MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [-1 + C >= 0 && -1 + A + C >= 0 && A >= 0] (?,1) 1. f3(A,B,C) -> f3(A,-1 + B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f5(A,B,C) -> f5(A,B,1) [-1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && A >= 0] (?,1) 3. f0(A,B,C) -> f2(0,B,C) [C >= 1] (1,1) 4. f0(A,B,C) -> f3(0,B,C) [0 >= C] (1,1) 5. f3(A,B,C) -> f5(0,B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && 0 >= B] (?,1) Signature: {(f0,3);(f2,3);(f3,3);(f5,3)} Flow Graph: [0->{0},1->{1,5},2->{2},3->{0},4->{1,5},5->{2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [-1 + C >= 0 && -1 + A + C >= 0 && A >= 0] (?,1) 1. f3(A,B,C) -> f3(A,-1 + B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f5(A,B,C) -> f5(A,B,1) [-1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && A >= 0] (?,1) 3. f0(A,B,C) -> f2(0,B,C) [C >= 1] (1,1) 4. f0(A,B,C) -> f3(0,B,C) [0 >= C] (1,1) 5. f3(A,B,C) -> f5(0,B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && 0 >= B] (1,1) Signature: {(f0,3);(f2,3);(f3,3);(f5,3)} Flow Graph: [0->{0},1->{1,5},2->{2},3->{0},4->{1,5},5->{2}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = x2 p(f2) = x2 p(f3) = x2 p(f5) = x2 Following rules are strictly oriented: [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && B >= 1] ==> f3(A,B,C) = B > -1 + B = f3(A,-1 + B,C) Following rules are weakly oriented: [-1 + C >= 0 && -1 + A + C >= 0 && A >= 0] ==> f2(A,B,C) = B >= B = f2(1 + A,B,C) [-1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && A >= 0] ==> f5(A,B,C) = B >= B = f5(A,B,1) [C >= 1] ==> f0(A,B,C) = B >= B = f2(0,B,C) [0 >= C] ==> f0(A,B,C) = B >= B = f3(0,B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && 0 >= B] ==> f3(A,B,C) = B >= B = f5(0,B,C) * Step 3: Failure MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [-1 + C >= 0 && -1 + A + C >= 0 && A >= 0] (?,1) 1. f3(A,B,C) -> f3(A,-1 + B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && B >= 1] (B,1) 2. f5(A,B,C) -> f5(A,B,1) [-1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && -1*A >= 0 && A >= 0] (?,1) 3. f0(A,B,C) -> f2(0,B,C) [C >= 1] (1,1) 4. f0(A,B,C) -> f3(0,B,C) [0 >= C] (1,1) 5. f3(A,B,C) -> f5(0,B,C) [-1*C >= 0 && A + -1*C >= 0 && -1*A + -1*C >= 0 && -1*A >= 0 && A >= 0 && 0 >= B] (1,1) Signature: {(f0,3);(f2,3);(f3,3);(f5,3)} Flow Graph: [0->{0},1->{1,5},2->{2},3->{0},4->{1,5},5->{2}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE