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) -> evalfbb9in(B,B,C,D,E,F) True (?,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (?,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (?,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (?,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + 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) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (?,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[3,11,7,5,14,13,12,9,6,10,8] c: [14] | `- p:[3,11,7,5,8,6] c: [11] YES