YES(?,POLY) * Step 1: ArgumentFilter WORST_CASE(?,POLY) + 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) -> f16(1,X,Y,Z,A1,B1,C1,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [A = 1] (1,1) 1. f16(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f18(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [1 + -1*A >= 0 && -1 + A >= 0 && H >= I] (?,1) 2. f18(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f18(A,B,C,D,E,F,G,H,I,J,1 + K,2 + L,M,N,O,P,Q,R,S,T,U,V,W) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && J >= K] (?,1) 3. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f28(A,X,Y,Z,A1,B1,C1,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [0 >= A] (1,1) 4. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f28(A,X,Y,Z,A1,B1,C1,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [A >= 2] (1,1) 5. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f35(A,B,C,D,E,F,G,H,I,J,K,L,2 + H + -1*I,1,0,P,Q,R,S,T,U,V,W) [0 >= I && H >= I] (?,1) 6. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f35(A,B,C,D,E,F,G,H,I,J,K,L,2 + H + -1*I,1,0,P,Q,R,S,T,U,V,W) [I >= 2 && H >= I] (?,1) 7. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f35(A,B,C,D,E,F,G,H,1,J,K,L,1,1,0,P,Q,R,S,T,U,V,W) [H >= 1 && I = 1] (?,1) 8. f35(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && 1 + X >= Q] (?,1) 9. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [H + -1*I >= 0 && 0 >= Q && J >= K] (?,1) 10. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [H + -1*I >= 0 && Q >= 2 && J >= K] (?,1) 11. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,1 + K,X,M,N,O,P,1,Y,Z,A1,B1,V,W) [H + -1*I >= 0 && 0 >= K && J >= K && Q = 1] (?,1) 12. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,1 + K,X,M,N,O,P,1,Y,Z,A1,B1,V,W) [H + -1*I >= 0 && J >= K && K >= 2 && Q = 1] (?,1) 13. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,2,1,M,N,O,P,1,X,Y,Z,A1,V,W) [H + -1*I >= 0 && J >= 1 && K = 1 && Q = 1] (?,1) 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,1 + K,2 + J + -1*K,M,N,O,P,Q,X,Y,Z,A1,B1,W) [H + -1*I >= 0 && J + -1*K >= 0 && 0 >= K] (?,1) 15. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,1 + K,2 + J + -1*K,M,N,O,P,Q,X,Y,Z,A1,B1,W) [H + -1*I >= 0 && J + -1*K >= 0 && K >= 2] (?,1) 16. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f37(A,B,C,D,E,F,G,H,I,J,2,1,M,N,O,P,Q,X,Y,Z,A1,B1,W) [H + -1*I >= 0 && J + -1*K >= 0 && K = 1] (?,1) 17. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f35(A,B,C,D,N,F,G,H,I,J,K,L,M,X,Y,P,1 + Q,R,S,T,U,V,2 + W) [H + -1*I >= 0 && K >= 1 + J] (?,1) 18. f35(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f28(A,B,C,D,E,F,G,H,1 + I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && Q >= 2 + X] (?,1) 19. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f76(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [0 >= 2 + A && I >= 1 + H] (?,1) 20. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f76(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [A >= 0 && I >= 1 + H] (?,1) 21. f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f76(-1,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [I >= 1 + H && 1 + A = 0] (?,1) 22. f18(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f16(A,B,C,D,E,F,G,H,1 + I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && K >= 1 + J] (?,1) 23. f16(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) -> f28(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W) [1 + -1*A >= 0 && -1 + A >= 0 && I >= 1 + H] (?,1) Signature: {(f0,23);(f16,23);(f18,23);(f28,23);(f35,23);(f37,23);(f52,23);(f76,23)} Flow Graph: [0->{1,23},1->{2,22},2->{2,22},3->{5,6,7,19,20,21},4->{5,6,7,19,20,21},5->{8,18},6->{8,18},7->{8,18},8->{9 ,10,11,12,13,17},9->{14,15,16},10->{14,15,16},11->{9,10,11,12,13,17},12->{9,10,11,12,13,17},13->{9,10,11,12 ,13,17},14->{9,10,11,12,13,17},15->{9,10,11,12,13,17},16->{9,10,11,12,13,17},17->{8,18},18->{5,6,7,19,20,21} ,19->{},20->{},21->{},22->{1,23},23->{5,6,7,19,20,21}] + Applied Processor: ArgumentFilter [1,2,3,4,5,6,11,12,13,14,17,18,19,20,21,22] + Details: We remove following argument positions: [1,2,3,4,5,6,11,12,13,14,17,18,19,20,21,22]. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,H,I,J,K,P,Q) -> f16(1,H,I,J,K,P,Q) [A = 1] (1,1) 1. f16(A,H,I,J,K,P,Q) -> f18(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && H >= I] (?,1) 2. f18(A,H,I,J,K,P,Q) -> f18(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && J >= K] (?,1) 3. f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [0 >= A] (1,1) 4. f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [A >= 2] (1,1) 5. f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [0 >= I && H >= I] (?,1) 6. f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [I >= 2 && H >= I] (?,1) 7. f28(A,H,I,J,K,P,Q) -> f35(A,H,1,J,K,P,Q) [H >= 1 && I = 1] (?,1) 8. f35(A,H,I,J,K,P,Q) -> f37(A,H,I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && 1 + X >= Q] (?,1) 9. f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && 0 >= Q && J >= K] (?,1) 10. f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && Q >= 2 && J >= K] (?,1) 11. f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && 0 >= K && J >= K && Q = 1] (?,1) 12. f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && J >= K && K >= 2 && Q = 1] (?,1) 13. f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,1) [H + -1*I >= 0 && J >= 1 && K = 1 && Q = 1] (?,1) 14. f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && 0 >= K] (?,1) 15. f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K >= 2] (?,1) 16. f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K = 1] (?,1) 17. f37(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,1 + Q) [H + -1*I >= 0 && K >= 1 + J] (?,1) 18. f35(A,H,I,J,K,P,Q) -> f28(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && Q >= 2 + X] (?,1) 19. f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [0 >= 2 + A && I >= 1 + H] (?,1) 20. f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [A >= 0 && I >= 1 + H] (?,1) 21. f28(A,H,I,J,K,P,Q) -> f76(-1,H,I,J,K,P,Q) [I >= 1 + H && 1 + A = 0] (?,1) 22. f18(A,H,I,J,K,P,Q) -> f16(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && K >= 1 + J] (?,1) 23. f16(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && I >= 1 + H] (?,1) Signature: {(f0,23);(f16,23);(f18,23);(f28,23);(f35,23);(f37,23);(f52,23);(f76,23)} Flow Graph: [0->{1,23},1->{2,22},2->{2,22},3->{5,6,7,19,20,21},4->{5,6,7,19,20,21},5->{8,18},6->{8,18},7->{8,18},8->{9 ,10,11,12,13,17},9->{14,15,16},10->{14,15,16},11->{9,10,11,12,13,17},12->{9,10,11,12,13,17},13->{9,10,11,12 ,13,17},14->{9,10,11,12,13,17},15->{9,10,11,12,13,17},16->{9,10,11,12,13,17},17->{8,18},18->{5,6,7,19,20,21} ,19->{},20->{},21->{},22->{1,23},23->{5,6,7,19,20,21}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,19) ,(4,21) ,(11,9) ,(11,10) ,(11,12) ,(12,9) ,(12,10) ,(12,11) ,(12,13) ,(13,9) ,(13,10) ,(13,11) ,(13,13) ,(14,12) ,(15,11) ,(15,13) ,(16,11) ,(16,13) ,(23,5) ,(23,6) ,(23,7) ,(23,19) ,(23,21)] * Step 3: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,H,I,J,K,P,Q) -> f16(1,H,I,J,K,P,Q) [A = 1] (1,1) 1. f16(A,H,I,J,K,P,Q) -> f18(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && H >= I] (?,1) 2. f18(A,H,I,J,K,P,Q) -> f18(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && J >= K] (?,1) 3. f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [0 >= A] (1,1) 4. f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [A >= 2] (1,1) 5. f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [0 >= I && H >= I] (?,1) 6. f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [I >= 2 && H >= I] (?,1) 7. f28(A,H,I,J,K,P,Q) -> f35(A,H,1,J,K,P,Q) [H >= 1 && I = 1] (?,1) 8. f35(A,H,I,J,K,P,Q) -> f37(A,H,I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && 1 + X >= Q] (?,1) 9. f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && 0 >= Q && J >= K] (?,1) 10. f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && Q >= 2 && J >= K] (?,1) 11. f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && 0 >= K && J >= K && Q = 1] (?,1) 12. f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && J >= K && K >= 2 && Q = 1] (?,1) 13. f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,1) [H + -1*I >= 0 && J >= 1 && K = 1 && Q = 1] (?,1) 14. f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && 0 >= K] (?,1) 15. f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K >= 2] (?,1) 16. f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K = 1] (?,1) 17. f37(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,1 + Q) [H + -1*I >= 0 && K >= 1 + J] (?,1) 18. f35(A,H,I,J,K,P,Q) -> f28(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && Q >= 2 + X] (?,1) 19. f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [0 >= 2 + A && I >= 1 + H] (?,1) 20. f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [A >= 0 && I >= 1 + H] (?,1) 21. f28(A,H,I,J,K,P,Q) -> f76(-1,H,I,J,K,P,Q) [I >= 1 + H && 1 + A = 0] (?,1) 22. f18(A,H,I,J,K,P,Q) -> f16(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && K >= 1 + J] (?,1) 23. f16(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && I >= 1 + H] (?,1) Signature: {(f0,23);(f16,23);(f18,23);(f28,23);(f35,23);(f37,23);(f52,23);(f76,23)} Flow Graph: [0->{1,23},1->{2,22},2->{2,22},3->{5,6,7,19,20,21},4->{5,6,7,20},5->{8,18},6->{8,18},7->{8,18},8->{9,10,11 ,12,13,17},9->{14,15,16},10->{14,15,16},11->{11,13,17},12->{12,17},13->{12,17},14->{9,10,11,13,17},15->{9,10 ,12,17},16->{9,10,12,17},17->{8,18},18->{5,6,7,19,20,21},19->{},20->{},21->{},22->{1,23},23->{20}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: f0(A,H,I,J,K,P,Q) -> f16(1,H,I,J,K,P,Q) [A = 1] f16(A,H,I,J,K,P,Q) -> f18(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && H >= I] f18(A,H,I,J,K,P,Q) -> f18(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && J >= K] f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [0 >= A] f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [A >= 2] f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [0 >= I && H >= I] f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [I >= 2 && H >= I] f28(A,H,I,J,K,P,Q) -> f35(A,H,1,J,K,P,Q) [H >= 1 && I = 1] f35(A,H,I,J,K,P,Q) -> f37(A,H,I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && 1 + X >= Q] f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && 0 >= Q && J >= K] f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && Q >= 2 && J >= K] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && 0 >= K && J >= K && Q = 1] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && J >= K && K >= 2 && Q = 1] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,1) [H + -1*I >= 0 && J >= 1 && K = 1 && Q = 1] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && 0 >= K] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K >= 2] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K = 1] f37(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,1 + Q) [H + -1*I >= 0 && K >= 1 + J] f35(A,H,I,J,K,P,Q) -> f28(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && Q >= 2 + X] f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [0 >= 2 + A && I >= 1 + H] f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [A >= 0 && I >= 1 + H] f28(A,H,I,J,K,P,Q) -> f76(-1,H,I,J,K,P,Q) [I >= 1 + H && 1 + A = 0] f18(A,H,I,J,K,P,Q) -> f16(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && K >= 1 + J] f16(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && I >= 1 + H] Signature: {(f0,23);(f16,23);(f18,23);(f28,23);(f35,23);(f37,23);(f52,23);(f76,23)} Rule Graph: [0->{1,23},1->{2,22},2->{2,22},3->{5,6,7,19,20,21},4->{5,6,7,20},5->{8,18},6->{8,18},7->{8,18},8->{9,10,11 ,12,13,17},9->{14,15,16},10->{14,15,16},11->{11,13,17},12->{12,17},13->{12,17},14->{9,10,11,13,17},15->{9,10 ,12,17},16->{9,10,12,17},17->{8,18},18->{5,6,7,19,20,21},19->{},20->{},21->{},22->{1,23},23->{20}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: f0(A,H,I,J,K,P,Q) -> f16(1,H,I,J,K,P,Q) [A = 1] f16(A,H,I,J,K,P,Q) -> f18(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && H >= I] f18(A,H,I,J,K,P,Q) -> f18(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && J >= K] f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [0 >= A] f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [A >= 2] f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [0 >= I && H >= I] f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [I >= 2 && H >= I] f28(A,H,I,J,K,P,Q) -> f35(A,H,1,J,K,P,Q) [H >= 1 && I = 1] f35(A,H,I,J,K,P,Q) -> f37(A,H,I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && 1 + X >= Q] f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && 0 >= Q && J >= K] f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && Q >= 2 && J >= K] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && 0 >= K && J >= K && Q = 1] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && J >= K && K >= 2 && Q = 1] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,1) [H + -1*I >= 0 && J >= 1 && K = 1 && Q = 1] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && 0 >= K] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K >= 2] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K = 1] f37(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,1 + Q) [H + -1*I >= 0 && K >= 1 + J] f35(A,H,I,J,K,P,Q) -> f28(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && Q >= 2 + X] f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [0 >= 2 + A && I >= 1 + H] f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [A >= 0 && I >= 1 + H] f28(A,H,I,J,K,P,Q) -> f76(-1,H,I,J,K,P,Q) [I >= 1 + H && 1 + A = 0] f18(A,H,I,J,K,P,Q) -> f16(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && K >= 1 + J] f16(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && I >= 1 + H] f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True Signature: {(exitus616,7);(f0,23);(f16,23);(f18,23);(f28,23);(f35,23);(f37,23);(f52,23);(f76,23)} Rule Graph: [0->{1,23},1->{2,22},2->{2,22},3->{5,6,7,19,20,21},4->{5,6,7,20},5->{8,18},6->{8,18},7->{8,18},8->{9,10,11 ,12,13,17},9->{14,15,16},10->{14,15,16},11->{11,13,17},12->{12,17},13->{12,17},14->{9,10,11,13,17},15->{9,10 ,12,17},16->{9,10,12,17},17->{8,18},18->{5,6,7,19,20,21},19->{25,28},20->{26,29,30},21->{24,27},22->{1,23} ,23->{20}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] | +- p:[5,18,6,7,17,8,11,14,9,15,10,16,12,13] c: [5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[1,22,2] c: [1,2,22] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: f0(A,H,I,J,K,P,Q) -> f16(1,H,I,J,K,P,Q) [A = 1] f16(A,H,I,J,K,P,Q) -> f18(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && H >= I] f18(A,H,I,J,K,P,Q) -> f18(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && J >= K] f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [0 >= A] f0(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [A >= 2] f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [0 >= I && H >= I] f28(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,Q) [I >= 2 && H >= I] f28(A,H,I,J,K,P,Q) -> f35(A,H,1,J,K,P,Q) [H >= 1 && I = 1] f35(A,H,I,J,K,P,Q) -> f37(A,H,I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && 1 + X >= Q] f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && 0 >= Q && J >= K] f37(A,H,I,J,K,P,Q) -> f52(A,H,I,J,K,P,Q) [H + -1*I >= 0 && Q >= 2 && J >= K] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && 0 >= K && J >= K && Q = 1] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,1) [H + -1*I >= 0 && J >= K && K >= 2 && Q = 1] f37(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,1) [H + -1*I >= 0 && J >= 1 && K = 1 && Q = 1] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && 0 >= K] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,1 + K,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K >= 2] f52(A,H,I,J,K,P,Q) -> f37(A,H,I,J,2,P,Q) [H + -1*I >= 0 && J + -1*K >= 0 && K = 1] f37(A,H,I,J,K,P,Q) -> f35(A,H,I,J,K,P,1 + Q) [H + -1*I >= 0 && K >= 1 + J] f35(A,H,I,J,K,P,Q) -> f28(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && P >= 2*X && 3*X >= 1 + P && Q >= 2 + X] f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [0 >= 2 + A && I >= 1 + H] f28(A,H,I,J,K,P,Q) -> f76(A,H,I,J,K,P,Q) [A >= 0 && I >= 1 + H] f28(A,H,I,J,K,P,Q) -> f76(-1,H,I,J,K,P,Q) [I >= 1 + H && 1 + A = 0] f18(A,H,I,J,K,P,Q) -> f16(A,H,1 + I,J,K,P,Q) [H + -1*I >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && K >= 1 + J] f16(A,H,I,J,K,P,Q) -> f28(A,H,I,J,K,P,Q) [1 + -1*A >= 0 && -1 + A >= 0 && I >= 1 + H] f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True f76(A,H,I,J,K,P,Q) -> exitus616(A,H,I,J,K,P,Q) True Signature: {(exitus616,7);(f0,23);(f16,23);(f18,23);(f28,23);(f35,23);(f37,23);(f52,23);(f76,23)} Rule Graph: [0->{1,23},1->{2,22},2->{2,22},3->{5,6,7,19,20,21},4->{5,6,7,20},5->{8,18},6->{8,18},7->{8,18},8->{9,10,11 ,12,13,17},9->{14,15,16},10->{14,15,16},11->{11,13,17},12->{12,17},13->{12,17},14->{9,10,11,13,17},15->{9,10 ,12,17},16->{9,10,12,17},17->{8,18},18->{5,6,7,19,20,21},19->{25,28},20->{26,29,30},21->{24,27},22->{1,23} ,23->{20}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] | +- p:[5,18,6,7,17,8,11,14,9,15,10,16,12,13] c: [5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[1,22,2] c: [1,2,22]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,H,I,J,K,P,Q,0.0,0.1] f0 ~> f16 [A <= K, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f16 ~> f18 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f18 ~> f18 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= Q] f0 ~> f28 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f0 ~> f28 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f35 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f35 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f35 [A <= A, H <= H, I <= K, J <= J, K <= K, P <= P, Q <= Q] f35 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f37 ~> f52 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f37 ~> f52 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f37 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= K] f37 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= K] f37 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= 2*K, P <= P, Q <= K] f52 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= Q] f52 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= Q] f52 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= 2*K, P <= P, Q <= Q] f37 ~> f35 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= K + Q] f35 ~> f28 [A <= A, H <= H, I <= K + I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f76 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f76 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f76 [A <= K, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f18 ~> f16 [A <= A, H <= H, I <= K + I, J <= J, K <= K, P <= P, Q <= Q] f16 ~> f28 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f76 ~> exitus616 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] + Loop: [0.0 <= K + H + I + J + K + P + Q] f28 ~> f35 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f35 ~> f28 [A <= A, H <= H, I <= K + I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f35 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f28 ~> f35 [A <= A, H <= H, I <= K, J <= J, K <= K, P <= P, Q <= Q] f37 ~> f35 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= K + Q] f35 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f37 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= K] f52 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= Q] f37 ~> f52 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f52 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= Q] f37 ~> f52 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f52 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= 2*K, P <= P, Q <= Q] f37 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= K] f37 ~> f37 [A <= A, H <= H, I <= I, J <= J, K <= 2*K, P <= P, Q <= K] + Loop: [0.1 <= H + I + J + K] f16 ~> f18 [A <= A, H <= H, I <= I, J <= J, K <= K, P <= P, Q <= Q] f18 ~> f16 [A <= A, H <= H, I <= K + I, J <= J, K <= K, P <= P, Q <= Q] f18 ~> f18 [A <= A, H <= H, I <= I, J <= J, K <= K + K, P <= P, Q <= Q] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,H,I,J,K,P,Q,0.0,0.1] f0 ~> f16 [K ~=> A] f16 ~> f18 [] f18 ~> f18 [K ~+> K,K ~+> K] f0 ~> f28 [] f0 ~> f28 [] f28 ~> f35 [] f28 ~> f35 [] f28 ~> f35 [K ~=> I] f35 ~> f37 [] f37 ~> f52 [] f37 ~> f52 [] f37 ~> f37 [K ~=> Q,K ~+> K,K ~+> K] f37 ~> f37 [K ~=> Q,K ~+> K,K ~+> K] f37 ~> f37 [K ~=> K,K ~=> Q] f52 ~> f37 [K ~+> K,K ~+> K] f52 ~> f37 [K ~+> K,K ~+> K] f52 ~> f37 [K ~=> K] f37 ~> f35 [Q ~+> Q,K ~+> Q] f35 ~> f28 [I ~+> I,K ~+> I] f28 ~> f76 [] f28 ~> f76 [] f28 ~> f76 [K ~=> A] f18 ~> f16 [I ~+> I,K ~+> I] f16 ~> f28 [] f76 ~> exitus616 [] f76 ~> exitus616 [] f76 ~> exitus616 [] f76 ~> exitus616 [] f76 ~> exitus616 [] f76 ~> exitus616 [] f76 ~> exitus616 [] + Loop: [H ~+> 0.0,I ~+> 0.0,J ~+> 0.0,K ~+> 0.0,P ~+> 0.0,Q ~+> 0.0,K ~+> 0.0] f28 ~> f35 [] f35 ~> f28 [I ~+> I,K ~+> I] f28 ~> f35 [] f28 ~> f35 [K ~=> I] f37 ~> f35 [Q ~+> Q,K ~+> Q] f35 ~> f37 [] f37 ~> f37 [K ~=> Q,K ~+> K,K ~+> K] f52 ~> f37 [K ~+> K,K ~+> K] f37 ~> f52 [] f52 ~> f37 [K ~+> K,K ~+> K] f37 ~> f52 [] f52 ~> f37 [K ~=> K] f37 ~> f37 [K ~=> Q,K ~+> K,K ~+> K] f37 ~> f37 [K ~=> K,K ~=> Q] + Loop: [H ~+> 0.1,I ~+> 0.1,J ~+> 0.1,K ~+> 0.1] f16 ~> f18 [] f18 ~> f16 [I ~+> I,K ~+> I] f18 ~> f18 [K ~+> K,K ~+> K] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A ,K ~=> K ,H ~+> 0.0 ,H ~+> 0.1 ,H ~+> tick ,I ~+> I ,I ~+> 0.0 ,I ~+> 0.1 ,I ~+> tick ,J ~+> 0.0 ,J ~+> 0.1 ,J ~+> tick ,K ~+> K ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,P ~+> 0.0 ,P ~+> tick ,Q ~+> Q ,Q ~+> 0.0 ,Q ~+> tick ,tick ~+> tick ,K ~+> I ,K ~+> K ,K ~+> Q ,K ~+> 0.0 ,K ~+> tick ,H ~*> I ,H ~*> K ,H ~*> Q ,H ~*> 0.0 ,H ~*> tick ,I ~*> I ,I ~*> K ,I ~*> Q ,I ~*> 0.0 ,I ~*> tick ,J ~*> I ,J ~*> K ,J ~*> Q ,J ~*> 0.0 ,J ~*> tick ,K ~*> I ,K ~*> K ,K ~*> Q ,K ~*> 0.0 ,K ~*> tick ,P ~*> I ,P ~*> K ,P ~*> Q ,Q ~*> I ,Q ~*> K ,Q ~*> Q ,K ~*> I ,K ~*> K ,K ~*> Q ,K ~*> 0.0 ,K ~*> tick] + f28> [K ~=> K ,H ~+> 0.0 ,H ~+> tick ,I ~+> I ,I ~+> 0.0 ,I ~+> tick ,J ~+> 0.0 ,J ~+> tick ,K ~+> K ,K ~+> 0.0 ,K ~+> tick ,P ~+> 0.0 ,P ~+> tick ,Q ~+> Q ,Q ~+> 0.0 ,Q ~+> tick ,tick ~+> tick ,K ~+> I ,K ~+> K ,K ~+> Q ,K ~+> 0.0 ,K ~+> tick ,H ~*> I ,H ~*> K ,H ~*> Q ,I ~*> I ,I ~*> K ,I ~*> Q ,J ~*> I ,J ~*> K ,J ~*> Q ,K ~*> I ,K ~*> K ,K ~*> Q ,P ~*> I ,P ~*> K ,P ~*> Q ,Q ~*> I ,Q ~*> K ,Q ~*> Q ,K ~*> I ,K ~*> K ,K ~*> Q] + f16> [H ~+> 0.1 ,H ~+> tick ,I ~+> I ,I ~+> 0.1 ,I ~+> tick ,J ~+> 0.1 ,J ~+> tick ,K ~+> K ,K ~+> 0.1 ,K ~+> tick ,tick ~+> tick ,K ~+> I ,K ~+> K ,H ~*> I ,H ~*> K ,I ~*> I ,I ~*> K ,J ~*> I ,J ~*> K ,K ~*> I ,K ~*> K ,K ~*> I ,K ~*> K] YES(?,POLY)