MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 2. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 3. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{1,2,3},3->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1),(2,3),(3,2)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 2. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 3. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{2},3->{1,3}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f1(A,B,C) -> f2(A,B,C) True f2(A,B,C) -> f300(A,B,D) [A = B] f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1,2,3},1->{},2->{2},3->{1,3}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f1.0(A,B,C) -> f2.1(A,B,C) True f1.0(A,B,C) -> f2.2(A,B,C) True f1.0(A,B,C) -> f2.3(A,B,C) True f2.1(A,B,C) -> f300.4(A,B,D) [A = B] f2.2(A,B,C) -> f2.2(1 + A,B,C) [A >= 1 + B && A >= B] f2.3(A,B,C) -> f2.1(1 + A,B,C) [B >= 1 + A] f2.3(A,B,C) -> f2.3(1 + A,B,C) [B >= 1 + A] Signature: {(f1.0,3);(f2.1,3);(f2.2,3);(f2.3,3);(f300.4,3)} Rule Graph: [0->{3},1->{4},2->{5,6},3->{},4->{4},5->{3},6->{5,6}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f1.0(A,B,C) -> f2.1(A,B,C) True f1.0(A,B,C) -> f2.2(A,B,C) True f1.0(A,B,C) -> f2.3(A,B,C) True f2.1(A,B,C) -> f300.4(A,B,D) [A = B] f2.2(A,B,C) -> f2.2(1 + A,B,C) [A >= 1 + B && A >= B] f2.3(A,B,C) -> f2.1(1 + A,B,C) [B >= 1 + A] f2.3(A,B,C) -> f2.3(1 + A,B,C) [B >= 1 + A] f300.4(A,B,C) -> exitus616(A,B,C) True f2.2(A,B,C) -> exitus616(A,B,C) True f300.4(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f1.0,3);(f2.1,3);(f2.2,3);(f2.3,3);(f300.4,3)} Rule Graph: [0->{3},1->{4},2->{5,6},3->{7,9},4->{4,8},5->{3},6->{5,6}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[6] c: [6] | `- p:[4] c: [] MAYBE