MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f300(A,B,C,D) True (1,1) 1. f300(A,B,C,D) -> f300(A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B,C,D) -> f300(A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B,C,D) -> f300(A,-1 + B,0,D) [B >= 1 + A] (?,1) 4. f300(A,B,C,D) -> f1(A,B,C,E) [A >= B] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,4),(2,4)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f300(A,B,C,D) True (1,1) 1. f300(A,B,C,D) -> f300(A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B,C,D) -> f300(A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B,C,D) -> f300(A,-1 + B,0,D) [B >= 1 + A] (?,1) 4. f300(A,B,C,D) -> f1(A,B,C,E) [A >= B] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4},1->{1,2,3},2->{1,2,3},3->{1,2,3,4},4->{}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f2(A,B,C,D) -> f300(A,B,C,D) True f300(A,B,C,D) -> f300(A,B,E,D) [E >= 1 && B >= 1 + A] f300(A,B,C,D) -> f300(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300(A,B,C,D) -> f300(A,-1 + B,0,D) [B >= 1 + A] f300(A,B,C,D) -> f1(A,B,C,E) [A >= B] Signature: {(f1,4);(f2,4);(f300,4)} Rule Graph: [0->{1,2,3,4},1->{1,2,3},2->{1,2,3},3->{1,2,3,4},4->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f2.0(A,B,C,D) -> f300.1(A,B,C,D) True f2.0(A,B,C,D) -> f300.2(A,B,C,D) True f2.0(A,B,C,D) -> f300.3(A,B,C,D) True f2.0(A,B,C,D) -> f300.4(A,B,C,D) True f300.1(A,B,C,D) -> f300.1(A,B,E,D) [E >= 1 && B >= 1 + A] f300.1(A,B,C,D) -> f300.2(A,B,E,D) [E >= 1 && B >= 1 + A] f300.1(A,B,C,D) -> f300.3(A,B,E,D) [E >= 1 && B >= 1 + A] f300.2(A,B,C,D) -> f300.1(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300.2(A,B,C,D) -> f300.2(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300.2(A,B,C,D) -> f300.3(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300.3(A,B,C,D) -> f300.1(A,-1 + B,0,D) [B >= 1 + A] f300.3(A,B,C,D) -> f300.2(A,-1 + B,0,D) [B >= 1 + A] f300.3(A,B,C,D) -> f300.3(A,-1 + B,0,D) [B >= 1 + A] f300.3(A,B,C,D) -> f300.4(A,-1 + B,0,D) [B >= 1 + A] f300.4(A,B,C,D) -> f1.5(A,B,C,E) [A >= B] Signature: {(f1.5,4);(f2.0,4);(f300.1,4);(f300.2,4);(f300.3,4);(f300.4,4)} Rule Graph: [0->{4,5,6},1->{7,8,9},2->{10,11,12,13},3->{14},4->{4,5,6},5->{7,8,9},6->{10,11,12,13},7->{4,5,6},8->{7,8 ,9},9->{10,11,12,13},10->{4,5,6},11->{7,8,9},12->{10,11,12,13},13->{14},14->{}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f2.0(A,B,C,D) -> f300.1(A,B,C,D) True f2.0(A,B,C,D) -> f300.2(A,B,C,D) True f2.0(A,B,C,D) -> f300.3(A,B,C,D) True f2.0(A,B,C,D) -> f300.4(A,B,C,D) True f300.1(A,B,C,D) -> f300.1(A,B,E,D) [E >= 1 && B >= 1 + A] f300.1(A,B,C,D) -> f300.2(A,B,E,D) [E >= 1 && B >= 1 + A] f300.1(A,B,C,D) -> f300.3(A,B,E,D) [E >= 1 && B >= 1 + A] f300.2(A,B,C,D) -> f300.1(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300.2(A,B,C,D) -> f300.2(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300.2(A,B,C,D) -> f300.3(A,B,E,D) [0 >= 1 + E && B >= 1 + A] f300.3(A,B,C,D) -> f300.1(A,-1 + B,0,D) [B >= 1 + A] f300.3(A,B,C,D) -> f300.2(A,-1 + B,0,D) [B >= 1 + A] f300.3(A,B,C,D) -> f300.3(A,-1 + B,0,D) [B >= 1 + A] f300.3(A,B,C,D) -> f300.4(A,-1 + B,0,D) [B >= 1 + A] f300.4(A,B,C,D) -> f1.5(A,B,C,E) [A >= B] f1.5(A,B,C,D) -> exitus616(A,B,C,D) True f1.5(A,B,C,D) -> exitus616(A,B,C,D) True f1.5(A,B,C,D) -> exitus616(A,B,C,D) True f1.5(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f1.5,4);(f2.0,4);(f300.1,4);(f300.2,4);(f300.3,4);(f300.4,4)} Rule Graph: [0->{4,5,6},1->{7,8,9},2->{10,11,12,13},3->{14},4->{4,5,6},5->{7,8,9},6->{10,11,12,13},7->{4,5,6},8->{7,8 ,9},9->{10,11,12,13},10->{4,5,6},11->{7,8,9},12->{10,11,12,13},13->{14},14->{15,16,17,18}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[4,7,5,10,6,9,8,11,12] c: [6,9,10,11,12] | `- p:[4,7,5,8] c: [] MAYBE