YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (?,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{4,5,6,7},9->{4,5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(8,4),(9,4)] * Step 2: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (?,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f10) = 10 p(f16) = 10 + -1*x1 p(f28) = 10 + -1*x1 p(f9) = 10 Following rules are strictly oriented: [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A > 9 + -1*A = f16(1 + A,B,C,D,A,H,H) Following rules are weakly oriented: True ==> f0(A,B,C,D,E,F,G) = 10 >= 10 = f9(0,0,H,D,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] ==> f9(A,B,C,D,E,F,G) = 10 >= 10 = f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] ==> f9(A,B,C,D,E,F,G) = 10 >= 10 = f10(A,B,C,C,E,F,G) [C + -1*D >= 0 ==> && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] f10(A,B,C,D,E,F,G) = 10 >= 10 = f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A >= 10 + -1*A = f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A >= 9 + -1*A = f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A >= 10 + -1*A = f28(A,B,C,D,A,0,0) [C + -1*D >= 0 ==> && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] f10(A,B,C,D,E,F,G) = 10 >= 10 = f16(0,B,C,D,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] ==> f9(A,B,C,D,E,F,G) = 10 >= 10 = f16(0,B,0,0,E,F,G) * Step 4: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (10,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f10) = 10 p(f16) = 10 + -1*x1 p(f28) = 10 + -1*x1 p(f9) = 10 Following rules are strictly oriented: [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A > 9 + -1*A = f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A > 9 + -1*A = f16(1 + A,B,C,D,A,H,H) Following rules are weakly oriented: True ==> f0(A,B,C,D,E,F,G) = 10 >= 10 = f9(0,0,H,D,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] ==> f9(A,B,C,D,E,F,G) = 10 >= 10 = f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] ==> f9(A,B,C,D,E,F,G) = 10 >= 10 = f10(A,B,C,C,E,F,G) [C + -1*D >= 0 ==> && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] f10(A,B,C,D,E,F,G) = 10 >= 10 = f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A >= 10 + -1*A = f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] ==> f16(A,B,C,D,E,F,G) = 10 + -1*A >= 10 + -1*A = f28(A,B,C,D,A,0,0) [C + -1*D >= 0 ==> && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] f10(A,B,C,D,E,F,G) = 10 >= 10 = f16(0,B,C,D,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] ==> f9(A,B,C,D,E,F,G) = 10 >= 10 = f16(0,B,0,0,E,F,G) * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (10,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (10,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f10) = 10 + -1*x1 p(f16) = -1*x2 p(f28) = -1*x2 p(f9) = 10 + -1*x2 Following rules are strictly oriented: [C + -1*D >= 0 ==> && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] f10(A,B,C,D,E,F,G) = 10 + -1*A > 9 + -1*A = f9(1 + A,1 + A,H,D,E,F,G) Following rules are weakly oriented: True ==> f0(A,B,C,D,E,F,G) = 10 >= 10 = f9(0,0,H,D,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] ==> f9(A,B,C,D,E,F,G) = 10 + -1*B >= 10 + -1*A = f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] ==> f9(A,B,C,D,E,F,G) = 10 + -1*B >= 10 + -1*A = f10(A,B,C,C,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] ==> f16(A,B,C,D,E,F,G) = -1*B >= -1*B = f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] ==> f16(A,B,C,D,E,F,G) = -1*B >= -1*B = f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] ==> f16(A,B,C,D,E,F,G) = -1*B >= -1*B = f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] ==> f16(A,B,C,D,E,F,G) = -1*B >= -1*B = f28(A,B,C,D,A,0,0) [C + -1*D >= 0 ==> && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] f10(A,B,C,D,E,F,G) = 10 + -1*A >= -1*B = f16(0,B,C,D,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] ==> f9(A,B,C,D,E,F,G) = 10 + -1*B >= -1*B = f16(0,B,0,0,E,F,G) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (10,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (10,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (10,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 7: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (11,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (11,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (10,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (10,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (10,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(1))