YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (?,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (?,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (?,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (?,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (?,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (?,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (?,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (?,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8,9},12->{8 ,9},13->{},14->{15},15->{16},16->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (1,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (1,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (1,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (1,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (1,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (1,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (1,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (1,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (1,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (1,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (1,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8,9},12->{8 ,9},13->{},14->{15},15->{16},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,9)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (1,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (1,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (1,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (1,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (1,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (1,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (1,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (1,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (1,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (1,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (1,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8},12->{8 ,9},13->{},14->{15},15->{16},16->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (?,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (?,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (?,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (?,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (?,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (?,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (?,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (?,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 17. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True (?,1) 18. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13,18},10->{12},11->{8,9} ,12->{8,9},13->{},14->{15},15->{16,17},16->{},17->{},18->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,9)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (?,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (?,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (?,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (?,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (?,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (?,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (?,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (?,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 17. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True (?,1) 18. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13,18},10->{12},11->{8} ,12->{8,9},13->{},14->{15},15->{16,17},16->{},17->{},18->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[8,11,12,10] c: [12] | `- p:[8,11] c: [11] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (?,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (?,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (?,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (?,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (?,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (?,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (?,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (?,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 17. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True (?,1) 18. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13,18},10->{12},11->{8} ,12->{8,9},13->{},14->{15},15->{16,17},16->{},17->{},18->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[8,11,12,10] c: [12] | `- p:[8,11] c: [11]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_m,v_n,v_va_0,v_vb_0,0.0,0.0.0] eval_start_start ~> eval_start_bb0_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb0_in ~> eval_start_0 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_0 ~> eval_start_1 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_1 ~> eval_start_2 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_2 ~> eval_start_3 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_3 ~> eval_start_4 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_4 ~> eval_start_bb1_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_n, v_vb_0 <= 0*K] eval_start_4 ~> eval_start_bb5_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb1_in ~> eval_start_bb2_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb1_in ~> eval_start_bb4_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in ~> eval_start_bb3_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in ~> eval_start_bb1_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= 0*K] eval_start_bb3_in ~> eval_start_bb1_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_m] eval_start_bb4_in ~> eval_start_stop [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb5_in ~> eval_start_8 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_8 ~> eval_start_9 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_9 ~> eval_start_stop [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_9 ~> exitus616 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb4_in ~> exitus616 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] + Loop: [0.0 <= v_va_0] eval_start_bb1_in ~> eval_start_bb2_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in ~> eval_start_bb1_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= 0*K] eval_start_bb3_in ~> eval_start_bb1_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_m] eval_start_bb2_in ~> eval_start_bb3_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] + Loop: [0.0.0 <= K + v_vb_0] eval_start_bb1_in ~> eval_start_bb2_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in ~> eval_start_bb1_in [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= 0*K] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_m,v_n,v_va_0,v_vb_0,0.0,0.0.0] eval_start_start ~> eval_start_bb0_in [] eval_start_bb0_in ~> eval_start_0 [] eval_start_0 ~> eval_start_1 [] eval_start_1 ~> eval_start_2 [] eval_start_2 ~> eval_start_3 [] eval_start_3 ~> eval_start_4 [] eval_start_4 ~> eval_start_bb1_in [v_n ~=> v_va_0,K ~=> v_vb_0] eval_start_4 ~> eval_start_bb5_in [] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb1_in ~> eval_start_bb4_in [] eval_start_bb2_in ~> eval_start_bb3_in [] eval_start_bb2_in ~> eval_start_bb1_in [K ~=> v_vb_0] eval_start_bb3_in ~> eval_start_bb1_in [v_m ~=> v_vb_0] eval_start_bb4_in ~> eval_start_stop [] eval_start_bb5_in ~> eval_start_8 [] eval_start_8 ~> eval_start_9 [] eval_start_9 ~> eval_start_stop [] eval_start_9 ~> exitus616 [] eval_start_bb4_in ~> exitus616 [] + Loop: [v_va_0 ~=> 0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb2_in ~> eval_start_bb1_in [K ~=> v_vb_0] eval_start_bb3_in ~> eval_start_bb1_in [v_m ~=> v_vb_0] eval_start_bb2_in ~> eval_start_bb3_in [] + Loop: [v_vb_0 ~+> 0.0.0,K ~+> 0.0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb2_in ~> eval_start_bb1_in [K ~=> v_vb_0] + Applied Processor: LareProcessor + Details: eval_start_start ~> exitus616 [v_m ~=> v_vb_0 ,v_n ~=> v_va_0 ,v_n ~=> 0.0 ,K ~=> v_vb_0 ,v_m ~+> 0.0.0 ,v_m ~+> tick ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,v_n ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] eval_start_start ~> eval_start_stop [v_m ~=> v_vb_0 ,v_n ~=> v_va_0 ,v_n ~=> 0.0 ,K ~=> v_vb_0 ,v_m ~+> 0.0.0 ,v_m ~+> tick ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,v_n ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + eval_start_bb1_in> [v_m ~=> v_vb_0 ,v_va_0 ~=> 0.0 ,K ~=> v_vb_0 ,v_m ~+> 0.0.0 ,v_m ~+> tick ,v_va_0 ~+> tick ,v_vb_0 ~+> 0.0.0 ,v_vb_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,v_va_0 ~*> tick ,v_vb_0 ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + eval_start_bb2_in> [K ~=> v_vb_0 ,v_vb_0 ~+> 0.0.0 ,v_vb_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] eval_start_bb1_in> [K ~=> v_vb_0 ,v_vb_0 ~+> 0.0.0 ,v_vb_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)