MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f1(A,B,C) -> f4(A,B,D) [-1*A >= 0 && A >= 0 && 0 >= B] (?,1) 3. f4(A,B,C) -> f4(1,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f1(A,B,C) -> f4(A,B,D) [-1*A >= 0 && A >= 0 && 0 >= B] (1,1) 3. f4(A,B,C) -> f4(1,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = x2 p(f1) = x2 p(f4) = x2 Following rules are strictly oriented: [-1*A >= 0 && A >= 0 && B >= 1] ==> f1(A,B,C) = B > -1 + B = f1(A,-1 + B,D) Following rules are weakly oriented: True ==> f0(A,B,C) = B >= B = f1(0,B,C) [-1*A >= 0 && A >= 0 && 0 >= B] ==> f1(A,B,C) = B >= B = f4(A,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] ==> f4(A,B,C) = B >= B = f4(1,B,D) * Step 3: Failure MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [-1*A >= 0 && A >= 0 && B >= 1] (B,1) 2. f1(A,B,C) -> f4(A,B,D) [-1*A >= 0 && A >= 0 && 0 >= B] (1,1) 3. f4(A,B,C) -> f4(1,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE