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