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) -> f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) [0 >= A] (?,1) 1. f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) True (?,1) 2. f43(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) True (?,1) 3. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) [A >= 1] (?,1) 4. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,P,0,P,P,G,H,I,J,K,L,M,N,O) [0 >= A && 999 + B >= P] (?,1) 5. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(1,B,P,0,P,P,G,H,I,J,K,L,M,N,O) [0 >= A && P >= 1000 + B] (?,1) 6. f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f29(0,P,P,D,E,F,0,P,I,J,K,L,M,N,O) [A >= 1] (?,1) 7. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f21(1,B,C,D,E,F,G,H,P,P,K,L,M,N,O) [0 >= P] (1,1) 8. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f21(1,B,C,D,E,F,G,H,P,0,1,Q,Q,Q,Q) [P >= 1 && Q >= 1] (1,1) 9. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(1,B,C,D,E,F,G,H,P,0,1,Q,Q,Q,Q) [P >= 1 && 0 >= Q] (1,1) Signature: {(f0,15);(f21,15);(f29,15);(f41,15);(f43,15);(f46,15)} 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 [2,3,4,5,6,7,8,9,10,11,12,13,14] + Details: We remove following argument positions: [2,3,4,5,6,7,8,9,10,11,12,13,14]. * Step 2: UnreachableRules MAYBE + Considered Problem: Rules: 0. f21(A,B) -> f29(A,B) [0 >= A] (?,1) 1. f41(A,B) -> f41(A,B) True (?,1) 2. f43(A,B) -> f46(A,B) True (?,1) 3. f29(A,B) -> f41(A,B) [A >= 1] (?,1) 4. f29(A,B) -> f41(A,B) [0 >= A && 999 + B >= P] (?,1) 5. f29(A,B) -> f41(1,B) [0 >= A && P >= 1000 + B] (?,1) 6. f21(A,B) -> f29(0,P) [A >= 1] (?,1) 7. f0(A,B) -> f21(1,B) [0 >= P] (1,1) 8. f0(A,B) -> f21(1,B) [P >= 1 && Q >= 1] (1,1) 9. f0(A,B) -> f41(1,B) [P >= 1 && 0 >= Q] (1,1) Signature: {(f0,15);(f21,15);(f29,15);(f41,15);(f43,15);(f46,15)} 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,B) -> f29(A,B) [0 >= A] (?,1) 1. f41(A,B) -> f41(A,B) True (?,1) 3. f29(A,B) -> f41(A,B) [A >= 1] (?,1) 4. f29(A,B) -> f41(A,B) [0 >= A && 999 + B >= P] (?,1) 5. f29(A,B) -> f41(1,B) [0 >= A && P >= 1000 + B] (?,1) 6. f21(A,B) -> f29(0,P) [A >= 1] (?,1) 7. f0(A,B) -> f21(1,B) [0 >= P] (1,1) 8. f0(A,B) -> f21(1,B) [P >= 1 && Q >= 1] (1,1) 9. f0(A,B) -> f41(1,B) [P >= 1 && 0 >= Q] (1,1) Signature: {(f0,15);(f21,15);(f29,15);(f41,15);(f43,15);(f46,15)} 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,B) -> f29(A,B) [0 >= A] (?,1) 1. f41(A,B) -> f41(A,B) True (?,1) 3. f29(A,B) -> f41(A,B) [A >= 1] (?,1) 4. f29(A,B) -> f41(A,B) [0 >= A && 999 + B >= P] (?,1) 5. f29(A,B) -> f41(1,B) [0 >= A && P >= 1000 + B] (?,1) 6. f21(A,B) -> f29(0,P) [A >= 1] (?,1) 7. f0(A,B) -> f21(1,B) [0 >= P] (1,1) 8. f0(A,B) -> f21(1,B) [P >= 1 && Q >= 1] (1,1) 9. f0(A,B) -> f41(1,B) [P >= 1 && 0 >= Q] (1,1) Signature: {(f0,15);(f21,15);(f29,15);(f41,15);(f43,15);(f46,15)} 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,B) -> f29(A,B) [0 >= A] f41(A,B) -> f41(A,B) True f29(A,B) -> f41(A,B) [A >= 1] f29(A,B) -> f41(A,B) [0 >= A && 999 + B >= P] f29(A,B) -> f41(1,B) [0 >= A && P >= 1000 + B] f21(A,B) -> f29(0,P) [A >= 1] f0(A,B) -> f21(1,B) [0 >= P] f0(A,B) -> f21(1,B) [P >= 1 && Q >= 1] f0(A,B) -> f41(1,B) [P >= 1 && 0 >= Q] Signature: {(f0,15);(f21,15);(f29,15);(f41,15);(f43,15);(f46,15)} 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,B) -> f29.4(A,B) [0 >= A] f21.0(A,B) -> f29.5(A,B) [0 >= A] f41.1(A,B) -> f41.1(A,B) True f29.3(A,B) -> f41.1(A,B) [A >= 1] f29.4(A,B) -> f41.1(A,B) [0 >= A && 999 + B >= P] f29.5(A,B) -> f41.1(1,B) [0 >= A && P >= 1000 + B] f21.6(A,B) -> f29.4(0,P) [A >= 1] f21.6(A,B) -> f29.5(0,P) [A >= 1] f0.7(A,B) -> f21.6(1,B) [0 >= P] f0.8(A,B) -> f21.6(1,B) [P >= 1 && Q >= 1] f0.9(A,B) -> f41.1(1,B) [P >= 1 && 0 >= Q] Signature: {(f0.7,2);(f0.8,2);(f0.9,2);(f21.0,2);(f21.6,2);(f29.3,2);(f29.4,2);(f29.5,2);(f41.1,2)} 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,B) -> f29.4(A,B) [0 >= A] f21.0(A,B) -> f29.5(A,B) [0 >= A] f41.1(A,B) -> f41.1(A,B) True f29.3(A,B) -> f41.1(A,B) [A >= 1] f29.4(A,B) -> f41.1(A,B) [0 >= A && 999 + B >= P] f29.5(A,B) -> f41.1(1,B) [0 >= A && P >= 1000 + B] f21.6(A,B) -> f29.4(0,P) [A >= 1] f21.6(A,B) -> f29.5(0,P) [A >= 1] f0.7(A,B) -> f21.6(1,B) [0 >= P] f0.8(A,B) -> f21.6(1,B) [P >= 1 && Q >= 1] f0.9(A,B) -> f41.1(1,B) [P >= 1 && 0 >= Q] f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True f41.1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0.7,2);(f0.8,2);(f0.9,2);(f21.0,2);(f21.6,2);(f29.3,2);(f29.4,2);(f29.5,2);(f41.1,2)} 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