YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f73(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. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f73(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) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 4. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(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) 5. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 6. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 7. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f29(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) 8. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f29(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) 9. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f34(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] 10. f34(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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] 11. f34(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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] 12. f53(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(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] 13. f53(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] 14. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f61(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] 15. f61(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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: {(f0,18);(f10,18);(f13,18);(f29,18);(f34,18);(f53,18);(f55,18);(f61,18);(f73,18)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{4,5,6,7,8},4->{1,2,3},5->{4,5,6,7,8},6->{4,5,6,7,8},7->{9},8->{9},9->{10,11} ,10->{12,13},11->{12,13},12->{1,2,3},13->{14},14->{15},15->{12,13}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f73(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. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f73(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) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 4. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(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) 5. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 6. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 7. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f29(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) 8. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f29(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) 9. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f34(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] 10. f34(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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] 11. f34(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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] 12. f53(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(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] 13. f53(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] 14. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f61(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] 15. f61(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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: {(f0,18);(f10,18);(f13,18);(f29,18);(f34,18);(f53,18);(f55,18);(f61,18);(f73,18)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{4,5,6,7,8},4->{1,2,3},5->{4,5,6,7,8},6->{4,5,6,7,8},7->{9},8->{9},9->{10,11} ,10->{12,13},11->{12,13},12->{1,2,3},13->{14},14->{15},15->{12,13}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,7),(3,8)] * Step 3: Looptree YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) [A >= 2] (1,1) 1. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f73(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. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f73(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) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 4. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(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) 5. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 6. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f13(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) 7. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f29(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) 8. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f29(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) 9. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f34(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] 10. f34(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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] 11. f34(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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] 12. f53(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f10(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] 13. f53(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] 14. f55(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f61(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] 15. f61(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) -> f53(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: {(f0,18);(f10,18);(f13,18);(f29,18);(f34,18);(f53,18);(f55,18);(f61,18);(f73,18)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{4,5,6},4->{1,2,3},5->{4,5,6,7,8},6->{4,5,6,7,8},7->{9},8->{9},9->{10,11} ,10->{12,13},11->{12,13},12->{1,2,3},13->{14},14->{15},15->{12,13}] + 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] | `- p:[3,4,5,6,12,10,9,7,8,11,15,14,13] c: [15] | `- p:[3,4,5,6,12,10,9,7,8,11] c: [12] | `- p:[3,4,5,6] c: [6] | `- p:[3,4,5] c: [5] | `- p:[3,4] c: [4] YES