YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (?,1) 2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1) 3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= B] (?,1) 4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B + C >= D] 7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 + B + C] 8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= E] 9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && E >= 1 + D] 10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 (?,1) && -1 + E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-2 + E >= 0 (?,1) && -3 + D + E >= 0 && -1 + -1*D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -1 + -1*B + E >= 0 && -3 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [-3 + D >= 0 (?,1) && -4 + C + D >= 0 && -2 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -4 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 14. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1*B >= 0] (?,1) Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfbb9in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{14},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7} ,12->{4,5},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,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,1) 2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1) 3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= B] (1,1) 4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B + C >= D] 7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 + B + C] 8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= E] 9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && E >= 1 + D] 10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 (?,1) && -1 + E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-2 + E >= 0 (?,1) && -3 + D + E >= 0 && -1 + -1*D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -1 + -1*B + E >= 0 && -3 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [-3 + D >= 0 (?,1) && -4 + C + D >= 0 && -2 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -4 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 14. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1*B >= 0] (1,1) Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfbb9in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{14},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7} ,12->{4,5},13->{2,3},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,7),(6,9)] * Step 3: Looptree YES + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,1) 2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1) 3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= B] (1,1) 4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B + C >= D] 7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 + B + C] 8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= E] 9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && E >= 1 + D] 10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 (?,1) && -1 + E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-2 + E >= 0 (?,1) && -3 + D + E >= 0 && -1 + -1*D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -1 + -1*B + E >= 0 && -3 + A + E >= 0 && -1 + D >= 0 && -2 + C + D >= 0 && -2 + B + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [-3 + D >= 0 (?,1) && -4 + C + D >= 0 && -2 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -4 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 14. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1*B >= 0] (1,1) Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfbb9in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{14},4->{6},5->{13},6->{8},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4 ,5},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:[2,13,5,12,7,11,9,10,8,6,4] c: [13] | `- p:[4,12,7,11,9,10,8,6] c: [12] | `- p:[6,11,9,10,8] c: [6] | `- p:[8,10] c: [10] YES