NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f0(A,1 + B,B1,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= B] (?,1) 1. f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f25(A,B,C,B1,C1,D1,E1,F1,1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1] (?,1) 2. f25(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + B >= 0 && G >= J && I >= 1 + J] (?,1) 3. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f30(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && F + J >= 2 + K] (?,1) 4. f30(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f30(A,B,C,D,E,F,G,H,I,J,K,G + L,I + -1*J + L,B1,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && H >= L] (?,1) 5. f25(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,B1,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + B >= 0 && G >= J && J >= I] (?,1) 6. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I + -1*O,J,K,L,M,N,B1,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [G + -1*J >= 0 && -1 + B >= 0 && O >= F && I >= 1 + O] (?,1) 7. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,B1,C1,D1,E1,F1,1,0,X,Y,Z,A1) [-1 + B >= 0 && G >= 1 + P] (?,1) 8. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + B >= 0 && P >= L] (?,1) 9. f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f68(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && F + L >= 2 + K] (?,1) 10. f68(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f68(A,B,C,D,E,F,G,H,I,J + Q,K,L,M,B1,O,P,Q,R,S,T,U,V,W,J,J + P,C1,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && H >= J] (?,1) 11. f68(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f66(A,B,C,D,E,F,G,H,I,J,2 + K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && J >= 1 + H] (?,1) 12. f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,J,K,F + L,M,N,O,P,Q,R,V,T,U,B1,C1,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && 1 + K >= F + L] (?,1) 13. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,Q,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + B >= 0 && L >= 1 + P] (?,1) 14. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f17(A,-1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,B1) [-1 + B >= 0 && P >= G] (?,1) 15. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f25(A,B,C,D,E,F,G,H,I + O,F + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [G + -1*J >= 0 && -1 + B >= 0 && O >= F && O >= I] (?,1) 16. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f25(A,B,C,D,E,F,G,H,I + O,F + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [G + -1*J >= 0 && -1 + B >= 0 && F >= 1 + O] (?,1) 17. f30(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f28(A,B,C,D,E,F,G,H,I,J,2 + K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && L >= 1 + H] (?,1) 18. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,B1,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && 1 + K >= F + J] (?,1) 19. f25(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,F,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + B >= 0 && J >= 1 + G] (?,1) 20. f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f93(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= B] (?,1) 21. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,1) [B >= 1 + A] (?,1) 22. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) Signature: {(f0,27) ;(f17,27) ;(f25,27) ;(f28,27) ;(f30,27) ;(f44,27) ;(f55,27) ;(f64,27) ;(f66,27) ;(f68,27) ;(f93,27) ;(start,27)} Flow Graph: [0->{0,21},1->{2,5,19},2->{3,18},3->{4,17},4->{4,17},5->{6,15,16},6->{6,15,16},7->{8,13},8->{9,12},9->{10 ,11},10->{10,11},11->{9,12},12->{8,13},13->{7,14},14->{1,20},15->{2,5,19},16->{2,5,19},17->{3,18},18->{6,15 ,16},19->{7,14},20->{},21->{1,20},22->{0,21}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f0(A,1 + B,B1,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= B] (?,1) 1. f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f25(A,B,C,B1,C1,D1,E1,F1,1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1] (?,1) 2. f25(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + B >= 0 && G >= J && I >= 1 + J] (?,1) 3. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f30(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && F + J >= 2 + K] (?,1) 4. f30(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f30(A,B,C,D,E,F,G,H,I,J,K,G + L,I + -1*J + L,B1,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && H >= L] (?,1) 5. f25(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,B1,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + B >= 0 && G >= J && J >= I] (?,1) 6. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I + -1*O,J,K,L,M,N,B1,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [G + -1*J >= 0 && -1 + B >= 0 && O >= F && I >= 1 + O] (?,1) 7. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,B1,C1,D1,E1,F1,1,0,X,Y,Z,A1) [-1 + B >= 0 && G >= 1 + P] (?,1) 8. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + B >= 0 && P >= L] (?,1) 9. f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f68(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && F + L >= 2 + K] (?,1) 10. f68(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f68(A,B,C,D,E,F,G,H,I,J + Q,K,L,M,B1,O,P,Q,R,S,T,U,V,W,J,J + P,C1,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && H >= J] (?,1) 11. f68(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f66(A,B,C,D,E,F,G,H,I,J,2 + K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && J >= 1 + H] (?,1) 12. f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,J,K,F + L,M,N,O,P,Q,R,V,T,U,B1,C1,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + G + -1*L >= 0 && -1 + B >= 0 && -1*L + P >= 0 && 1 + K >= F + L] (?,1) 13. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,Q,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + G + -1*P >= 0 && -1 + B >= 0 && L >= 1 + P] (?,1) 14. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f17(A,-1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,B1) [-1 + B >= 0 && P >= G] (?,1) 15. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f25(A,B,C,D,E,F,G,H,I + O,F + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [G + -1*J >= 0 && -1 + B >= 0 && O >= F && O >= I] (?,1) 16. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f25(A,B,C,D,E,F,G,H,I + O,F + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [G + -1*J >= 0 && -1 + B >= 0 && F >= 1 + O] (?,1) 17. f30(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f28(A,B,C,D,E,F,G,H,I,J,2 + K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && L >= 1 + H] (?,1) 18. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,B1,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + I + -1*J >= 0 && G + -1*J >= 0 && -1 + B >= 0 && 1 + K >= F + J] (?,1) 19. f25(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,F,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + B >= 0 && J >= 1 + G] (?,1) 20. f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f93(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= B] (1,1) 21. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,1) [B >= 1 + A] (1,1) 22. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) Signature: {(f0,27) ;(f17,27) ;(f25,27) ;(f28,27) ;(f30,27) ;(f44,27) ;(f55,27) ;(f64,27) ;(f66,27) ;(f68,27) ;(f93,27) ;(start,27)} Flow Graph: [0->{0,21},1->{2,5,19},2->{3,18},3->{4,17},4->{4,17},5->{6,15,16},6->{6,15,16},7->{8,13},8->{9,12},9->{10 ,11},10->{10,11},11->{9,12},12->{8,13},13->{7,14},14->{1,20},15->{2,5,19},16->{2,5,19},17->{3,18},18->{6,15 ,16},19->{7,14},20->{},21->{1,20},22->{0,21}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] | +- p:[0] c: [0] | `- p:[1,14,13,7,19,15,5,16,6,18,2,17,3,4,12,8,11,9,10] c: [19] | +- p:[7,13,12,8,11,9,10] c: [9] | | | +- p:[10] c: [] | | | `- p:[7,13,12,8] c: [] | `- p:[2,15,5,16,6,18,17,3,4] c: [3] | +- p:[4] c: [] | `- p:[2,15,5,16,6,18] c: [] NO