YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,B,C) True (1,1) 1. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A && 9 >= D] (?,1) 2. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A] (?,1) 3. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A] (?,1) 5. f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 9 >= A] (?,1) 6. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0 && 8 >= D] (?,1) 8. f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 10] (?,1) 9. f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 9 >= A] (?,1) 10. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] 11. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] 12. f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 10] (?,1) Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Flow Graph: [0->{1,2,9,12},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1 ,2,9,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5,8}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,B,C) True (1,1) 1. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A && 9 >= D] (?,1) 2. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A] (?,1) 3. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A] (?,1) 5. f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 9 >= A] (?,1) 6. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0 && 8 >= D] (?,1) 8. f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 10] (1,1) 9. f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 9 >= A] (?,1) 10. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] 11. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] 12. f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 10] (1,1) Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Flow Graph: [0->{1,2,9,12},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1 ,2,9,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12),(12,8)] * Step 3: Looptree YES + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,B,C) True (1,1) 1. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A && 9 >= D] (?,1) 2. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A] (?,1) 3. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A] (?,1) 5. f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 9 >= A] (?,1) 6. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0 && 8 >= D] (?,1) 8. f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 10] (1,1) 9. f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 9 >= A] (?,1) 10. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] 11. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] 12. f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 10] (1,1) Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Flow Graph: [0->{1,2,9},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1,2,9 ,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | +- p:[1,9,10,2,11] c: [11] | | | `- p:[1,9,10,2] c: [10] | | | `- p:[9] c: [9] | `- p:[3,5,6,4,7] c: [7] | `- p:[3,5,6,4] c: [6] | `- p:[5] c: [5] YES