MAYBE * Step 1: ArgumentFilter 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: ArgumentFilter [2,3,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] + Details: We remove following argument positions: [2,3,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f8(A,B,E,F,G,H) -> f8(A,B,E,F,G,H) [A >= 1 + B] (?,1) 1. f8(A,B,E,F,G,H) -> f8(A,B,E,F,G,H) [B >= 1 + A] (?,1) 2. f2(A,B,E,F,G,H) -> f2(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,E,F,G,H) -> f2(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,E,F,G,H) -> f2(A,B,E,B1,2,1) [E >= 1 + E1] (1,1) 5. f23(A,B,E,F,G,H) -> f2(A,B,E,B1,2,1) [E1 >= 1 + E] (1,1) 6. f2(A,B,E,F,G,H) -> f8(A,C1,F,F,G,H) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (?,1) 7. f2(A,B,E,F,G,H) -> f8(A,C1,F,F,G,H) [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: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(1,0),(6,1),(7,0)] * Step 3: FromIts MAYBE + Considered Problem: Rules: 0. f8(A,B,E,F,G,H) -> f8(A,B,E,F,G,H) [A >= 1 + B] (?,1) 1. f8(A,B,E,F,G,H) -> f8(A,B,E,F,G,H) [B >= 1 + A] (?,1) 2. f2(A,B,E,F,G,H) -> f2(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] (?,1) 3. f2(A,B,E,F,G,H) -> f2(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] (?,1) 4. f23(A,B,E,F,G,H) -> f2(A,B,E,B1,2,1) [E >= 1 + E1] (1,1) 5. f23(A,B,E,F,G,H) -> f2(A,B,E,B1,2,1) [E1 >= 1 + E] (1,1) 6. f2(A,B,E,F,G,H) -> f8(A,C1,F,F,G,H) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] (?,1) 7. f2(A,B,E,F,G,H) -> f8(A,C1,F,F,G,H) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] (?,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: FromIts + Details: () * Step 4: Unfold MAYBE + Considered Problem: Rules: f8(A,B,E,F,G,H) -> f8(A,B,E,F,G,H) [A >= 1 + B] f8(A,B,E,F,G,H) -> f8(A,B,E,F,G,H) [B >= 1 + A] f2(A,B,E,F,G,H) -> f2(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2(A,B,E,F,G,H) -> f2(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f23(A,B,E,F,G,H) -> f2(A,B,E,B1,2,1) [E >= 1 + E1] f23(A,B,E,F,G,H) -> f2(A,B,E,B1,2,1) [E1 >= 1 + E] f2(A,B,E,F,G,H) -> f8(A,C1,F,F,G,H) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] f2(A,B,E,F,G,H) -> f8(A,C1,F,F,G,H) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] Signature: {(f2,27);(f23,27);(f8,27)} Rule 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: Unfold + Details: () * Step 5: AddSinks MAYBE + Considered Problem: Rules: f8.0(A,B,E,F,G,H) -> f8.0(A,B,E,F,G,H) [A >= 1 + B] f8.1(A,B,E,F,G,H) -> f8.1(A,B,E,F,G,H) [B >= 1 + A] f2.2(A,B,E,F,G,H) -> f2.2(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.2(A,B,E,F,G,H) -> f2.3(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.2(A,B,E,F,G,H) -> f2.6(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.2(A,B,E,F,G,H) -> f2.7(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.2(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.3(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.6(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.7(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f23.4(A,B,E,F,G,H) -> f2.2(A,B,E,B1,2,1) [E >= 1 + E1] f23.4(A,B,E,F,G,H) -> f2.3(A,B,E,B1,2,1) [E >= 1 + E1] f23.4(A,B,E,F,G,H) -> f2.6(A,B,E,B1,2,1) [E >= 1 + E1] f23.4(A,B,E,F,G,H) -> f2.7(A,B,E,B1,2,1) [E >= 1 + E1] f23.5(A,B,E,F,G,H) -> f2.2(A,B,E,B1,2,1) [E1 >= 1 + E] f23.5(A,B,E,F,G,H) -> f2.3(A,B,E,B1,2,1) [E1 >= 1 + E] f23.5(A,B,E,F,G,H) -> f2.6(A,B,E,B1,2,1) [E1 >= 1 + E] f23.5(A,B,E,F,G,H) -> f2.7(A,B,E,B1,2,1) [E1 >= 1 + E] f2.6(A,B,E,F,G,H) -> f8.0(A,C1,F,F,G,H) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] f2.7(A,B,E,F,G,H) -> f8.1(A,C1,F,F,G,H) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] Signature: {(f2.2,6);(f2.3,6);(f2.6,6);(f2.7,6);(f23.4,6);(f23.5,6);(f8.0,6);(f8.1,6)} Rule Graph: [0->{0},1->{1},2->{2,3,4,5},3->{6,7,8,9},4->{18},5->{19},6->{2,3,4,5},7->{6,7,8,9},8->{18},9->{19},10->{2 ,3,4,5},11->{6,7,8,9},12->{18},13->{19},14->{2,3,4,5},15->{6,7,8,9},16->{18},17->{19},18->{0},19->{1}] + Applied Processor: AddSinks + Details: () * Step 6: Failure MAYBE + Considered Problem: Rules: f8.0(A,B,E,F,G,H) -> f8.0(A,B,E,F,G,H) [A >= 1 + B] f8.1(A,B,E,F,G,H) -> f8.1(A,B,E,F,G,H) [B >= 1 + A] f2.2(A,B,E,F,G,H) -> f2.2(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.2(A,B,E,F,G,H) -> f2.3(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.2(A,B,E,F,G,H) -> f2.6(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.2(A,B,E,F,G,H) -> f2.7(A,B,E,B1,-1 + G,1 + H) [E >= 1 + F && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.2(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.3(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.6(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f2.3(A,B,E,F,G,H) -> f2.7(A,B,E,B1,-1 + G,1 + H) [F >= 1 + E && G >= 1 && H >= 0] f23.4(A,B,E,F,G,H) -> f2.2(A,B,E,B1,2,1) [E >= 1 + E1] f23.4(A,B,E,F,G,H) -> f2.3(A,B,E,B1,2,1) [E >= 1 + E1] f23.4(A,B,E,F,G,H) -> f2.6(A,B,E,B1,2,1) [E >= 1 + E1] f23.4(A,B,E,F,G,H) -> f2.7(A,B,E,B1,2,1) [E >= 1 + E1] f23.5(A,B,E,F,G,H) -> f2.2(A,B,E,B1,2,1) [E1 >= 1 + E] f23.5(A,B,E,F,G,H) -> f2.3(A,B,E,B1,2,1) [E1 >= 1 + E] f23.5(A,B,E,F,G,H) -> f2.6(A,B,E,B1,2,1) [E1 >= 1 + E] f23.5(A,B,E,F,G,H) -> f2.7(A,B,E,B1,2,1) [E1 >= 1 + E] f2.6(A,B,E,F,G,H) -> f8.0(A,C1,F,F,G,H) [A >= 1 + C1 && G >= 1 && H >= 0 && F = E] f2.7(A,B,E,F,G,H) -> f8.1(A,C1,F,F,G,H) [C1 >= 1 + A && G >= 1 && H >= 0 && F = E] f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.1(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True f8.0(A,B,E,F,G,H) -> exitus616(A,B,E,F,G,H) True Signature: {(exitus616,6);(f2.2,6);(f2.3,6);(f2.6,6);(f2.7,6);(f23.4,6);(f23.5,6);(f8.0,6);(f8.1,6)} Rule Graph: [0->{0,21,23,25,27,29,31,33,35,37,39},1->{1,20,22,24,26,28,30,32,34,36,38},2->{2,3,4,5},3->{6,7,8,9} ,4->{18},5->{19},6->{2,3,4,5},7->{6,7,8,9},8->{18},9->{19},10->{2,3,4,5},11->{6,7,8,9},12->{18},13->{19} ,14->{2,3,4,5},15->{6,7,8,9},16->{18},17->{19},18->{0},19->{1}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] | +- p:[2,6,3,7] c: [2,3,6,7] | +- p:[1] c: [] | `- p:[0] c: [] MAYBE