YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (?,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7,8,9},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,8),(4,9)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (?,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = 1 + x1 + -1*x11 p(f2) = 1 + x1 + -1*x11 p(f26) = 1 + x1 + -1*x11 p(f32) = 1 + x1 + -1*x11 p(f5) = 1 + x1 + -1*x11 p(f52) = 1 + x1 + -1*x11 p(f55) = 1 + x1 + -1*x11 p(f62) = 1 + x1 + -1*x11 p(f9) = 1 + x1 + -1*x11 Following rules are strictly oriented: [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K > A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = 1 + x1 + -1*x11 p(f2) = 1 + x1 + -1*x11 p(f26) = 1 + x1 + -1*x11 p(f32) = 1 + x1 + -1*x11 p(f5) = 1 + x1 + -1*x11 p(f52) = 1 + x1 + -1*x11 p(f55) = 1 + x1 + -1*x11 p(f62) = x1 + -1*x11 p(f9) = 1 + x1 + -1*x11 Following rules are strictly oriented: [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K > A + -1*K = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*K >= A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = 1 + x1 + -1*x11 p(f2) = 1 + x1 + -1*x11 p(f26) = 1 + x1 + -1*x11 p(f32) = 1 + x1 + -1*x11 p(f5) = 1 + x1 + -1*x11 p(f52) = 1 + x1 + -1*x11 p(f55) = x1 + -1*x11 p(f62) = x1 + -1*x11 p(f9) = 1 + x1 + -1*x11 Following rules are strictly oriented: [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K > A + -1*K = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*K >= 1 + A + -1*K = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*K >= A + -1*K = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*K >= A + -1*K = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x1 + -1*x2 p(f2) = x1 + -1*x2 p(f26) = x1 + -1*x2 p(f32) = x1 + -1*x2 p(f5) = x1 + -1*x2 p(f52) = x1 + -1*x2 p(f55) = x1 + -1*x2 p(f62) = x1 + -1*x2 p(f9) = x1 + -1*x2 Following rules are strictly oriented: [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B > -1 + A + -1*B = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= -1 + A + -1*B = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x1 + -1*x2 p(f2) = x1 + -1*x2 p(f26) = x1 + -1*x2 p(f32) = x1 + -1*x2 p(f5) = x1 + -1*x2 p(f52) = -1 + x1 + -1*x2 p(f55) = -1 + x1 + -1*x2 p(f62) = -1 + x1 + -1*x2 p(f9) = x1 + -1*x2 Following rules are strictly oriented: [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B > -1 + A + -1*B = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B > -1 + A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= -1 + A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 8: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (A + B,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 9: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (1 + 2*A + 2*B,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (A + B,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x1 + -1*x2 p(f2) = x1 + -1*x2 p(f26) = x1 + -1*x2 p(f32) = x1 + -1*x2 p(f5) = x1 + -1*x2 p(f52) = -1 + x1 + -1*x2 p(f55) = -1 + x1 + -1*x2 p(f62) = -1 + x1 + -1*x2 p(f9) = x1 + -1*x2 Following rules are strictly oriented: [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B > -1 + A + -1*B = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B > -1 + A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B > -1 + A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = A + -1*B >= A + -1*B = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = -1 + A + -1*B >= -1 + A + -1*B = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 10: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (1 + 2*A + 2*B,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (A + B,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = 1 + x1 + -1*x4 p(f2) = 1 + x1 + -1*x4 p(f26) = 1 + x1 + -1*x4 p(f32) = 1 + x1 + -1*x4 p(f5) = 1 + x1 + -1*x4 p(f52) = 1 + x1 + -1*x4 p(f55) = 1 + x1 + -1*x4 p(f62) = 1 + x1 + -1*x4 p(f9) = 1 + x1 + -1*x4 Following rules are strictly oriented: [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D > A + -1*D = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= A + -1*D = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 11: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (1 + 2*A + 2*B,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (A + B,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (1 + A + D,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = 1 + x1 + -1*x4 p(f2) = 1 + x1 + -1*x4 p(f26) = 1 + x1 + -1*x4 p(f32) = 1 + x1 + -1*x4 p(f5) = 1 + x1 + -1*x4 p(f52) = 1 + x1 + -1*x4 p(f55) = 1 + x1 + -1*x4 p(f62) = 1 + x1 + -1*x4 p(f9) = 1 + x1 + -1*x4 Following rules are strictly oriented: [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D > A + -1*D = f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D > A + -1*D = f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) Following rules are weakly oriented: [A >= 2] ==> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] ==> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] ==> f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 ==> && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) = 1 + A + -1*D >= 1 + A + -1*D = f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) * Step 12: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (1 + 2*A + 2*B,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (A + B,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (1 + A + D,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (1 + A + D,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (?,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 13: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A] (1,1) 2. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && S >= 1] (1,1) 3. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (1,1) 4. f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-2 + A >= 0 && A >= 1 + B] (1 + 2*A + 2*B,1) 5. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,0,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,0) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (A + B,1) 6. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,S,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (1 + A + D,1) 7. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f9(A,B,C,1 + D,C,S,S,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (1 + A + D,1) 8. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (2 + 2*A + 2*D,1) 9. f9(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (2 + 2*A + 2*D,1) 10. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (4 + 4*A + 4*D,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 11. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,-1*S,T,S,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 12. f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,K,L,S,T,T,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A] 13. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f5(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (A + B,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && K >= 1 + A] 14. f52(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= K] 15. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f62(A,B,C,D,E,F,G,H,I,J,K,S,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && J >= T*U && T + T*U >= 1 + J && T >= S && J >= U*V && U*V + V >= 1 + J && S >= V && D >= 1 + A] 16. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f52(A,B,C,D,E,F,G,H,I,J,1 + K,L,M,N,O,P,Q,R) [-3 + D >= 0 (1 + A + K,1) && -2 + -1*B + D >= 0 && -1 + D + -1*K >= 0 && -5 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + A + -1*B >= 0 && A + -1*K >= 0 && -2 + A >= 0 && D >= 1 + A] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{},4->{5,6,7},5->{1,2,3,4},6->{5,6,7,8,9},7->{5,6,7,8,9},8->{10},9->{10} ,10->{11,12},11->{13,14},12->{13,14},13->{1,2,3,4},14->{15},15->{16},16->{13,14}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))