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