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