YES(?,O(n^1)) * Step 1: ArgumentFilter 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 && 0 >= 1 + U && 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 && U >= 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 && 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: ArgumentFilter [4,5,6,7,8,9,11,12,13,14,15,16,17] + Details: We remove following argument positions: [4,5,6,7,8,9,11,12,13,14,15,16,17]. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,K) -> f5(A,B,C,D,K) [A >= 2] (1,1) 1. f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A] (?,1) 2. f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && S >= 1] (?,1) 3. f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (?,1) 4. f5(A,B,C,D,K) -> f9(A,B,0,D,K) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,K) -> f5(A,1 + B,0,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,K) -> f9(A,B,S,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,K) -> f9(A,B,C,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,K) -> f32(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,K) [-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 && 0 >= 1 + U && D >= 1 + A] 12. f32(A,B,C,D,K) -> f52(A,B,C,D,K) [-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 && U >= 0 && D >= 1 + A] 13. f52(A,B,C,D,K) -> f5(A,1 + B,C,D,K) [-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,K) -> f55(A,B,C,D,K) [-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,K) -> f62(A,B,C,D,K) [-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] 16. f62(A,B,C,D,K) -> f52(A,B,C,D,1 + K) [-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 3: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,K) -> f5(A,B,C,D,K) [A >= 2] (1,1) 1. f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A] (?,1) 2. f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && S >= 1] (?,1) 3. f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && 0 >= 1 + S] (?,1) 4. f5(A,B,C,D,K) -> f9(A,B,0,D,K) [-2 + A >= 0 && A >= 1 + B] (?,1) 5. f9(A,B,C,D,K) -> f5(A,1 + B,0,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] (?,1) 6. f9(A,B,C,D,K) -> f9(A,B,S,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] (?,1) 7. f9(A,B,C,D,K) -> f9(A,B,C,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] (?,1) 8. f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] (?,1) 9. f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] (?,1) 10. f26(A,B,C,D,K) -> f32(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,K) [-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 && 0 >= 1 + U && D >= 1 + A] 12. f32(A,B,C,D,K) -> f52(A,B,C,D,K) [-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 && U >= 0 && D >= 1 + A] 13. f52(A,B,C,D,K) -> f5(A,1 + B,C,D,K) [-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,K) -> f55(A,B,C,D,K) [-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,K) -> f62(A,B,C,D,K) [-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] 16. f62(A,B,C,D,K) -> f52(A,B,C,D,1 + K) [-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: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B,C,D,K) -> f5(A,B,C,D,K) [A >= 2] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && S >= 1] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && 0 >= 1 + S] f5(A,B,C,D,K) -> f9(A,B,0,D,K) [-2 + A >= 0 && A >= 1 + B] f9(A,B,C,D,K) -> f5(A,1 + B,0,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] f9(A,B,C,D,K) -> f9(A,B,S,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] f9(A,B,C,D,K) -> f9(A,B,C,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] f26(A,B,C,D,K) -> f32(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,K) [-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 && 0 >= 1 + U && D >= 1 + A] f32(A,B,C,D,K) -> f52(A,B,C,D,K) [-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 && U >= 0 && D >= 1 + A] f52(A,B,C,D,K) -> f5(A,1 + B,C,D,K) [-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,K) -> f55(A,B,C,D,K) [-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] f55(A,B,C,D,K) -> f62(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,1 + K) [-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] Signature: {(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Rule 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: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B,C,D,K) -> f5(A,B,C,D,K) [A >= 2] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && S >= 1] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && 0 >= 1 + S] f5(A,B,C,D,K) -> f9(A,B,0,D,K) [-2 + A >= 0 && A >= 1 + B] f9(A,B,C,D,K) -> f5(A,1 + B,0,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] f9(A,B,C,D,K) -> f9(A,B,S,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] f9(A,B,C,D,K) -> f9(A,B,C,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] f26(A,B,C,D,K) -> f32(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,K) [-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 && 0 >= 1 + U && D >= 1 + A] f32(A,B,C,D,K) -> f52(A,B,C,D,K) [-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 && U >= 0 && D >= 1 + A] f52(A,B,C,D,K) -> f5(A,1 + B,C,D,K) [-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,K) -> f55(A,B,C,D,K) [-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] f55(A,B,C,D,K) -> f62(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,1 + K) [-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] f1(A,B,C,D,K) -> exitus616(A,B,C,D,K) True f1(A,B,C,D,K) -> exitus616(A,B,C,D,K) True f1(A,B,C,D,K) -> exitus616(A,B,C,D,K) True Signature: {(exitus616,5);(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Rule Graph: [0->{1,2,3,4},1->{19},2->{18},3->{17},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: 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] | `- p:[4,5,6,7,13,11,10,8,9,12,16,15,14] c: [4,5,6,7,8,9,10,11,12,13,14,15,16] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f2(A,B,C,D,K) -> f5(A,B,C,D,K) [A >= 2] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && S >= 1] f5(A,B,C,D,K) -> f1(A,B,C,D,K) [-2 + A >= 0 && B >= A && 0 >= 1 + S] f5(A,B,C,D,K) -> f9(A,B,0,D,K) [-2 + A >= 0 && A >= 1 + B] f9(A,B,C,D,K) -> f5(A,1 + B,0,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && D >= 1 + A && C = 0] f9(A,B,C,D,K) -> f9(A,B,S,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && S >= C && A >= D] f9(A,B,C,D,K) -> f9(A,B,C,1 + D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + S && A >= D] f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && C >= 1 && D >= 1 + A] f9(A,B,C,D,K) -> f26(A,B,C,D,K) [-1 + A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + C && D >= 1 + A] f26(A,B,C,D,K) -> f32(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,K) [-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 && 0 >= 1 + U && D >= 1 + A] f32(A,B,C,D,K) -> f52(A,B,C,D,K) [-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 && U >= 0 && D >= 1 + A] f52(A,B,C,D,K) -> f5(A,1 + B,C,D,K) [-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,K) -> f55(A,B,C,D,K) [-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] f55(A,B,C,D,K) -> f62(A,B,C,D,K) [-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,K) -> f52(A,B,C,D,1 + K) [-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] f1(A,B,C,D,K) -> exitus616(A,B,C,D,K) True f1(A,B,C,D,K) -> exitus616(A,B,C,D,K) True f1(A,B,C,D,K) -> exitus616(A,B,C,D,K) True Signature: {(exitus616,5);(f1,18);(f2,18);(f26,18);(f32,18);(f5,18);(f52,18);(f55,18);(f62,18);(f9,18)} Rule Graph: [0->{1,2,3,4},1->{19},2->{18},3->{17},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}] ,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] | `- p:[4,5,6,7,13,11,10,8,9,12,16,15,14] c: [4,5,6,7,8,9,10,11,12,13,14,15,16]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,K,0.0] f2 ~> f5 [A <= A, B <= B, C <= C, D <= D, K <= K] f5 ~> f1 [A <= A, B <= B, C <= C, D <= D, K <= K] f5 ~> f1 [A <= A, B <= B, C <= C, D <= D, K <= K] f5 ~> f1 [A <= A, B <= B, C <= C, D <= D, K <= K] f5 ~> f9 [A <= A, B <= B, C <= 0*K, D <= D, K <= K] f9 ~> f5 [A <= A, B <= A + B, C <= 0*K, D <= D, K <= K] f9 ~> f9 [A <= A, B <= B, C <= unknown, D <= A + D, K <= K] f9 ~> f9 [A <= A, B <= B, C <= C, D <= A + D, K <= K] f9 ~> f26 [A <= A, B <= B, C <= C, D <= D, K <= K] f9 ~> f26 [A <= A, B <= B, C <= C, D <= D, K <= K] f26 ~> f32 [A <= A, B <= B, C <= C, D <= D, K <= K] f32 ~> f52 [A <= A, B <= B, C <= C, D <= D, K <= K] f32 ~> f52 [A <= A, B <= B, C <= C, D <= D, K <= K] f52 ~> f5 [A <= A, B <= B + K, C <= C, D <= D, K <= K] f52 ~> f55 [A <= A, B <= B, C <= C, D <= D, K <= K] f55 ~> f62 [A <= A, B <= B, C <= C, D <= D, K <= K] f62 ~> f52 [A <= A, B <= B, C <= C, D <= D, K <= D + K] f1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, K <= K] f1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, K <= K] f1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, K <= K] + Loop: [0.0 <= A + B + D + K] f5 ~> f9 [A <= A, B <= B, C <= 0*K, D <= D, K <= K] f9 ~> f5 [A <= A, B <= A + B, C <= 0*K, D <= D, K <= K] f9 ~> f9 [A <= A, B <= B, C <= unknown, D <= A + D, K <= K] f9 ~> f9 [A <= A, B <= B, C <= C, D <= A + D, K <= K] f52 ~> f5 [A <= A, B <= B + K, C <= C, D <= D, K <= K] f32 ~> f52 [A <= A, B <= B, C <= C, D <= D, K <= K] f26 ~> f32 [A <= A, B <= B, C <= C, D <= D, K <= K] f9 ~> f26 [A <= A, B <= B, C <= C, D <= D, K <= K] f9 ~> f26 [A <= A, B <= B, C <= C, D <= D, K <= K] f32 ~> f52 [A <= A, B <= B, C <= C, D <= D, K <= K] f62 ~> f52 [A <= A, B <= B, C <= C, D <= D, K <= D + K] f55 ~> f62 [A <= A, B <= B, C <= C, D <= D, K <= K] f52 ~> f55 [A <= A, B <= B, C <= C, D <= D, K <= K] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,K,0.0] f2 ~> f5 [] f5 ~> f1 [] f5 ~> f1 [] f5 ~> f1 [] f5 ~> f9 [K ~=> C] f9 ~> f5 [K ~=> C,A ~+> B,B ~+> B] f9 ~> f9 [huge ~=> C,A ~+> D,D ~+> D] f9 ~> f9 [A ~+> D,D ~+> D] f9 ~> f26 [] f9 ~> f26 [] f26 ~> f32 [] f32 ~> f52 [] f32 ~> f52 [] f52 ~> f5 [B ~+> B,K ~+> B] f52 ~> f55 [] f55 ~> f62 [] f62 ~> f52 [D ~+> K,K ~+> K] f1 ~> exitus616 [] f1 ~> exitus616 [] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,D ~+> 0.0,K ~+> 0.0] f5 ~> f9 [K ~=> C] f9 ~> f5 [K ~=> C,A ~+> B,B ~+> B] f9 ~> f9 [huge ~=> C,A ~+> D,D ~+> D] f9 ~> f9 [A ~+> D,D ~+> D] f52 ~> f5 [B ~+> B,K ~+> B] f32 ~> f52 [] f26 ~> f32 [] f9 ~> f26 [] f9 ~> f26 [] f32 ~> f52 [] f62 ~> f52 [D ~+> K,K ~+> K] f55 ~> f62 [] f52 ~> f55 [] + Applied Processor: Lare + Details: f2 ~> exitus616 [K ~=> C ,huge ~=> C ,A ~+> B ,A ~+> D ,A ~+> K ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,D ~+> B ,D ~+> D ,D ~+> K ,D ~+> 0.0 ,D ~+> tick ,K ~+> B ,K ~+> K ,K ~+> 0.0 ,K ~+> tick ,tick ~+> tick ,A ~*> B ,A ~*> D ,A ~*> K ,B ~*> B ,B ~*> D ,B ~*> K ,D ~*> B ,D ~*> D ,D ~*> K ,K ~*> B ,K ~*> D ,K ~*> K] + f5> [K ~=> C ,huge ~=> C ,A ~+> B ,A ~+> D ,A ~+> K ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,D ~+> B ,D ~+> D ,D ~+> K ,D ~+> 0.0 ,D ~+> tick ,K ~+> B ,K ~+> K ,K ~+> 0.0 ,K ~+> tick ,tick ~+> tick ,A ~*> B ,A ~*> D ,A ~*> K ,B ~*> B ,B ~*> D ,B ~*> K ,D ~*> B ,D ~*> D ,D ~*> K ,K ~*> B ,K ~*> D ,K ~*> K] YES(?,O(n^1))