YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + L] (?,1) 1. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && L >= 1] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,B,C,D,E,F,G,H,I,J,K) True (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,0,D,E,F,G,H,I,J,K) [A >= B] (?,1) 4. f9(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,C,1 + D,L,L,G,H,I,J,K) [A + -1*B >= 0 && C >= L && A >= D] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,L,1 + D,L,L,G,H,I,J,K) [A + -1*B >= 0 && L >= 1 + C && A >= D] (?,1) 6. f23(A,B,C,D,E,F,G,H,I,J,K) -> f26(A,B,C,D,E,F,G,H,I,J,K) [-1 + -1*A + B >= 0 && A >= D] (?,1) 7. f59(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,1 + H,L,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A >= H] (?,1) 8. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0] (?,1) 9. f71(A,B,C,D,E,F,G,H,I,J,K) -> f74(A,B,C,D,E,F,G,H,L,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A >= 1 + D] (?,1) 10. f71(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,1 + A,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A = D] (?,1) 11. f74(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,1 + D,E,F,G,H,I,J,K) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 12. f59(A,B,C,D,E,F,G,H,I,J,K) -> f69(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && H >= 1 + A] (?,1) 13. f40(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 (?,1) && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && K >= 1 + D] 14. f40(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 (?,1) && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && D >= 1 + K] 15. f40(A,B,C,D,E,F,G,H,I,J,K) -> f69(A,B,C,D,E,F,G,H,I,J,D) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && D = K] (?,1) 16. f26(A,B,C,D,E,F,G,H,I,J,K) -> f40(A,B,0,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + -1*A + B >= 0 && B >= D] (?,1) 17. f23(A,B,C,D,E,F,G,H,I,J,K) -> f1(A,B,C,D,E,F,G,H,I,J,K) [-1 + -1*A + B >= 0 && D >= 1 + A] (?,1) 18. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 19. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && C >= 1 && D >= 1 + A] (?,1) 20. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && D >= 1 + A && C = 0] (?,1) 21. f5(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,D,E,F,G,H,I,J,K) [B >= 1 + A] (?,1) Signature: {(f1,11);(f2,11);(f23,11);(f26,11);(f40,11);(f5,11);(f59,11);(f69,11);(f71,11);(f74,11);(f9,11)} Flow Graph: [0->{9,10},1->{9,10},2->{3,21},3->{4,5,18,19,20},4->{4,5,18,19,20},5->{4,5,18,19,20},6->{16},7->{7,12} ,8->{9,10},9->{11},10->{6,17},11->{6,17},12->{0,1,8},13->{7,12},14->{7,12},15->{0,1,8},16->{13,14,15},17->{} ,18->{3,21},19->{3,21},20->{3,21},21->{6,17}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + L] (?,1) 1. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && L >= 1] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,B,C,D,E,F,G,H,I,J,K) True (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,0,D,E,F,G,H,I,J,K) [A >= B] (?,1) 4. f9(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,C,1 + D,L,L,G,H,I,J,K) [A + -1*B >= 0 && C >= L && A >= D] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,L,1 + D,L,L,G,H,I,J,K) [A + -1*B >= 0 && L >= 1 + C && A >= D] (?,1) 6. f23(A,B,C,D,E,F,G,H,I,J,K) -> f26(A,B,C,D,E,F,G,H,I,J,K) [-1 + -1*A + B >= 0 && A >= D] (?,1) 7. f59(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,1 + H,L,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A >= H] (?,1) 8. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0] (?,1) 9. f71(A,B,C,D,E,F,G,H,I,J,K) -> f74(A,B,C,D,E,F,G,H,L,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A >= 1 + D] (?,1) 10. f71(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,1 + A,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A = D] (?,1) 11. f74(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,1 + D,E,F,G,H,I,J,K) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 12. f59(A,B,C,D,E,F,G,H,I,J,K) -> f69(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && H >= 1 + A] (?,1) 13. f40(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 (?,1) && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && K >= 1 + D] 14. f40(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 (?,1) && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && D >= 1 + K] 15. f40(A,B,C,D,E,F,G,H,I,J,K) -> f69(A,B,C,D,E,F,G,H,I,J,D) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && D = K] (?,1) 16. f26(A,B,C,D,E,F,G,H,I,J,K) -> f40(A,B,0,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + -1*A + B >= 0 && B >= D] (?,1) 17. f23(A,B,C,D,E,F,G,H,I,J,K) -> f1(A,B,C,D,E,F,G,H,I,J,K) [-1 + -1*A + B >= 0 && D >= 1 + A] (1,1) 18. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 19. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && C >= 1 && D >= 1 + A] (?,1) 20. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && D >= 1 + A && C = 0] (?,1) 21. f5(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,D,E,F,G,H,I,J,K) [B >= 1 + A] (1,1) Signature: {(f1,11);(f2,11);(f23,11);(f26,11);(f40,11);(f5,11);(f59,11);(f69,11);(f71,11);(f74,11);(f9,11)} Flow Graph: [0->{9,10},1->{9,10},2->{3,21},3->{4,5,18,19,20},4->{4,5,18,19,20},5->{4,5,18,19,20},6->{16},7->{7,12} ,8->{9,10},9->{11},10->{6,17},11->{6,17},12->{0,1,8},13->{7,12},14->{7,12},15->{0,1,8},16->{13,14,15},17->{} ,18->{3,21},19->{3,21},20->{3,21},21->{6,17}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,18),(3,19),(10,6),(11,17)] * Step 3: Looptree YES + Considered Problem: Rules: 0. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + L] (?,1) 1. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && L >= 1] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,B,C,D,E,F,G,H,I,J,K) True (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,0,D,E,F,G,H,I,J,K) [A >= B] (?,1) 4. f9(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,C,1 + D,L,L,G,H,I,J,K) [A + -1*B >= 0 && C >= L && A >= D] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K) -> f9(A,B,L,1 + D,L,L,G,H,I,J,K) [A + -1*B >= 0 && L >= 1 + C && A >= D] (?,1) 6. f23(A,B,C,D,E,F,G,H,I,J,K) -> f26(A,B,C,D,E,F,G,H,I,J,K) [-1 + -1*A + B >= 0 && A >= D] (?,1) 7. f59(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,1 + H,L,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A >= H] (?,1) 8. f69(A,B,C,D,E,F,G,H,I,J,K) -> f71(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0] (?,1) 9. f71(A,B,C,D,E,F,G,H,I,J,K) -> f74(A,B,C,D,E,F,G,H,L,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A >= 1 + D] (?,1) 10. f71(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,1 + A,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && A = D] (?,1) 11. f74(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,1 + D,E,F,G,H,I,J,K) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 12. f59(A,B,C,D,E,F,G,H,I,J,K) -> f69(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && H >= 1 + A] (?,1) 13. f40(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 (?,1) && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && K >= 1 + D] 14. f40(A,B,C,D,E,F,G,H,I,J,K) -> f59(A,B,C,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 (?,1) && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && D >= 1 + K] 15. f40(A,B,C,D,E,F,G,H,I,J,K) -> f69(A,B,C,D,E,F,G,H,I,J,D) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A && D = K] (?,1) 16. f26(A,B,C,D,E,F,G,H,I,J,K) -> f40(A,B,0,D,E,F,G,H,I,J,K) [-1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + -1*A + B >= 0 && B >= D] (?,1) 17. f23(A,B,C,D,E,F,G,H,I,J,K) -> f1(A,B,C,D,E,F,G,H,I,J,K) [-1 + -1*A + B >= 0 && D >= 1 + A] (1,1) 18. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 19. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && C >= 1 && D >= 1 + A] (?,1) 20. f9(A,B,C,D,E,F,G,H,I,J,K) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K) [A + -1*B >= 0 && D >= 1 + A && C = 0] (?,1) 21. f5(A,B,C,D,E,F,G,H,I,J,K) -> f23(A,B,C,D,E,F,G,H,I,J,K) [B >= 1 + A] (1,1) Signature: {(f1,11);(f2,11);(f23,11);(f26,11);(f40,11);(f5,11);(f59,11);(f69,11);(f71,11);(f74,11);(f9,11)} Flow Graph: [0->{9,10},1->{9,10},2->{3,21},3->{4,5,20},4->{4,5,18,19,20},5->{4,5,18,19,20},6->{16},7->{7,12},8->{9,10} ,9->{11},10->{17},11->{6},12->{0,1,8},13->{7,12},14->{7,12},15->{0,1,8},16->{13,14,15},17->{},18->{3,21} ,19->{3,21},20->{3,21},21->{6,17}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] | +- p:[3,18,4,5,19,20] c: [20] | | | `- p:[3,18,4,5,19] c: [19] | | | `- p:[3,18,4,5] c: [18] | | | `- p:[4,5] c: [5] | | | `- p:[4] c: [4] | `- p:[0,12,7,13,16,6,11,9,1,15,8,14] c: [16] | `- p:[7] c: [7] YES