MAYBE * Step 1: ArgumentFilter MAYBE + 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: ArgumentFilter [0,1,2,3,4,8,9,10,11,12,13,14,15,17,18,19,20] + Details: We remove following argument positions: [0,1,2,3,4,8,9,10,11,12,13,14,15,17,18,19,20]. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(F,G,H,Q) -> f3(F,G,H,Q) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 1. f1(F,G,H,Q) -> f3(F,G,H,Q) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] (?,1) 2. f1(F,G,H,Q) -> f3(F,G,H,Q) [H >= 1 && 255 >= H && 1 + F = G] (?,1) 3. f1(F,G,H,Q) -> f3(F,G,H,Q) [H >= 1 && H >= 257 && 1 + F = G] (?,1) 4. f1(F,G,H,Q) -> f2(F,G,H,Q) [F >= G] (?,1) 5. f1(F,G,H,Q) -> f1(F,G,H,Q) [0 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 6. f1(F,G,H,Q) -> f1(F,G,H,256) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] (?,1) 7. f1(F,G,H,Q) -> f1(F,G,H,Q) [0 >= H && 1 + F = G] (?,1) 8. f1(F,G,H,Q) -> f1(F,G,256,Q) [A1 >= 1 && 1 + F = G && H = 256] (?,1) 9. f300(F,G,H,Q) -> f1(F,G,H,Q) 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: FromIts MAYBE + Considered Problem: Rules: 0. f1(F,G,H,Q) -> f3(F,G,H,Q) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 1. f1(F,G,H,Q) -> f3(F,G,H,Q) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] (?,1) 2. f1(F,G,H,Q) -> f3(F,G,H,Q) [H >= 1 && 255 >= H && 1 + F = G] (?,1) 3. f1(F,G,H,Q) -> f3(F,G,H,Q) [H >= 1 && H >= 257 && 1 + F = G] (?,1) 4. f1(F,G,H,Q) -> f2(F,G,H,Q) [F >= G] (?,1) 5. f1(F,G,H,Q) -> f1(F,G,H,Q) [0 >= Q && G >= 1 + F && G >= 2 + F] (?,1) 6. f1(F,G,H,Q) -> f1(F,G,H,256) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] (?,1) 7. f1(F,G,H,Q) -> f1(F,G,H,Q) [0 >= H && 1 + F = G] (?,1) 8. f1(F,G,H,Q) -> f1(F,G,256,Q) [A1 >= 1 && 1 + F = G && H = 256] (?,1) 9. f300(F,G,H,Q) -> f1(F,G,H,Q) 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: FromIts + Details: () * Step 4: Unfold MAYBE + Considered Problem: Rules: f1(F,G,H,Q) -> f3(F,G,H,Q) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] f1(F,G,H,Q) -> f3(F,G,H,Q) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] f1(F,G,H,Q) -> f3(F,G,H,Q) [H >= 1 && 255 >= H && 1 + F = G] f1(F,G,H,Q) -> f3(F,G,H,Q) [H >= 1 && H >= 257 && 1 + F = G] f1(F,G,H,Q) -> f2(F,G,H,Q) [F >= G] f1(F,G,H,Q) -> f1(F,G,H,Q) [0 >= Q && G >= 1 + F && G >= 2 + F] f1(F,G,H,Q) -> f1(F,G,H,256) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] f1(F,G,H,Q) -> f1(F,G,H,Q) [0 >= H && 1 + F = G] f1(F,G,H,Q) -> f1(F,G,256,Q) [A1 >= 1 && 1 + F = G && H = 256] f300(F,G,H,Q) -> f1(F,G,H,Q) True Signature: {(f1,21);(f2,21);(f3,21);(f300,21)} Rule 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: Unfold + Details: () * Step 5: AddSinks MAYBE + Considered Problem: Rules: f1.0(F,G,H,Q) -> f3.10(F,G,H,Q) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] f1.1(F,G,H,Q) -> f3.10(F,G,H,Q) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] f1.2(F,G,H,Q) -> f3.10(F,G,H,Q) [H >= 1 && 255 >= H && 1 + F = G] f1.3(F,G,H,Q) -> f3.10(F,G,H,Q) [H >= 1 && H >= 257 && 1 + F = G] f1.4(F,G,H,Q) -> f2.10(F,G,H,Q) [F >= G] f1.5(F,G,H,Q) -> f1.5(F,G,H,Q) [0 >= Q && G >= 1 + F && G >= 2 + F] f1.6(F,G,H,Q) -> f1.6(F,G,H,256) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] f1.7(F,G,H,Q) -> f1.7(F,G,H,Q) [0 >= H && 1 + F = G] f1.8(F,G,H,Q) -> f1.8(F,G,256,Q) [A1 >= 1 && 1 + F = G && H = 256] f300.9(F,G,H,Q) -> f1.0(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.1(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.2(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.3(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.4(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.5(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.6(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.7(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.8(F,G,H,Q) True Signature: {(f1.0,4) ;(f1.1,4) ;(f1.2,4) ;(f1.3,4) ;(f1.4,4) ;(f1.5,4) ;(f1.6,4) ;(f1.7,4) ;(f1.8,4) ;(f2.10,4) ;(f3.10,4) ;(f300.9,4)} Rule Graph: [0->{},1->{},2->{},3->{},4->{},5->{5},6->{6},7->{7},8->{8},9->{0},10->{1},11->{2},12->{3},13->{4},14->{5} ,15->{6},16->{7},17->{8}] + Applied Processor: AddSinks + Details: () * Step 6: Failure MAYBE + Considered Problem: Rules: f1.0(F,G,H,Q) -> f3.10(F,G,H,Q) [Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F] f1.1(F,G,H,Q) -> f3.10(F,G,H,Q) [Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F] f1.2(F,G,H,Q) -> f3.10(F,G,H,Q) [H >= 1 && 255 >= H && 1 + F = G] f1.3(F,G,H,Q) -> f3.10(F,G,H,Q) [H >= 1 && H >= 257 && 1 + F = G] f1.4(F,G,H,Q) -> f2.10(F,G,H,Q) [F >= G] f1.5(F,G,H,Q) -> f1.5(F,G,H,Q) [0 >= Q && G >= 1 + F && G >= 2 + F] f1.6(F,G,H,Q) -> f1.6(F,G,H,256) [A1 >= 1 && G >= 1 + F && G >= 2 + F && Q = 256] f1.7(F,G,H,Q) -> f1.7(F,G,H,Q) [0 >= H && 1 + F = G] f1.8(F,G,H,Q) -> f1.8(F,G,256,Q) [A1 >= 1 && 1 + F = G && H = 256] f300.9(F,G,H,Q) -> f1.0(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.1(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.2(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.3(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.4(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.5(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.6(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.7(F,G,H,Q) True f300.9(F,G,H,Q) -> f1.8(F,G,H,Q) True f1.8(F,G,H,Q) -> exitus616(F,G,H,Q) True f1.7(F,G,H,Q) -> exitus616(F,G,H,Q) True f1.6(F,G,H,Q) -> exitus616(F,G,H,Q) True f1.5(F,G,H,Q) -> exitus616(F,G,H,Q) True f2.10(F,G,H,Q) -> exitus616(F,G,H,Q) True f3.10(F,G,H,Q) -> exitus616(F,G,H,Q) True f3.10(F,G,H,Q) -> exitus616(F,G,H,Q) True f3.10(F,G,H,Q) -> exitus616(F,G,H,Q) True f3.10(F,G,H,Q) -> exitus616(F,G,H,Q) True Signature: {(exitus616,4) ;(f1.0,4) ;(f1.1,4) ;(f1.2,4) ;(f1.3,4) ;(f1.4,4) ;(f1.5,4) ;(f1.6,4) ;(f1.7,4) ;(f1.8,4) ;(f2.10,4) ;(f3.10,4) ;(f300.9,4)} Rule Graph: [0->{26},1->{25},2->{24},3->{23},4->{22},5->{5,21},6->{6,20},7->{7,19},8->{8,18},9->{0},10->{1},11->{2} ,12->{3},13->{4},14->{5},15->{6},16->{7},17->{8}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] | +- p:[8] c: [] | +- p:[7] c: [] | +- p:[6] c: [] | `- p:[5] c: [] MAYBE