MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D,E) -> f0(A,B,C,D,E) True (1,1) 1. f0(A,B,C,D,E) -> f0(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] (?,1) 2. f0(A,B,C,D,E) -> f0(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] (?,1) 3. f0(A,B,C,D,E) -> f0(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] (?,1) 4. f0(A,B,C,D,E) -> f2(A,F,C,D,E) [0 >= A] (?,1) Signature: {(f0,5);(f1,5);(f2,5)} 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),(3,4)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D,E) -> f0(A,B,C,D,E) True (1,1) 1. f0(A,B,C,D,E) -> f0(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] (?,1) 2. f0(A,B,C,D,E) -> f0(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] (?,1) 3. f0(A,B,C,D,E) -> f0(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] (?,1) 4. f0(A,B,C,D,E) -> f2(A,F,C,D,E) [0 >= A] (?,1) Signature: {(f0,5);(f1,5);(f2,5)} Flow Graph: [0->{1,2,3,4},1->{1,2,3},2->{1,2,3},3->{1,2,3},4->{}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f1(A,B,C,D,E) -> f0(A,B,C,D,E) True f0(A,B,C,D,E) -> f0(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0(A,B,C,D,E) -> f0(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0(A,B,C,D,E) -> f0(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0(A,B,C,D,E) -> f2(A,F,C,D,E) [0 >= A] Signature: {(f0,5);(f1,5);(f2,5)} Rule Graph: [0->{1,2,3,4},1->{1,2,3},2->{1,2,3},3->{1,2,3},4->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f1.0(A,B,C,D,E) -> f0.1(A,B,C,D,E) True f1.0(A,B,C,D,E) -> f0.2(A,B,C,D,E) True f1.0(A,B,C,D,E) -> f0.3(A,B,C,D,E) True f1.0(A,B,C,D,E) -> f0.4(A,B,C,D,E) True f0.1(A,B,C,D,E) -> f0.1(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0.1(A,B,C,D,E) -> f0.2(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0.1(A,B,C,D,E) -> f0.3(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0.2(A,B,C,D,E) -> f0.1(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0.2(A,B,C,D,E) -> f0.2(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0.2(A,B,C,D,E) -> f0.3(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0.3(A,B,C,D,E) -> f0.1(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0.3(A,B,C,D,E) -> f0.2(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0.3(A,B,C,D,E) -> f0.3(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0.4(A,B,C,D,E) -> f2.5(A,F,C,D,E) [0 >= A] Signature: {(f0.1,5);(f0.2,5);(f0.3,5);(f0.4,5);(f1.0,5);(f2.5,5)} Rule Graph: [0->{4,5,6},1->{7,8,9},2->{10,11,12},3->{13},4->{4,5,6},5->{7,8,9},6->{10,11,12},7->{4,5,6},8->{7,8,9} ,9->{10,11,12},10->{4,5,6},11->{7,8,9},12->{10,11,12},13->{}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f1.0(A,B,C,D,E) -> f0.1(A,B,C,D,E) True f1.0(A,B,C,D,E) -> f0.2(A,B,C,D,E) True f1.0(A,B,C,D,E) -> f0.3(A,B,C,D,E) True f1.0(A,B,C,D,E) -> f0.4(A,B,C,D,E) True f0.1(A,B,C,D,E) -> f0.1(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0.1(A,B,C,D,E) -> f0.2(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0.1(A,B,C,D,E) -> f0.3(F,B,C,H,F) [2*F >= 1 && G >= 1 && A = 2*F] f0.2(A,B,C,D,E) -> f0.1(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0.2(A,B,C,D,E) -> f0.2(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0.2(A,B,C,D,E) -> f0.3(1 + 3*A,B,F,H,G) [A >= 1 && 2*G >= 1 + A && 3*A >= 3*F && 3*F >= 3*A && 2*G >= 1 + F && F >= 1] f0.3(A,B,C,D,E) -> f0.1(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0.3(A,B,C,D,E) -> f0.2(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0.3(A,B,C,D,E) -> f0.3(1 + 3*A,B,F,H,G) [A >= 1 && A >= 1 + 2*G && 3*A >= 3*F && 3*F >= 3*A && F >= 1 + 2*G && F >= 1] f0.4(A,B,C,D,E) -> f2.5(A,F,C,D,E) [0 >= A] f2.5(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.1(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f0.3(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(exitus616,5);(f0.1,5);(f0.2,5);(f0.3,5);(f0.4,5);(f1.0,5);(f2.5,5)} Rule Graph: [0->{4,5,6},1->{7,8,9},2->{10,11,12},3->{13},4->{4,5,6,15,24,33},5->{7,8,9,17,26,35},6->{10,11,12,19,28 ,37},7->{4,5,6,16,25,34},8->{7,8,9,21,30,39},9->{10,11,12,20,29,38},10->{4,5,6,18,27,36},11->{7,8,9,22,31 ,40},12->{10,11,12,23,32,41},13->{14}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] | `- p:[4,7,5,10,6,9,8,11,12] c: [] MAYBE