MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= 1 + B] (?,1) 1. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E >= 1 + E1] (1,1) 5. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E1 >= 1 + E] (1,1) 6. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (?,1) 7. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] (?,1) Signature: {(f2,27);(f23,27);(f8,27)} Flow Graph: [0->{0,1},1->{0,1},2->{2,3,6,7},3->{2,3,6,7},4->{2,3,6,7},5->{2,3,6,7},6->{0,1},7->{0,1}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= 1 + B] (?,1) 1. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E >= 1 + E1] (1,1) 5. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E1 >= 1 + E] (1,1) 6. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (1,1) 7. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] (1,1) Signature: {(f2,27);(f23,27);(f8,27)} Flow Graph: [0->{0,1},1->{0,1},2->{2,3,6,7},3->{2,3,6,7},4->{2,3,6,7},5->{2,3,6,7},6->{0,1},7->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(1,0),(6,1),(7,0)] * Step 3: AddSinks MAYBE + Considered Problem: Rules: 0. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= 1 + B] (?,1) 1. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E >= 1 + E1] (1,1) 5. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E1 >= 1 + E] (1,1) 6. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (1,1) 7. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] (1,1) Signature: {(f2,27);(f23,27);(f8,27)} Flow Graph: [0->{0},1->{1},2->{2,3,6,7},3->{2,3,6,7},4->{2,3,6,7},5->{2,3,6,7},6->{0},7->{1}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths MAYBE + Considered Problem: Rules: 0. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= 1 + B] (?,1) 1. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E >= 1 + E1] (1,1) 5. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E1 >= 1 + E] (1,1) 6. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (?,1) 7. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] (?,1) 8. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (?,1) Signature: {(exitus616,27);(f2,27);(f23,27);(f8,27)} Flow Graph: [0->{0,1,8},1->{0,1,8},2->{2,3,6,7},3->{2,3,6,7},4->{2,3,6,7},5->{2,3,6,7},6->{0,1,8},7->{0,1,8},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(1,0),(6,1),(7,0)] * Step 5: Failure MAYBE + Considered Problem: Rules: 0. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= 1 + B] (?,1) 1. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,B,B,B,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,-1 + G,1 + H,1 + H,-1 + G,C1,D1,-1 + G,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E >= 1 + E1] (1,1) 5. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,B1,2,1,1,2,K,L,M,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0,A1) [E1 >= 1 + E] (1,1) 6. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (?,1) 7. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f8(A,C1,C1,C1,F,F,G,H,I,J,K,L,M,N,O,P,B1,R,S,T,D1,V,W,X,Y,Z,F1) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] (?,1) 8. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (?,1) Signature: {(exitus616,27);(f2,27);(f23,27);(f8,27)} Flow Graph: [0->{0,8},1->{1,8},2->{2,3,6,7},3->{2,3,6,7},4->{2,3,6,7},5->{2,3,6,7},6->{0,8},7->{1,8},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[2,3] c: [3] | | | `- p:[2] c: [2] | +- p:[1] c: [] | `- p:[0] c: [] MAYBE