MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 8. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && B >= 1 + A] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7,8},1->{1,2,3,4,5,6,7,8},2->{1,2,3,4,5,6,7,8},3->{1,2,3,4,5,6,7,8},4->{1,2,3,4,5,6,7,8} ,5->{1,2,3,4,5,6,7,8},6->{1,2,3,4,5,6,7,8},7->{},8->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (1,1) 8. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && B >= 1 + A] (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7,8},1->{1,2,3,4,5,6,7,8},2->{1,2,3,4,5,6,7,8},3->{1,2,3,4,5,6,7,8},4->{1,2,3,4,5,6,7,8} ,5->{1,2,3,4,5,6,7,8},6->{1,2,3,4,5,6,7,8},7->{},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,8) ,(1,7) ,(1,8) ,(2,7) ,(2,8) ,(3,4) ,(3,5) ,(3,6) ,(3,7) ,(3,8) ,(4,1) ,(4,2) ,(4,3) ,(4,4) ,(4,5) ,(4,6) ,(4,8) ,(5,1) ,(5,2) ,(5,3) ,(5,4) ,(5,5) ,(5,6) ,(5,8) ,(6,1) ,(6,2) ,(6,3) ,(6,7) ,(6,8)] * Step 3: UnreachableRules MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (1,1) 8. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && B >= 1 + A] (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3},4->{7},5->{7},6->{4,5,6},7->{},8->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [8] * Step 4: AddSinks MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3},4->{7},5->{7},6->{4,5,6},7->{}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 8. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7,8},1->{1,2,3,4,5,6,7,8},2->{1,2,3,4,5,6,7,8},3->{1,2,3,4,5,6,7,8},4->{1,2,3,4,5,6,7,8} ,5->{1,2,3,4,5,6,7,8},6->{1,2,3,4,5,6,7,8},7->{},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,7) ,(2,7) ,(3,4) ,(3,5) ,(3,6) ,(3,7) ,(4,1) ,(4,2) ,(4,3) ,(4,4) ,(4,5) ,(4,6) ,(5,1) ,(5,2) ,(5,3) ,(5,4) ,(5,5) ,(5,6) ,(6,1) ,(6,2) ,(6,3) ,(6,7)] * Step 6: Failure MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 8. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7,8},1->{1,2,3,4,5,6,8},2->{1,2,3,4,5,6,8},3->{1,2,3,8},4->{7,8},5->{7,8},6->{4,5,6,8} ,7->{},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[1,2,3] c: [2] | | | `- p:[1,3] c: [1] | | | `- p:[3] c: [] | `- p:[6] c: [] MAYBE