MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(B,B,D,D) True (1,1) 1. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] (?,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] (?,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] (?,1) Signature: {(f0,4);(f14,4);(f6,4)} Flow Graph: [0->{1,2,3,4,5},1->{1,2,3,4,5},2->{1,2,3,4,5},3->{},4->{},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(1,3),(1,4),(1,5),(2,1)] * Step 2: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(B,B,D,D) True (1,1) 1. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] (?,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] (?,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] (?,1) Signature: {(f0,4);(f14,4);(f6,4)} Flow Graph: [0->{1,2,3,4,5},1->{1},2->{2,3,4,5},3->{},4->{},5->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(B,B,D,D) True (1,1) 1. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] (1,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] (1,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] (1,1) Signature: {(f0,4);(f14,4);(f6,4)} Flow Graph: [0->{1,2,3,4,5},1->{1},2->{2,3,4,5},3->{},4->{},5->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = x2 p(f14) = 0 p(f6) = x1 Following rules are strictly oriented: [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] ==> f6(A,B,C,D) = A > -1 + A = f6(-1 + A,B,-1 + C,D) Following rules are weakly oriented: True ==> f0(A,B,C,D) = B >= B = f6(B,B,D,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] ==> f6(A,B,C,D) = A >= -1 + A = f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] ==> f6(A,B,C,D) = A >= 0 = f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] ==> f6(A,B,C,D) = A >= 0 = f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] ==> f6(A,B,C,D) = A >= 0 = f14(0,B,C,B) * Step 4: Failure MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(B,B,D,D) True (1,1) 1. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 2. f6(A,B,C,D) -> f6(-1 + A,B,-1 + C,D) [-1*C + D >= 0 && -1*A + B >= 0 && A >= 1] (B,1) 3. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && D >= 1 + B && A = 0] (1,1) 4. f6(A,B,C,D) -> f14(0,B,C,D) [-1*C + D >= 0 && -1*A + B >= 0 && B >= 1 + D && A = 0] (1,1) 5. f6(A,B,C,D) -> f14(0,B,C,B) [-1*C + D >= 0 && -1*A + B >= 0 && A = 0 && B = D] (1,1) Signature: {(f0,4);(f14,4);(f6,4)} Flow Graph: [0->{1,2,3,4,5},1->{1},2->{2,3,4,5},3->{},4->{},5->{}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE