MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [-1*A >= 0 && A >= 0 && B >= C] (?,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] (?,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] (?,1) Signature: {(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,1),(3,2)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [-1*A >= 0 && A >= 0 && B >= C] (?,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] (?,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] (?,1) Signature: {(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{3}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f3(A,B,C,D) -> f1(0,B,C,D) True f1(A,B,C,D) -> f2(A,B,C,E) [-1*A >= 0 && A >= 0 && B >= C] f1(A,B,C,D) -> f2(1,1 + B,C,E) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] Signature: {(f1,4);(f2,4);(f3,4)} Rule Graph: [0->{1,2,3},1->{},2->{},3->{3}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f3.0(A,B,C,D) -> f1.1(0,B,C,D) True f3.0(A,B,C,D) -> f1.2(0,B,C,D) True f3.0(A,B,C,D) -> f1.3(0,B,C,D) True f1.1(A,B,C,D) -> f2.4(A,B,C,E) [-1*A >= 0 && A >= 0 && B >= C] f1.2(A,B,C,D) -> f2.4(1,1 + B,C,E) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] f1.3(A,B,C,D) -> f1.3(0,1 + B,1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] Signature: {(f1.1,4);(f1.2,4);(f1.3,4);(f2.4,4);(f3.0,4)} Rule Graph: [0->{3},1->{4},2->{5},3->{},4->{},5->{5}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f3.0(A,B,C,D) -> f1.1(0,B,C,D) True f3.0(A,B,C,D) -> f1.2(0,B,C,D) True f3.0(A,B,C,D) -> f1.3(0,B,C,D) True f1.1(A,B,C,D) -> f2.4(A,B,C,E) [-1*A >= 0 && A >= 0 && B >= C] f1.2(A,B,C,D) -> f2.4(1,1 + B,C,E) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] f1.3(A,B,C,D) -> f1.3(0,1 + B,1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] f1.3(A,B,C,D) -> exitus616(A,B,C,D) True f2.4(A,B,C,D) -> exitus616(A,B,C,D) True f2.4(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f1.1,4);(f1.2,4);(f1.3,4);(f2.4,4);(f3.0,4)} Rule Graph: [0->{3},1->{4},2->{5},3->{8},4->{7},5->{5,6}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[5] c: [] MAYBE