YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f11(100,O,1,D,E,F,G,H,I,J,K,L,M,N) True (1,1) 1. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f11(100,O,0,D,E,F,G,H,I,J,K,L,M,N) True (1,1) 2. f11(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f23(A,B,1,1,1,100,O,1,I,J,K,L,M,N) [C = 1] (?,1) 3. f11(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f23(A,B,1,1,1,100,O,0,I,J,K,L,M,N) [C = 1] (?,1) 4. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f26(A,B,C,D,H,F,G,H,100,J,K,L,M,N) [0 >= H] (?,1) 5. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f26(A,B,C,D,H,F,G,H,100,J,K,L,M,N) [H >= 2] (?,1) 6. f11(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f36(A,B,C,C,C,F,G,H,I,100,K,L,M,N) [0 >= C] (?,1) 7. f11(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f36(A,B,C,C,C,F,G,H,I,100,K,L,M,N) [C >= 2] (?,1) 8. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,1,F,G,1,I,J,O,P,M,N) [0 >= 2 + O && H = 1] (?,1) 9. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,1,F,G,1,I,J,O,P,M,N) [O >= 0 && H = 1] (?,1) 10. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,1,F,G,1,I,J,-1,L,100,O) [H = 1] (?,1) 11. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [0 >= 1 + O] (?,1) 12. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N) True (?,1) 13. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [0 >= 1 + O] (?,1) 14. f26(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f32(A,B,C,D,E,F,G,H,I,J,K,L,M,N) True (?,1) Signature: {(f0,14);(f11,14);(f23,14);(f26,14);(f32,14);(f36,14)} Flow Graph: [0->{2,3,6,7},1->{2,3,6,7},2->{4,5,8,9,10},3->{4,5,8,9,10},4->{13,14},5->{13,14},6->{11,12},7->{11,12} ,8->{},9->{},10->{},11->{},12->{},13->{},14->{}] + Applied Processor: ArgumentFilter [0,1,3,4,5,6,8,9,10,11,12,13] + Details: We remove following argument positions: [0,1,3,4,5,6,8,9,10,11,12,13]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(C,H) -> f11(1,H) True (1,1) 1. f0(C,H) -> f11(0,H) True (1,1) 2. f11(C,H) -> f23(1,1) [C = 1] (?,1) 3. f11(C,H) -> f23(1,0) [C = 1] (?,1) 4. f23(C,H) -> f26(C,H) [0 >= H] (?,1) 5. f23(C,H) -> f26(C,H) [H >= 2] (?,1) 6. f11(C,H) -> f36(C,H) [0 >= C] (?,1) 7. f11(C,H) -> f36(C,H) [C >= 2] (?,1) 8. f23(C,H) -> f32(C,1) [0 >= 2 + O && H = 1] (?,1) 9. f23(C,H) -> f32(C,1) [O >= 0 && H = 1] (?,1) 10. f23(C,H) -> f32(C,1) [H = 1] (?,1) 11. f36(C,H) -> f32(C,H) [0 >= 1 + O] (?,1) 12. f36(C,H) -> f32(C,H) True (?,1) 13. f26(C,H) -> f32(C,H) [0 >= 1 + O] (?,1) 14. f26(C,H) -> f32(C,H) True (?,1) Signature: {(f0,14);(f11,14);(f23,14);(f26,14);(f32,14);(f36,14)} Flow Graph: [0->{2,3,6,7},1->{2,3,6,7},2->{4,5,8,9,10},3->{4,5,8,9,10},4->{13,14},5->{13,14},6->{11,12},7->{11,12} ,8->{},9->{},10->{},11->{},12->{},13->{},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6) ,(0,7) ,(1,2) ,(1,3) ,(1,7) ,(2,4) ,(2,5) ,(3,5) ,(3,8) ,(3,9) ,(3,10)] * Step 3: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(C,H) -> f11(1,H) True (1,1) 1. f0(C,H) -> f11(0,H) True (1,1) 2. f11(C,H) -> f23(1,1) [C = 1] (?,1) 3. f11(C,H) -> f23(1,0) [C = 1] (?,1) 4. f23(C,H) -> f26(C,H) [0 >= H] (?,1) 5. f23(C,H) -> f26(C,H) [H >= 2] (?,1) 6. f11(C,H) -> f36(C,H) [0 >= C] (?,1) 7. f11(C,H) -> f36(C,H) [C >= 2] (?,1) 8. f23(C,H) -> f32(C,1) [0 >= 2 + O && H = 1] (?,1) 9. f23(C,H) -> f32(C,1) [O >= 0 && H = 1] (?,1) 10. f23(C,H) -> f32(C,1) [H = 1] (?,1) 11. f36(C,H) -> f32(C,H) [0 >= 1 + O] (?,1) 12. f36(C,H) -> f32(C,H) True (?,1) 13. f26(C,H) -> f32(C,H) [0 >= 1 + O] (?,1) 14. f26(C,H) -> f32(C,H) True (?,1) Signature: {(f0,14);(f11,14);(f23,14);(f26,14);(f32,14);(f36,14)} Flow Graph: [0->{2,3},1->{6},2->{8,9,10},3->{4},4->{13,14},5->{13,14},6->{11,12},7->{11,12},8->{},9->{},10->{},11->{} ,12->{},13->{},14->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [5,7] * Step 4: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(C,H) -> f11(1,H) True (1,1) 1. f0(C,H) -> f11(0,H) True (1,1) 2. f11(C,H) -> f23(1,1) [C = 1] (?,1) 3. f11(C,H) -> f23(1,0) [C = 1] (?,1) 4. f23(C,H) -> f26(C,H) [0 >= H] (?,1) 6. f11(C,H) -> f36(C,H) [0 >= C] (?,1) 8. f23(C,H) -> f32(C,1) [0 >= 2 + O && H = 1] (?,1) 9. f23(C,H) -> f32(C,1) [O >= 0 && H = 1] (?,1) 10. f23(C,H) -> f32(C,1) [H = 1] (?,1) 11. f36(C,H) -> f32(C,H) [0 >= 1 + O] (?,1) 12. f36(C,H) -> f32(C,H) True (?,1) 13. f26(C,H) -> f32(C,H) [0 >= 1 + O] (?,1) 14. f26(C,H) -> f32(C,H) True (?,1) Signature: {(f0,14);(f11,14);(f23,14);(f26,14);(f32,14);(f36,14)} Flow Graph: [0->{2,3},1->{6},2->{8,9,10},3->{4},4->{13,14},6->{11,12},8->{},9->{},10->{},11->{},12->{},13->{},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 5: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(C,H) -> f11(1,H) True (1,1) 1. f0(C,H) -> f11(0,H) True (1,1) 2. f11(C,H) -> f23(1,1) [C = 1] (1,1) 3. f11(C,H) -> f23(1,0) [C = 1] (1,1) 4. f23(C,H) -> f26(C,H) [0 >= H] (1,1) 6. f11(C,H) -> f36(C,H) [0 >= C] (1,1) 8. f23(C,H) -> f32(C,1) [0 >= 2 + O && H = 1] (1,1) 9. f23(C,H) -> f32(C,1) [O >= 0 && H = 1] (1,1) 10. f23(C,H) -> f32(C,1) [H = 1] (1,1) 11. f36(C,H) -> f32(C,H) [0 >= 1 + O] (1,1) 12. f36(C,H) -> f32(C,H) True (1,1) 13. f26(C,H) -> f32(C,H) [0 >= 1 + O] (1,1) 14. f26(C,H) -> f32(C,H) True (1,1) Signature: {(f0,14);(f11,14);(f23,14);(f26,14);(f32,14);(f36,14)} Flow Graph: [0->{2,3},1->{6},2->{8,9,10},3->{4},4->{13,14},6->{11,12},8->{},9->{},10->{},11->{},12->{},13->{},14->{}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))