3 && z519^0==z519^post_3 ], cost: 1 3: l3 -> l1 : constant22^0'=constant22^post_4, i20^0'=i20^post_4, lx2^0'=lx2^post_4, tmp03^0'=tmp03^post_4, tmp1011^0'=tmp1011^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=tmp1213^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp25^post_4, tmp36^0'=tmp36^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^post_4, z418^0'=z418^post_4, z519^0'=z519^post_4, [ 1+i20^0<=8 && tmp03^post_4==tmp03^post_4 && tmp710^1_2_1==tmp710^1_2_1 && tmp14^post_4==tmp14^post_4 && tmp69^1_2_1==tmp69^1_2_1 && tmp25^post_4==tmp25^post_4 && tmp58^1_2_1==tmp58^1_2_1 && tmp36^post_4==tmp36^post_4 && tmp47^1_2_1==tmp47^1_2_1 && tmp1011^post_4==tmp36^post_4+tmp03^post_4 && tmp1314^post_4==-tmp36^post_4+tmp03^post_4 && tmp1112^post_4==tmp25^post_4+tmp14^post_4 && tmp1213^post_4==-tmp25^post_4+tmp14^post_4 && constant22^1_2==4433 && z115^1_2_1==z115^1_2_1 && constant22^2_2_1==6270 && constant22^3_2_1==-15137 && z115^2_2_1==tmp47^1_2_1+tmp710^1_2_1 && z216^1_2_1==tmp69^1_2_1+tmp58^1_2_1 && z317^1_2_1==tmp69^1_2_1+tmp47^1_2_1 && z418^1_2_1==tmp58^1_2_1+tmp710^1_2_1 && constant22^4_2_1==9633 && z519^post_4==z519^post_4 && constant22^5_2_1==2446 && tmp47^post_4==tmp47^post_4 && constant22^6_2_1==16819 && tmp58^post_4==tmp58^post_4 && constant22^7_2_1==25172 && tmp69^post_4==tmp69^post_4 && constant22^8_2_1==12299 && tmp710^post_4==tmp710^post_4 && constant22^9_2_1==-7373 && z115^post_4==z115^post_4 && constant22^10_2_1==-20995 && z216^post_4==z216^post_4 && constant22^11_2_1==-16069 && z317^2_2_1==z317^2_2_1 && constant22^post_4==-3196 && z418^2_2_1==z418^2_2_1 && z317^post_4==z317^2_2_1+z519^post_4 && z418^post_4==z519^post_4+z418^2_2_1 && i20^post_4==1+i20^0 && lx2^0==lx2^post_4 ], cost: 1 6: l5 -> l2 : constant22^0'=constant22^post_7, i20^0'=i20^post_7, lx2^0'=lx2^post_7, tmp03^0'=tmp03^post_7, tmp1011^0'=tmp1011^post_7, tmp1112^0'=tmp1112^post_7, tmp1213^0'=tmp1213^post_7, tmp1314^0'=tmp1314^post_7, tmp14^0'=tmp14^post_7, tmp25^0'=tmp25^post_7, tmp36^0'=tmp36^post_7, tmp47^0'=tmp47^post_7, tmp58^0'=tmp58^post_7, tmp69^0'=tmp69^post_7, tmp710^0'=tmp710^post_7, z115^0'=z115^post_7, z216^0'=z216^post_7, z317^0'=z317^post_7, z418^0'=z418^post_7, z519^0'=z519^post_7, [ lx2^post_7==8 && i20^post_7==0 && constant22^0==constant22^post_7 && tmp03^0==tmp03^post_7 && tmp1011^0==tmp1011^post_7 && tmp1112^0==tmp1112^post_7 && tmp1213^0==tmp1213^post_7 && tmp1314^0==tmp1314^post_7 && tmp14^0==tmp14^post_7 && tmp25^0==tmp25^post_7 && tmp36^0==tmp36^post_7 && tmp47^0==tmp47^post_7 && tmp58^0==tmp58^post_7 && tmp69^0==tmp69^post_7 && tmp710^0==tmp710^post_7 && z115^0==z115^post_7 && z216^0==z216^post_7 && z317^0==z317^post_7 && z418^0==z418^post_7 && z519^0==z519^post_7 ], cost: 1 7: l6 -> l5 : constant22^0'=constant22^post_8, i20^0'=i20^post_8, lx2^0'=lx2^post_8, tmp03^0'=tmp03^post_8, tmp1011^0'=tmp1011^post_8, tmp1112^0'=tmp1112^post_8, tmp1213^0'=tmp1213^post_8, tmp1314^0'=tmp1314^post_8, tmp14^0'=tmp14^post_8, tmp25^0'=tmp25^post_8, tmp36^0'=tmp36^post_8, tmp47^0'=tmp47^post_8, tmp58^0'=tmp58^post_8, tmp69^0'=tmp69^post_8, tmp710^0'=tmp710^post_8, z115^0'=z115^post_8, z216^0'=z216^post_8, z317^0'=z317^post_8, z418^0'=z418^post_8, z519^0'=z519^post_8, [ constant22^0==constant22^post_8 && i20^0==i20^post_8 && lx2^0==lx2^post_8 && tmp03^0==tmp03^post_8 && tmp1011^0==tmp1011^post_8 && tmp1112^0==tmp1112^post_8 && tmp1213^0==tmp1213^post_8 && tmp1314^0==tmp1314^post_8 && tmp14^0==tmp14^post_8 && tmp25^0==tmp25^post_8 && tmp36^0==tmp36^post_8 && tmp47^0==tmp47^post_8 && tmp58^0==tmp58^post_8 && tmp69^0==tmp69^post_8 && tmp710^0==tmp710^post_8 && z115^0==z115^post_8 && z216^0==z216^post_8 && z317^0==z317^post_8 && z418^0==z418^post_8 && z519^0==z519^post_8 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: l6 -> l5 : constant22^0'=constant22^post_8, i20^0'=i20^post_8, lx2^0'=lx2^post_8, tmp03^0'=tmp03^post_8, tmp1011^0'=tmp1011^post_8, tmp1112^0'=tmp1112^post_8, tmp1213^0'=tmp1213^post_8, tmp1314^0'=tmp1314^post_8, tmp14^0'=tmp14^post_8, tmp25^0'=tmp25^post_8, tmp36^0'=tmp36^post_8, tmp47^0'=tmp47^post_8, tmp58^0'=tmp58^post_8, tmp69^0'=tmp69^post_8, tmp710^0'=tmp710^post_8, z115^0'=z115^post_8, z216^0'=z216^post_8, z317^0'=z317^post_8, z418^0'=z418^post_8, z519^0'=z519^post_8, [ constant22^0==constant22^post_8 && i20^0==i20^post_8 && lx2^0==lx2^post_8 && tmp03^0==tmp03^post_8 && tmp1011^0==tmp1011^post_8 && tmp1112^0==tmp1112^post_8 && tmp1213^0==tmp1213^post_8 && tmp1314^0==tmp1314^post_8 && tmp14^0==tmp14^post_8 && tmp25^0==tmp25^post_8 && tmp36^0==tmp36^post_8 && tmp47^0==tmp47^post_8 && tmp58^0==tmp58^post_8 && tmp69^0==tmp69^post_8 && tmp710^0==tmp710^post_8 && z115^0==z115^post_8 && z216^0==z216^post_8 && z317^0==z317^post_8 && z418^0==z418^post_8 && z519^0==z519^post_8 ], cost: 1 Removed unreachable and leaf rules: Start location: l6 0: l0 -> l1 : constant22^0'=constant22^post_1, i20^0'=i20^post_1, lx2^0'=lx2^post_1, tmp03^0'=tmp03^post_1, tmp1011^0'=tmp1011^post_1, tmp1112^0'=tmp1112^post_1, tmp1213^0'=tmp1213^post_1, tmp1314^0'=tmp1314^post_1, tmp14^0'=tmp14^post_1, tmp25^0'=tmp25^post_1, tmp36^0'=tmp36^post_1, tmp47^0'=tmp47^post_1, tmp58^0'=tmp58^post_1, tmp69^0'=tmp69^post_1, tmp710^0'=tmp710^post_1, z115^0'=z115^post_1, z216^0'=z216^post_1, z317^0'=z317^post_1, z418^0'=z418^post_1, z519^0'=z519^post_1, [ 8<=i20^0 && i20^post_1==0 && constant22^0==constant22^post_1 && lx2^0==lx2^post_1 && tmp03^0==tmp03^post_1 && tmp1011^0==tmp1011^post_1 && tmp1112^0==tmp1112^post_1 && tmp1213^0==tmp1213^post_1 && tmp1314^0==tmp1314^post_1 && tmp14^0==tmp14^post_1 && tmp25^0==tmp25^post_1 && tmp36^0==tmp36^post_1 && tmp47^0==tmp47^post_1 && tmp58^0==tmp58^post_1 && tmp69^0==tmp69^post_1 && tmp710^0==tmp710^post_1 && z115^0==z115^post_1 && z216^0==z216^post_1 && z317^0==z317^post_1 && z418^0==z418^post_1 && z519^0==z519^post_1 ], cost: 1 1: l0 -> l2 : constant22^0'=constant22^post_2, i20^0'=i20^post_2, lx2^0'=lx2^post_2, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp1011^post_2, tmp1112^0'=tmp1112^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp1314^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp25^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=z418^post_2, z519^0'=z519^post_2, [ 1+i20^0<=8 && tmp03^post_2==tmp03^post_2 && tmp710^1_1==tmp710^1_1 && tmp14^post_2==tmp14^post_2 && tmp69^1_1==tmp69^1_1 && tmp25^post_2==tmp25^post_2 && tmp58^1_1==tmp58^1_1 && tmp36^post_2==tmp36^post_2 && tmp47^1_1==tmp47^1_1 && tmp1011^post_2==tmp03^post_2+tmp36^post_2 && tmp1314^post_2==tmp03^post_2-tmp36^post_2 && tmp1112^post_2==tmp25^post_2+tmp14^post_2 && tmp1213^post_2==-tmp25^post_2+tmp14^post_2 && constant22^1_1==4433 && z115^1_1==z115^1_1 && constant22^2_1==6270 && constant22^3_1==-15137 && z115^2_1==tmp47^1_1+tmp710^1_1 && z216^1_1==tmp58^1_1+tmp69^1_1 && z317^1_1==tmp47^1_1+tmp69^1_1 && z418^1_1==tmp710^1_1+tmp58^1_1 && constant22^4_1==9633 && z519^post_2==z519^post_2 && constant22^5_1==2446 && tmp47^post_2==tmp47^post_2 && constant22^6_1==16819 && tmp58^post_2==tmp58^post_2 && constant22^7_1==25172 && tmp69^post_2==tmp69^post_2 && constant22^8_1==12299 && tmp710^post_2==tmp710^post_2 && constant22^9_1==-7373 && z115^post_2==z115^post_2 && constant22^10_1==-20995 && z216^post_2==z216^post_2 && constant22^11_1==-16069 && z317^2_1==z317^2_1 && constant22^post_2==-3196 && z418^2_1==z418^2_1 && z317^post_2==z519^post_2+z317^2_1 && z418^post_2==z519^post_2+z418^2_1 && i20^post_2==1+i20^0 && lx2^0==lx2^post_2 ], cost: 1 5: l1 -> l3 : constant22^0'=constant22^post_6, i20^0'=i20^post_6, lx2^0'=lx2^post_6, tmp03^0'=tmp03^post_6, tmp1011^0'=tmp1011^post_6, tmp1112^0'=tmp1112^post_6, tmp1213^0'=tmp1213^post_6, tmp1314^0'=tmp1314^post_6, tmp14^0'=tmp14^post_6, tmp25^0'=tmp25^post_6, tmp36^0'=tmp36^post_6, tmp47^0'=tmp47^post_6, tmp58^0'=tmp58^post_6, tmp69^0'=tmp69^post_6, tmp710^0'=tmp710^post_6, z115^0'=z115^post_6, z216^0'=z216^post_6, z317^0'=z317^post_6, z418^0'=z418^post_6, z519^0'=z519^post_6, [ constant22^0==constant22^post_6 && i20^0==i20^post_6 && lx2^0==lx2^post_6 && tmp03^0==tmp03^post_6 && tmp1011^0==tmp1011^post_6 && tmp1112^0==tmp1112^post_6 && tmp1213^0==tmp1213^post_6 && tmp1314^0==tmp1314^post_6 && tmp14^0==tmp14^post_6 && tmp25^0==tmp25^post_6 && tmp36^0==tmp36^post_6 && tmp47^0==tmp47^post_6 && tmp58^0==tmp58^post_6 && tmp69^0==tmp69^post_6 && tmp710^0==tmp710^post_6 && z115^0==z115^post_6 && z216^0==z216^post_6 && z317^0==z317^post_6 && z418^0==z418^post_6 && z519^0==z519^post_6 ], cost: 1 4: l2 -> l0 : constant22^0'=constant22^post_5, i20^0'=i20^post_5, lx2^0'=lx2^post_5, tmp03^0'=tmp03^post_5, tmp1011^0'=tmp1011^post_5, tmp1112^0'=tmp1112^post_5, tmp1213^0'=tmp1213^post_5, tmp1314^0'=tmp1314^post_5, tmp14^0'=tmp14^post_5, tmp25^0'=tmp25^post_5, tmp36^0'=tmp36^post_5, tmp47^0'=tmp47^post_5, tmp58^0'=tmp58^post_5, tmp69^0'=tmp69^post_5, tmp710^0'=tmp710^post_5, z115^0'=z115^post_5, z216^0'=z216^post_5, z317^0'=z317^post_5, z418^0'=z418^post_5, z519^0'=z519^post_5, [ constant22^0==constant22^post_5 && i20^0==i20^post_5 && lx2^0==lx2^post_5 && tmp03^0==tmp03^post_5 && tmp1011^0==tmp1011^post_5 && tmp1112^0==tmp1112^post_5 && tmp1213^0==tmp1213^post_5 && tmp1314^0==tmp1314^post_5 && tmp14^0==tmp14^post_5 && tmp25^0==tmp25^post_5 && tmp36^0==tmp36^post_5 && tmp47^0==tmp47^post_5 && tmp58^0==tmp58^post_5 && tmp69^0==tmp69^post_5 && tmp710^0==tmp710^post_5 && z115^0==z115^post_5 && z216^0==z216^post_5 && z317^0==z317^post_5 && z418^0==z418^post_5 && z519^0==z519^post_5 ], cost: 1 3: l3 -> l1 : constant22^0'=constant22^post_4, i20^0'=i20^post_4, lx2^0'=lx2^post_4, tmp03^0'=tmp03^post_4, tmp1011^0'=tmp1011^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=tmp1213^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp25^post_4, tmp36^0'=tmp36^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^post_4, z418^0'=z418^post_4, z519^0'=z519^post_4, [ 1+i20^0<=8 && tmp03^post_4==tmp03^post_4 && tmp710^1_2_1==tmp710^1_2_1 && tmp14^post_4==tmp14^post_4 && tmp69^1_2_1==tmp69^1_2_1 && tmp25^post_4==tmp25^post_4 && tmp58^1_2_1==tmp58^1_2_1 && tmp36^post_4==tmp36^post_4 && tmp47^1_2_1==tmp47^1_2_1 && tmp1011^post_4==tmp36^post_4+tmp03^post_4 && tmp1314^post_4==-tmp36^post_4+tmp03^post_4 && tmp1112^post_4==tmp25^post_4+tmp14^post_4 && tmp1213^post_4==-tmp25^post_4+tmp14^post_4 && constant22^1_2==4433 && z115^1_2_1==z115^1_2_1 && constant22^2_2_1==6270 && constant22^3_2_1==-15137 && z115^2_2_1==tmp47^1_2_1+tmp710^1_2_1 && z216^1_2_1==tmp69^1_2_1+tmp58^1_2_1 && z317^1_2_1==tmp69^1_2_1+tmp47^1_2_1 && z418^1_2_1==tmp58^1_2_1+tmp710^1_2_1 && constant22^4_2_1==9633 && z519^post_4==z519^post_4 && constant22^5_2_1==2446 && tmp47^post_4==tmp47^post_4 && constant22^6_2_1==16819 && tmp58^post_4==tmp58^post_4 && constant22^7_2_1==25172 && tmp69^post_4==tmp69^post_4 && constant22^8_2_1==12299 && tmp710^post_4==tmp710^post_4 && constant22^9_2_1==-7373 && z115^post_4==z115^post_4 && constant22^10_2_1==-20995 && z216^post_4==z216^post_4 && constant22^11_2_1==-16069 && z317^2_2_1==z317^2_2_1 && constant22^post_4==-3196 && z418^2_2_1==z418^2_2_1 && z317^post_4==z317^2_2_1+z519^post_4 && z418^post_4==z519^post_4+z418^2_2_1 && i20^post_4==1+i20^0 && lx2^0==lx2^post_4 ], cost: 1 6: l5 -> l2 : constant22^0'=constant22^post_7, i20^0'=i20^post_7, lx2^0'=lx2^post_7, tmp03^0'=tmp03^post_7, tmp1011^0'=tmp1011^post_7, tmp1112^0'=tmp1112^post_7, tmp1213^0'=tmp1213^post_7, tmp1314^0'=tmp1314^post_7, tmp14^0'=tmp14^post_7, tmp25^0'=tmp25^post_7, tmp36^0'=tmp36^post_7, tmp47^0'=tmp47^post_7, tmp58^0'=tmp58^post_7, tmp69^0'=tmp69^post_7, tmp710^0'=tmp710^post_7, z115^0'=z115^post_7, z216^0'=z216^post_7, z317^0'=z317^post_7, z418^0'=z418^post_7, z519^0'=z519^post_7, [ lx2^post_7==8 && i20^post_7==0 && constant22^0==constant22^post_7 && tmp03^0==tmp03^post_7 && tmp1011^0==tmp1011^post_7 && tmp1112^0==tmp1112^post_7 && tmp1213^0==tmp1213^post_7 && tmp1314^0==tmp1314^post_7 && tmp14^0==tmp14^post_7 && tmp25^0==tmp25^post_7 && tmp36^0==tmp36^post_7 && tmp47^0==tmp47^post_7 && tmp58^0==tmp58^post_7 && tmp69^0==tmp69^post_7 && tmp710^0==tmp710^post_7 && z115^0==z115^post_7 && z216^0==z216^post_7 && z317^0==z317^post_7 && z418^0==z418^post_7 && z519^0==z519^post_7 ], cost: 1 7: l6 -> l5 : constant22^0'=constant22^post_8, i20^0'=i20^post_8, lx2^0'=lx2^post_8, tmp03^0'=tmp03^post_8, tmp1011^0'=tmp1011^post_8, tmp1112^0'=tmp1112^post_8, tmp1213^0'=tmp1213^post_8, tmp1314^0'=tmp1314^post_8, tmp14^0'=tmp14^post_8, tmp25^0'=tmp25^post_8, tmp36^0'=tmp36^post_8, tmp47^0'=tmp47^post_8, tmp58^0'=tmp58^post_8, tmp69^0'=tmp69^post_8, tmp710^0'=tmp710^post_8, z115^0'=z115^post_8, z216^0'=z216^post_8, z317^0'=z317^post_8, z418^0'=z418^post_8, z519^0'=z519^post_8, [ constant22^0==constant22^post_8 && i20^0==i20^post_8 && lx2^0==lx2^post_8 && tmp03^0==tmp03^post_8 && tmp1011^0==tmp1011^post_8 && tmp1112^0==tmp1112^post_8 && tmp1213^0==tmp1213^post_8 && tmp1314^0==tmp1314^post_8 && tmp14^0==tmp14^post_8 && tmp25^0==tmp25^post_8 && tmp36^0==tmp36^post_8 && tmp47^0==tmp47^post_8 && tmp58^0==tmp58^post_8 && tmp69^0==tmp69^post_8 && tmp710^0==tmp710^post_8 && z115^0==z115^post_8 && z216^0==z216^post_8 && z317^0==z317^post_8 && z418^0==z418^post_8 && z519^0==z519^post_8 ], cost: 1 Simplified all rules, resulting in: Start location: l6 0: l0 -> l1 : i20^0'=0, [ 8<=i20^0 ], cost: 1 1: l0 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 1 5: l1 -> l3 : [], cost: 1 4: l2 -> l0 : [], cost: 1 3: l3 -> l1 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_4, tmp1011^0'=2*tmp03^post_4-tmp1314^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=-tmp1112^post_4+2*tmp14^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp1112^post_4-tmp14^post_4, tmp36^0'=tmp03^post_4-tmp1314^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^2_2_1-z418^2_2_1+z418^post_4, z418^0'=z418^post_4, z519^0'=-z418^2_2_1+z418^post_4, [ 1+i20^0<=8 ], cost: 1 6: l5 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 1 7: l6 -> l5 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l6 0: l0 -> l1 : i20^0'=0, [ 8<=i20^0 ], cost: 1 1: l0 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 1 9: l1 -> l1 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_4, tmp1011^0'=2*tmp03^post_4-tmp1314^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=-tmp1112^post_4+2*tmp14^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp1112^post_4-tmp14^post_4, tmp36^0'=tmp03^post_4-tmp1314^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^2_2_1-z418^2_2_1+z418^post_4, z418^0'=z418^post_4, z519^0'=-z418^2_2_1+z418^post_4, [ 1+i20^0<=8 ], cost: 2 4: l2 -> l0 : [], cost: 1 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 9: l1 -> l1 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_4, tmp1011^0'=2*tmp03^post_4-tmp1314^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=-tmp1112^post_4+2*tmp14^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp1112^post_4-tmp14^post_4, tmp36^0'=tmp03^post_4-tmp1314^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^2_2_1-z418^2_2_1+z418^post_4, z418^0'=z418^post_4, z519^0'=-z418^2_2_1+z418^post_4, [ 1+i20^0<=8 ], 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: l6 0: l0 -> l1 : i20^0'=0, [ 8<=i20^0 ], cost: 1 1: l0 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 1 10: l1 -> l1 : constant22^0'=-3196, i20^0'=8, tmp03^0'=tmp03^post_4, tmp1011^0'=2*tmp03^post_4-tmp1314^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=-tmp1112^post_4+2*tmp14^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp1112^post_4-tmp14^post_4, tmp36^0'=tmp03^post_4-tmp1314^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^2_2_1-z418^2_2_1+z418^post_4, z418^0'=z418^post_4, z519^0'=-z418^2_2_1+z418^post_4, [ 8-i20^0>=1 ], cost: 16-2*i20^0 4: l2 -> l0 : [], cost: 1 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l6 0: l0 -> l1 : i20^0'=0, [ 8<=i20^0 ], cost: 1 1: l0 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 1 11: l0 -> l1 : constant22^0'=-3196, i20^0'=8, tmp03^0'=tmp03^post_4, tmp1011^0'=2*tmp03^post_4-tmp1314^post_4, tmp1112^0'=tmp1112^post_4, tmp1213^0'=-tmp1112^post_4+2*tmp14^post_4, tmp1314^0'=tmp1314^post_4, tmp14^0'=tmp14^post_4, tmp25^0'=tmp1112^post_4-tmp14^post_4, tmp36^0'=tmp03^post_4-tmp1314^post_4, tmp47^0'=tmp47^post_4, tmp58^0'=tmp58^post_4, tmp69^0'=tmp69^post_4, tmp710^0'=tmp710^post_4, z115^0'=z115^post_4, z216^0'=z216^post_4, z317^0'=z317^2_2_1-z418^2_2_1+z418^post_4, z418^0'=z418^post_4, z519^0'=-z418^2_2_1+z418^post_4, [ 8<=i20^0 ], cost: 17 4: l2 -> l0 : [], cost: 1 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 Removed unreachable locations (and leaf rules with constant cost): Start location: l6 1: l0 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 1 4: l2 -> l0 : [], cost: 1 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 Eliminated locations (on linear paths): Start location: l6 12: l2 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 2 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 12: l2 -> l2 : constant22^0'=-3196, i20^0'=1+i20^0, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 1+i20^0<=8 ], cost: 2 Accelerated rule 12 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 12. Accelerated all simple loops using metering functions (where possible): Start location: l6 13: l2 -> l2 : constant22^0'=-3196, i20^0'=8, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [ 8-i20^0>=1 ], cost: 16-2*i20^0 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l6 8: l6 -> l2 : i20^0'=0, lx2^0'=8, [], cost: 2 14: l6 -> l2 : constant22^0'=-3196, i20^0'=8, lx2^0'=8, tmp03^0'=tmp03^post_2, tmp1011^0'=tmp03^post_2+tmp36^post_2, tmp1112^0'=2*tmp14^post_2-tmp1213^post_2, tmp1213^0'=tmp1213^post_2, tmp1314^0'=tmp03^post_2-tmp36^post_2, tmp14^0'=tmp14^post_2, tmp25^0'=tmp14^post_2-tmp1213^post_2, tmp36^0'=tmp36^post_2, tmp47^0'=tmp47^post_2, tmp58^0'=tmp58^post_2, tmp69^0'=tmp69^post_2, tmp710^0'=tmp710^post_2, z115^0'=z115^post_2, z216^0'=z216^post_2, z317^0'=z317^post_2, z418^0'=-z317^2_1+z418^2_1+z317^post_2, z519^0'=-z317^2_1+z317^post_2, [], cost: 18 Removed unreachable locations (and leaf rules with constant cost): Start location: l6 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 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: [ constant22^0==constant22^post_8 && i20^0==i20^post_8 && lx2^0==lx2^post_8 && tmp03^0==tmp03^post_8 && tmp1011^0==tmp1011^post_8 && tmp1112^0==tmp1112^post_8 && tmp1213^0==tmp1213^post_8 && tmp1314^0==tmp1314^post_8 && tmp14^0==tmp14^post_8 && tmp25^0==tmp25^post_8 && tmp36^0==tmp36^post_8 && tmp47^0==tmp47^post_8 && tmp58^0==tmp58^post_8 && tmp69^0==tmp69^post_8 && tmp710^0==tmp710^post_8 && z115^0==z115^post_8 && z216^0==z216^post_8 && z317^0==z317^post_8 && z418^0==z418^post_8 && z519^0==z519^post_8 ] WORST_CASE(Omega(1),?)