YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (?,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (?,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (?,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (?,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (?,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (?,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4)} Flow Graph: [0->{1,2},1->{15},2->{3},3->{4,5},4->{6,7},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4,5},12->{15},13->{15},14->{15},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (1,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (1,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (1,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (1,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (1,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (1,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (1,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (1,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4)} Flow Graph: [0->{1,2},1->{15},2->{3},3->{4,5},4->{6,7},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4,5},12->{15},13->{15},14->{15},15->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5),(4,7),(11,5)] * Step 3: Looptree YES + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (1,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (1,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (1,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (1,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (1,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (1,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (1,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (1,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4)} Flow Graph: [0->{1,2},1->{15},2->{3},3->{4},4->{6},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4},12->{15},13->{15},14->{15},15->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[4,9,7,8,6,10,11] c: [11] | `- p:[4,9,7,8,6,10] c: [10] | `- p:[4,9,7,8,6] c: [9] | `- p:[6,8] c: [8] YES