MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{},1->{0,1,2,3,4,5,6},2->{0,1,2,3,4,5,6},3->{0,1,2,3,4,5,6},4->{0,1,2,3,4,5,6},5->{0,1,2,3,4,5,6} ,6->{0,1,2,3,4,5,6},7->{0,1,2,3,4,5,6}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (1,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{},1->{0,1,2,3,4,5,6},2->{0,1,2,3,4,5,6},3->{0,1,2,3,4,5,6},4->{0,1,2,3,4,5,6},5->{0,1,2,3,4,5,6} ,6->{0,1,2,3,4,5,6},7->{0,1,2,3,4,5,6}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,0) ,(1,4) ,(1,5) ,(1,6) ,(2,1) ,(2,2) ,(2,3) ,(2,4) ,(2,5) ,(2,6) ,(3,1) ,(3,2) ,(3,3) ,(3,4) ,(3,5) ,(3,6) ,(4,0) ,(4,1) ,(4,2) ,(4,3) ,(5,0) ,(6,0)] * Step 3: AddSinks MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (1,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{},1->{1,2,3},2->{0},3->{0},4->{4,5,6},5->{1,2,3,4,5,6},6->{1,2,3,4,5,6},7->{0,1,2,3,4,5,6}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 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->{0,1,2,3,4,5,6,8},2->{0,1,2,3,4,5,6,8},3->{0,1,2,3,4,5,6,8},4->{0,1,2,3,4,5,6,8},5->{0,1,2,3,4,5 ,6,8},6->{0,1,2,3,4,5,6,8},7->{0,1,2,3,4,5,6,8},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,0) ,(1,4) ,(1,5) ,(1,6) ,(2,1) ,(2,2) ,(2,3) ,(2,4) ,(2,5) ,(2,6) ,(3,1) ,(3,2) ,(3,3) ,(3,4) ,(3,5) ,(3,6) ,(4,0) ,(4,1) ,(4,2) ,(4,3) ,(5,0) ,(6,0)] * Step 5: Failure MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 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->{1,2,3,8},2->{0,8},3->{0,8},4->{4,5,6,8},5->{1,2,3,4,5,6,8},6->{1,2,3,4,5,6,8},7->{0,1,2,3,4,5,6 ,8},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[4,5,6] c: [6] | | | `- p:[4,5] c: [5] | | | `- p:[4] c: [] | `- p:[1] c: [] MAYBE