YES * Step 1: TrivialSCCs YES + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + 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 && 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: UnsatPaths + Details: We remove following edges from the transition graph: [(4,8),(4,9)] * Step 3: Looptree YES + 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 && 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},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: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[4,5,6,7,13,11,10,8,9,12,16,15,14] c: [16] | `- p:[4,5,6,7,13,11,10,8,9,12] c: [13] | `- p:[4,5,6,7] c: [7] | `- p:[4,5,6] c: [6] | `- p:[4,5] c: [5] YES