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