MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 2: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + 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,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (1,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 8 p(f11) = 8 + -1*x3 p(f21) = 8 + -1*x3 Following rules are strictly oriented: [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11(A,B,C,D,E) = 8 + -1*C > 7 + -1*C = f11(-1 + A,-1 + B,1 + C,F,E) Following rules are weakly oriented: [F >= 1] ==> f0(A,B,C,D,E) = 8 >= 8 = f11(8,F,0,D,8) [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11(A,B,C,D,E) = 8 + -1*C >= 8 + -1*C = f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] f11(A,B,C,D,E) = 8 + -1*C >= 8 + -1*C = f21(A,B,C,D,E) [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] f21(A,B,C,D,E) = 8 + -1*C >= 8 + -1*C = f21(A,B,C,D,E) * Step 4: PolyRank MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (8,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (1,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 8 p(f11) = x1 p(f21) = x1 Following rules are strictly oriented: [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11(A,B,C,D,E) = A > -1 + A = f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11(A,B,C,D,E) = A > -1 + A = f11(-1 + A,-1 + B,1 + C,F,E) Following rules are weakly oriented: [F >= 1] ==> f0(A,B,C,D,E) = 8 >= 8 = f11(8,F,0,D,8) [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] f11(A,B,C,D,E) = A >= A = f21(A,B,C,D,E) [8 + -1*E >= 0 ==> && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] f21(A,B,C,D,E) = A >= A = f21(A,B,C,D,E) * Step 5: Failure MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (8,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (8,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (1,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE