MAYBE * Step 1: ArgumentFilter MAYBE + Considered Problem: Rules: 0. f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) [0 >= A] (?,1) 1. f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) True (?,1) 2. f43(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) True (?,1) 3. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f41(A,R,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) [A >= 1] (?,1) 4. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f41(A,S,C,0,R,R,R,H,I,J,K,L,M,N,O,P,Q) [0 >= A && 999 + C >= R] (?,1) 5. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f41(1,S,C,0,R,R,R,H,I,J,K,L,M,N,O,P,Q) [0 >= A && R >= 1000 + C] (?,1) 6. f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f29(0,B,R,D,E,F,G,0,R,R,K,L,M,N,O,P,Q) [A >= 1] (?,1) 7. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f21(1,B,C,D,E,F,G,H,I,J,K,R,K,N,O,P,Q) [0 >= K] (1,1) 8. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f21(1,B,C,D,E,F,G,H,I,J,S,R,0,1,S,S,S) [S >= 1 && K >= 1] (1,1) 9. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f41(1,B,C,D,E,F,G,H,I,J,S,R,0,1,S,S,S) [0 >= S && K >= 1] (1,1) Signature: {(f0,17);(f21,17);(f29,17);(f41,17);(f43,17);(f46,17)} Flow Graph: [0->{3,4,5},1->{1},2->{},3->{1},4->{1},5->{1},6->{3,4,5},7->{0,6},8->{0,6},9->{1}] + Applied Processor: ArgumentFilter [1,3,4,5,6,7,8,9,11,12,13,14,15,16] + Details: We remove following argument positions: [1,3,4,5,6,7,8,9,11,12,13,14,15,16]. * Step 2: UnreachableRules MAYBE + Considered Problem: Rules: 0. f21(A,C,K) -> f29(A,C,K) [0 >= A] (?,1) 1. f41(A,C,K) -> f41(A,C,K) True (?,1) 2. f43(A,C,K) -> f46(A,C,K) True (?,1) 3. f29(A,C,K) -> f41(A,C,K) [A >= 1] (?,1) 4. f29(A,C,K) -> f41(A,C,K) [0 >= A && 999 + C >= R] (?,1) 5. f29(A,C,K) -> f41(1,C,K) [0 >= A && R >= 1000 + C] (?,1) 6. f21(A,C,K) -> f29(0,R,K) [A >= 1] (?,1) 7. f0(A,C,K) -> f21(1,C,K) [0 >= K] (1,1) 8. f0(A,C,K) -> f21(1,C,S) [S >= 1 && K >= 1] (1,1) 9. f0(A,C,K) -> f41(1,C,S) [0 >= S && K >= 1] (1,1) Signature: {(f0,17);(f21,17);(f29,17);(f41,17);(f43,17);(f46,17)} Flow Graph: [0->{3,4,5},1->{1},2->{},3->{1},4->{1},5->{1},6->{3,4,5},7->{0,6},8->{0,6},9->{1}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [2] * Step 3: UnsatPaths MAYBE + Considered Problem: Rules: 0. f21(A,C,K) -> f29(A,C,K) [0 >= A] (?,1) 1. f41(A,C,K) -> f41(A,C,K) True (?,1) 3. f29(A,C,K) -> f41(A,C,K) [A >= 1] (?,1) 4. f29(A,C,K) -> f41(A,C,K) [0 >= A && 999 + C >= R] (?,1) 5. f29(A,C,K) -> f41(1,C,K) [0 >= A && R >= 1000 + C] (?,1) 6. f21(A,C,K) -> f29(0,R,K) [A >= 1] (?,1) 7. f0(A,C,K) -> f21(1,C,K) [0 >= K] (1,1) 8. f0(A,C,K) -> f21(1,C,S) [S >= 1 && K >= 1] (1,1) 9. f0(A,C,K) -> f41(1,C,S) [0 >= S && K >= 1] (1,1) Signature: {(f0,17);(f21,17);(f29,17);(f41,17);(f43,17);(f46,17)} Flow Graph: [0->{3,4,5},1->{1},3->{1},4->{1},5->{1},6->{3,4,5},7->{0,6},8->{0,6},9->{1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(6,3),(7,0),(8,0)] * Step 4: FromIts MAYBE + Considered Problem: Rules: 0. f21(A,C,K) -> f29(A,C,K) [0 >= A] (?,1) 1. f41(A,C,K) -> f41(A,C,K) True (?,1) 3. f29(A,C,K) -> f41(A,C,K) [A >= 1] (?,1) 4. f29(A,C,K) -> f41(A,C,K) [0 >= A && 999 + C >= R] (?,1) 5. f29(A,C,K) -> f41(1,C,K) [0 >= A && R >= 1000 + C] (?,1) 6. f21(A,C,K) -> f29(0,R,K) [A >= 1] (?,1) 7. f0(A,C,K) -> f21(1,C,K) [0 >= K] (1,1) 8. f0(A,C,K) -> f21(1,C,S) [S >= 1 && K >= 1] (1,1) 9. f0(A,C,K) -> f41(1,C,S) [0 >= S && K >= 1] (1,1) Signature: {(f0,17);(f21,17);(f29,17);(f41,17);(f43,17);(f46,17)} Flow Graph: [0->{4,5},1->{1},3->{1},4->{1},5->{1},6->{4,5},7->{6},8->{6},9->{1}] + Applied Processor: FromIts + Details: () * Step 5: Unfold MAYBE + Considered Problem: Rules: f21(A,C,K) -> f29(A,C,K) [0 >= A] f41(A,C,K) -> f41(A,C,K) True f29(A,C,K) -> f41(A,C,K) [A >= 1] f29(A,C,K) -> f41(A,C,K) [0 >= A && 999 + C >= R] f29(A,C,K) -> f41(1,C,K) [0 >= A && R >= 1000 + C] f21(A,C,K) -> f29(0,R,K) [A >= 1] f0(A,C,K) -> f21(1,C,K) [0 >= K] f0(A,C,K) -> f21(1,C,S) [S >= 1 && K >= 1] f0(A,C,K) -> f41(1,C,S) [0 >= S && K >= 1] Signature: {(f0,17);(f21,17);(f29,17);(f41,17);(f43,17);(f46,17)} Rule Graph: [0->{4,5},1->{1},3->{1},4->{1},5->{1},6->{4,5},7->{6},8->{6},9->{1}] + Applied Processor: Unfold + Details: () * Step 6: AddSinks MAYBE + Considered Problem: Rules: f21.0(A,C,K) -> f29.4(A,C,K) [0 >= A] f21.0(A,C,K) -> f29.5(A,C,K) [0 >= A] f41.1(A,C,K) -> f41.1(A,C,K) True f29.3(A,C,K) -> f41.1(A,C,K) [A >= 1] f29.4(A,C,K) -> f41.1(A,C,K) [0 >= A && 999 + C >= R] f29.5(A,C,K) -> f41.1(1,C,K) [0 >= A && R >= 1000 + C] f21.6(A,C,K) -> f29.4(0,R,K) [A >= 1] f21.6(A,C,K) -> f29.5(0,R,K) [A >= 1] f0.7(A,C,K) -> f21.6(1,C,K) [0 >= K] f0.8(A,C,K) -> f21.6(1,C,S) [S >= 1 && K >= 1] f0.9(A,C,K) -> f41.1(1,C,S) [0 >= S && K >= 1] Signature: {(f0.7,3);(f0.8,3);(f0.9,3);(f21.0,3);(f21.6,3);(f29.3,3);(f29.4,3);(f29.5,3);(f41.1,3)} Rule Graph: [0->{4},1->{5},2->{2},3->{2},4->{2},5->{2},6->{4},7->{5},8->{6,7},9->{6,7},10->{2}] + Applied Processor: AddSinks + Details: () * Step 7: Failure MAYBE + Considered Problem: Rules: f21.0(A,C,K) -> f29.4(A,C,K) [0 >= A] f21.0(A,C,K) -> f29.5(A,C,K) [0 >= A] f41.1(A,C,K) -> f41.1(A,C,K) True f29.3(A,C,K) -> f41.1(A,C,K) [A >= 1] f29.4(A,C,K) -> f41.1(A,C,K) [0 >= A && 999 + C >= R] f29.5(A,C,K) -> f41.1(1,C,K) [0 >= A && R >= 1000 + C] f21.6(A,C,K) -> f29.4(0,R,K) [A >= 1] f21.6(A,C,K) -> f29.5(0,R,K) [A >= 1] f0.7(A,C,K) -> f21.6(1,C,K) [0 >= K] f0.8(A,C,K) -> f21.6(1,C,S) [S >= 1 && K >= 1] f0.9(A,C,K) -> f41.1(1,C,S) [0 >= S && K >= 1] f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True f41.1(A,C,K) -> exitus616(A,C,K) True Signature: {(exitus616,3);(f0.7,3);(f0.8,3);(f0.9,3);(f21.0,3);(f21.6,3);(f29.3,3);(f29.4,3);(f29.5,3);(f41.1,3)} Rule Graph: [0->{4},1->{5},2->{2,11,12,13,14,15,16,17,18},3->{2},4->{2},5->{2},6->{4},7->{5},8->{6,7},9->{6,7} ,10->{2}] + 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] | `- p:[2] c: [] MAYBE