NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,Q,Q,Q,A1) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,Q,Q,Q,A1) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] (?,1) 2. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,H,H,H,A1) [H >= 1 && 255 >= H && 1 + F = G] (?,1) 3. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,H,H,H,A1) [H >= 1 && H >= 257 && 1 + F = G] (?,1) 4. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f2(A,B,C,D,E,F,G,H,V,W,K,L,M,N,O,P,Q,0,0,0,U) [F >= G] (?,1) 5. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,P,Q,R,S,T,U) [0 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 6. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,256,R,S,T,U) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] (?,1) 7. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,P,Q,R,S,T,U) [0 >= H && 1 + F = G] (?,1) 8. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,256,V,W,X,Y,Z,B1,C1,D1,Q,R,S,T,U) [A1 >= 1 && 1 + F = G && H = 256] (?,1) 9. f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(V,W,X,Y,Z,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) True (1,1) Signature: {(f1,21);(f2,21);(f3,21);(f300,21)} Flow Graph: [0->{},1->{},2->{},3->{},4->{},5->{0,1,2,3,4,5,6,7,8},6->{0,1,2,3,4,5,6,7,8},7->{0,1,2,3,4,5,6,7,8},8->{0 ,1,2,3,4,5,6,7,8},9->{0,1,2,3,4,5,6,7,8}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths NO + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,Q,Q,Q,A1) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] (1,1) 1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,Q,Q,Q,A1) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] (1,1) 2. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,H,H,H,A1) [H >= 1 && 255 >= H && 1 + F = G] (1,1) 3. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,H,H,H,A1) [H >= 1 && H >= 257 && 1 + F = G] (1,1) 4. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f2(A,B,C,D,E,F,G,H,V,W,K,L,M,N,O,P,Q,0,0,0,U) [F >= G] (1,1) 5. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,P,Q,R,S,T,U) [0 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 6. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,256,R,S,T,U) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] (?,1) 7. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,P,Q,R,S,T,U) [0 >= H && 1 + F = G] (?,1) 8. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,256,V,W,X,Y,Z,B1,C1,D1,Q,R,S,T,U) [A1 >= 1 && 1 + F = G && H = 256] (?,1) 9. f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(V,W,X,Y,Z,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) True (1,1) Signature: {(f1,21);(f2,21);(f3,21);(f300,21)} Flow Graph: [0->{},1->{},2->{},3->{},4->{},5->{0,1,2,3,4,5,6,7,8},6->{0,1,2,3,4,5,6,7,8},7->{0,1,2,3,4,5,6,7,8},8->{0 ,1,2,3,4,5,6,7,8},9->{0,1,2,3,4,5,6,7,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,0) ,(5,1) ,(5,2) ,(5,3) ,(5,4) ,(5,6) ,(5,7) ,(5,8) ,(6,0) ,(6,1) ,(6,2) ,(6,3) ,(6,4) ,(6,5) ,(6,7) ,(6,8) ,(7,0) ,(7,1) ,(7,2) ,(7,3) ,(7,4) ,(7,5) ,(7,6) ,(7,8) ,(8,0) ,(8,1) ,(8,2) ,(8,3) ,(8,4) ,(8,5) ,(8,6) ,(8,7)] * Step 3: Looptree NO + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,Q,Q,Q,A1) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] (1,1) 1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,Q,Q,Q,A1) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] (1,1) 2. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,H,H,H,A1) [H >= 1 && 255 >= H && 1 + F = G] (1,1) 3. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f3(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,Q,H,H,H,A1) [H >= 1 && H >= 257 && 1 + F = G] (1,1) 4. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f2(A,B,C,D,E,F,G,H,V,W,K,L,M,N,O,P,Q,0,0,0,U) [F >= G] (1,1) 5. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,P,Q,R,S,T,U) [0 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 6. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,D1,256,R,S,T,U) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] (?,1) 7. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,H,V,W,X,Y,Z,B1,C1,P,Q,R,S,T,U) [0 >= H && 1 + F = G] (?,1) 8. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(A,B,C,D,E,F,G,256,V,W,X,Y,Z,B1,C1,D1,Q,R,S,T,U) [A1 >= 1 && 1 + F = G && H = 256] (?,1) 9. f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) -> f1(V,W,X,Y,Z,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) True (1,1) Signature: {(f1,21);(f2,21);(f3,21);(f300,21)} Flow Graph: [0->{},1->{},2->{},3->{},4->{},5->{5},6->{6},7->{7},8->{8},9->{0,1,2,3,4,5,6,7,8}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[8] c: [] | +- p:[7] c: [] | +- p:[6] c: [] | `- p:[5] c: [] NO