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