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