MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 2. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 3. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{1,2,3},3->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1),(2,3),(3,2)] * Step 2: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 2. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 3. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{2},3->{1,3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f300(A,B,D) [A = B] (1,1) 2. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 3. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{2},3->{1,3}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = -1*x1 + x2 p(f2) = -1*x1 + x2 p(f300) = -1*x1 + x2 Following rules are strictly oriented: [B >= 1 + A] ==> f2(A,B,C) = -1*A + B > -1 + -1*A + B = f2(1 + A,B,C) Following rules are weakly oriented: True ==> f1(A,B,C) = -1*A + B >= -1*A + B = f2(A,B,C) [A = B] ==> f2(A,B,C) = -1*A + B >= -1*A + B = f300(A,B,D) [A >= 1 + B && A >= B] ==> f2(A,B,C) = -1*A + B >= -1 + -1*A + B = f2(1 + A,B,C) * Step 4: Failure MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,C) True (1,1) 1. f2(A,B,C) -> f300(A,B,D) [A = B] (1,1) 2. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 3. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (A + B,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{2},3->{1,3}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE