YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalnestedLoopstart(A,B,C,D,E,F,G,H) -> evalnestedLoopentryin(A,B,C,D,E,F,G,H) True (1,1) 1. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopbb9in(A,B,C,0,E,F,G,H) [A >= 0 && B >= 0 && C >= 0] (?,1) 2. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [0 >= 1 + A] (?,1) 3. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [0 >= 1 + B] (?,1) 4. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [0 >= 1 + C] (?,1) 5. evalnestedLoopbb9in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb7in(A,B,C,D,0,D,G,H) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + D] 6. evalnestedLoopbb9in(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= A] 7. evalnestedLoopbb7in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb4in(A,B,C,D,E,F,G,H) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && B + F >= 0 && -1 + A + F >= 0 && B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 + E] 8. evalnestedLoopbb7in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb8in(A,B,C,D,E,F,G,H) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && B + F >= 0 && -1 + A + F >= 0 && B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= B] 9. evalnestedLoopbb4in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb6in(A,B,C,D,E,F,1 + E,F) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 10. evalnestedLoopbb6in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb5in(A,B,C,D,E,F,G,H) [H >= 0 (?,1) && -1 + G + H >= 0 && F + H >= 0 && -1*F + H >= 0 && E + H >= 0 && D + H >= 0 && -1*D + H >= 0 && C + H >= 0 && -1 + B + H >= 0 && -1 + A + H >= 0 && 1 + E + -1*G >= 0 && B + -1*G >= 0 && -1 + G >= 0 && -1 + F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -1 + D + G >= 0 && -1 + C + G >= 0 && -2 + B + G >= 0 && -2 + A + G >= 0 && F >= 0 && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 1 + H] 11. evalnestedLoopbb6in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb7in(A,B,C,D,G,H,G,H) [H >= 0 (?,1) && -1 + G + H >= 0 && F + H >= 0 && -1*F + H >= 0 && E + H >= 0 && D + H >= 0 && -1*D + H >= 0 && C + H >= 0 && -1 + B + H >= 0 && -1 + A + H >= 0 && 1 + E + -1*G >= 0 && B + -1*G >= 0 && -1 + G >= 0 && -1 + F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -1 + D + G >= 0 && -1 + C + G >= 0 && -2 + B + G >= 0 && -2 + A + G >= 0 && F >= 0 && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && H >= C] 12. evalnestedLoopbb5in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb6in(A,B,C,D,E,F,G,1 + H) [-1 + C + -1*H >= 0 (?,1) && H >= 0 && -1 + G + H >= 0 && F + H >= 0 && -1*F + H >= 0 && E + H >= 0 && D + H >= 0 && -1*D + H >= 0 && -1 + C + H >= 0 && -1 + B + H >= 0 && -1 + A + H >= 0 && 1 + E + -1*G >= 0 && B + -1*G >= 0 && -1 + G >= 0 && -1 + F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -2 + A + G >= 0 && -1 + C + -1*F >= 0 && F >= 0 && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 13. evalnestedLoopbb8in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb9in(A,B,C,1 + F,E,F,G,H) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && B + F >= 0 && -1 + A + F >= 0 && B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 14. evalnestedLoopreturnin(A,B,C,D,E,F,G,H) -> evalnestedLoopstop(A,B,C,D,E,F,G,H) True (?,1) Signature: {(evalnestedLoopbb4in,8) ;(evalnestedLoopbb5in,8) ;(evalnestedLoopbb6in,8) ;(evalnestedLoopbb7in,8) ;(evalnestedLoopbb8in,8) ;(evalnestedLoopbb9in,8) ;(evalnestedLoopentryin,8) ;(evalnestedLoopreturnin,8) ;(evalnestedLoopstart,8) ;(evalnestedLoopstop,8)} Flow Graph: [0->{1,2,3,4},1->{5,6},2->{14},3->{14},4->{14},5->{7,8},6->{14},7->{9},8->{13},9->{10,11},10->{12},11->{7 ,8},12->{10,11},13->{5,6},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalnestedLoopstart(A,B,C,D,E,F,G,H) -> evalnestedLoopentryin(A,B,C,D,E,F,G,H) True (1,1) 1. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopbb9in(A,B,C,0,E,F,G,H) [A >= 0 && B >= 0 && C >= 0] (1,1) 2. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [0 >= 1 + A] (1,1) 3. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [0 >= 1 + B] (1,1) 4. evalnestedLoopentryin(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [0 >= 1 + C] (1,1) 5. evalnestedLoopbb9in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb7in(A,B,C,D,0,D,G,H) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + D] 6. evalnestedLoopbb9in(A,B,C,D,E,F,G,H) -> evalnestedLoopreturnin(A,B,C,D,E,F,G,H) [D >= 0 (1,1) && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= A] 7. evalnestedLoopbb7in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb4in(A,B,C,D,E,F,G,H) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && B + F >= 0 && -1 + A + F >= 0 && B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 + E] 8. evalnestedLoopbb7in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb8in(A,B,C,D,E,F,G,H) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && B + F >= 0 && -1 + A + F >= 0 && B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= B] 9. evalnestedLoopbb4in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb6in(A,B,C,D,E,F,1 + E,F) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 10. evalnestedLoopbb6in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb5in(A,B,C,D,E,F,G,H) [H >= 0 (?,1) && -1 + G + H >= 0 && F + H >= 0 && -1*F + H >= 0 && E + H >= 0 && D + H >= 0 && -1*D + H >= 0 && C + H >= 0 && -1 + B + H >= 0 && -1 + A + H >= 0 && 1 + E + -1*G >= 0 && B + -1*G >= 0 && -1 + G >= 0 && -1 + F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -1 + D + G >= 0 && -1 + C + G >= 0 && -2 + B + G >= 0 && -2 + A + G >= 0 && F >= 0 && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && C >= 1 + H] 11. evalnestedLoopbb6in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb7in(A,B,C,D,G,H,G,H) [H >= 0 (?,1) && -1 + G + H >= 0 && F + H >= 0 && -1*F + H >= 0 && E + H >= 0 && D + H >= 0 && -1*D + H >= 0 && C + H >= 0 && -1 + B + H >= 0 && -1 + A + H >= 0 && 1 + E + -1*G >= 0 && B + -1*G >= 0 && -1 + G >= 0 && -1 + F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -1 + D + G >= 0 && -1 + C + G >= 0 && -2 + B + G >= 0 && -2 + A + G >= 0 && F >= 0 && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && H >= C] 12. evalnestedLoopbb5in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb6in(A,B,C,D,E,F,G,1 + H) [-1 + C + -1*H >= 0 (?,1) && H >= 0 && -1 + G + H >= 0 && F + H >= 0 && -1*F + H >= 0 && E + H >= 0 && D + H >= 0 && -1*D + H >= 0 && -1 + C + H >= 0 && -1 + B + H >= 0 && -1 + A + H >= 0 && 1 + E + -1*G >= 0 && B + -1*G >= 0 && -1 + G >= 0 && -1 + F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -2 + A + G >= 0 && -1 + C + -1*F >= 0 && F >= 0 && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && -1 + A + F >= 0 && -1 + B + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 13. evalnestedLoopbb8in(A,B,C,D,E,F,G,H) -> evalnestedLoopbb9in(A,B,C,1 + F,E,F,G,H) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1*D + F >= 0 && C + F >= 0 && B + F >= 0 && -1 + A + F >= 0 && B + -1*E >= 0 && E >= 0 && D + E >= 0 && C + E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1 + A + E >= 0 && -1 + A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 14. evalnestedLoopreturnin(A,B,C,D,E,F,G,H) -> evalnestedLoopstop(A,B,C,D,E,F,G,H) True (1,1) Signature: {(evalnestedLoopbb4in,8) ;(evalnestedLoopbb5in,8) ;(evalnestedLoopbb6in,8) ;(evalnestedLoopbb7in,8) ;(evalnestedLoopbb8in,8) ;(evalnestedLoopbb9in,8) ;(evalnestedLoopentryin,8) ;(evalnestedLoopreturnin,8) ;(evalnestedLoopstart,8) ;(evalnestedLoopstop,8)} Flow Graph: [0->{1,2,3,4},1->{5,6},2->{14},3->{14},4->{14},5->{7,8},6->{14},7->{9},8->{13},9->{10,11},10->{12},11->{7 ,8},12->{10,11},13->{5,6},14->{}] + 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:[5,13,8,11,9,7,12,10] c: [13] | `- p:[7,11,9,12,10] c: [12] | `- p:[7,11,9] c: [11] YES