YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb8in(B,A,C,D,E,F) True (?,1) 2. evalfbb8in(A,B,C,D,E,F) -> evalfbb2in(A,B,A,D,E,F) [B >= 0] (?,1) 3. evalfbb8in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [0 >= 1 + B] (?,1) 4. evalfbb2in(A,B,C,D,E,F) -> evalfbb4in(A,B,C,D,E,F) [A + -1*C >= 0 && B >= 0 && 0 >= 1 + C] (?,1) 5. evalfbb2in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,E,F) [A + -1*C >= 0 && B >= 0 && C >= 0] (?,1) 6. evalfbb3in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + G] (?,1) 7. evalfbb3in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1] (?,1) 8. evalfbb3in(A,B,C,D,E,F) -> evalfbb4in(A,B,C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) 9. evalfbb1in(A,B,C,D,E,F) -> evalfbb2in(A,B,-1 + C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) 10. evalfbb4in(A,B,C,D,E,F) -> evalfbb6in(A,B,C,-1 + B,C,F) [A + -1*C >= 0 && B >= 0] (?,1) 11. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(E,D,C,D,E,F) [-1*C + E >= 0 (?,1) && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && E >= 1 + F] 12. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1*C + E >= 0 (?,1) && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && F >= E] 13. evalfbb7in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && 0 >= 1 + G] 14. evalfbb7in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && G >= 1] 15. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(E,D,C,D,E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0] 16. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,C,D,1 + E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0] 17. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [-1 + -1*B >= 0] (?,1) Signature: {(evalfbb1in,6) ;(evalfbb2in,6) ;(evalfbb3in,6) ;(evalfbb4in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{17},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{11,12},11->{2,3} ,12->{13,14,15},13->{16},14->{16},15->{2,3},16->{11,12},17->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb8in(B,A,C,D,E,F) True (1,1) 2. evalfbb8in(A,B,C,D,E,F) -> evalfbb2in(A,B,A,D,E,F) [B >= 0] (?,1) 3. evalfbb8in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [0 >= 1 + B] (1,1) 4. evalfbb2in(A,B,C,D,E,F) -> evalfbb4in(A,B,C,D,E,F) [A + -1*C >= 0 && B >= 0 && 0 >= 1 + C] (?,1) 5. evalfbb2in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,E,F) [A + -1*C >= 0 && B >= 0 && C >= 0] (?,1) 6. evalfbb3in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + G] (?,1) 7. evalfbb3in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1] (?,1) 8. evalfbb3in(A,B,C,D,E,F) -> evalfbb4in(A,B,C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) 9. evalfbb1in(A,B,C,D,E,F) -> evalfbb2in(A,B,-1 + C,D,E,F) [A + -1*C >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) 10. evalfbb4in(A,B,C,D,E,F) -> evalfbb6in(A,B,C,-1 + B,C,F) [A + -1*C >= 0 && B >= 0] (?,1) 11. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(E,D,C,D,E,F) [-1*C + E >= 0 (?,1) && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && E >= 1 + F] 12. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1*C + E >= 0 (?,1) && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && F >= E] 13. evalfbb7in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && 0 >= 1 + G] 14. evalfbb7in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0 && G >= 1] 15. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(E,D,C,D,E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0] 16. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,C,D,1 + E,F) [-1*E + F >= 0 (?,1) && -1*C + F >= 0 && -1*C + E >= 0 && -1 + B + -1*D >= 0 && 1 + D >= 0 && 1 + B + D >= 0 && 1 + -1*B + D >= 0 && A + -1*C >= 0 && B >= 0] 17. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [-1 + -1*B >= 0] (1,1) Signature: {(evalfbb1in,6) ;(evalfbb2in,6) ;(evalfbb3in,6) ;(evalfbb4in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{17},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{11,12},11->{2,3} ,12->{13,14,15},13->{16},14->{16},15->{2,3},16->{11,12},17->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | `- p:[2,11,10,4,9,6,5,7,8,16,13,12,14,15] c: [15] | `- p:[2,11,10,4,9,6,5,7,8,16,13,12,14] c: [11] | +- p:[5,9,6,7] c: [9] | `- p:[12,16,13,14] c: [16] YES