YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval0(A,B,C,D) -> eval1(B,B,1,D) True (1,1) 1. eval1(A,B,C,D) -> end(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 101] (?,1) 2. eval1(A,B,C,D) -> eval3(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 100 >= A] (?,1) 3. eval3(A,B,C,D) -> eval3(11 + A,B,1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && 100 >= A] (?,1) 4. eval3(A,B,C,D) -> eval5(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && A >= 101] (?,1) 5. eval5(A,B,C,D) -> eval7(-10 + A,B,-1 + C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -102 + A + C >= 0 && 100 + -1*B >= 0 && -1 + A + -1*B >= 0 && -101 + A >= 0 && C >= 2] 6. eval7(A,B,C,D) -> eval5(A,B,C,-10 + A) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101 && C = 1] 7. eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] 8. eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 2 >= C] 9. eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && C >= 0] 10. eval9(A,B,C,D) -> eval11(-10 + A,B,-1 + C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101] 11. eval9(A,B,C,D) -> eval11(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] 12. eval11(A,B,C,D) -> eval5(11 + A,B,1 + C,D) [C >= 0 && 100 + -1*B + C >= 0 && -91 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0] (?,1) Signature: {(end,4);(eval0,4);(eval1,4);(eval11,4);(eval3,4);(eval5,4);(eval7,4);(eval9,4)} Flow Graph: [0->{1,2},1->{},2->{3,4},3->{3,4},4->{5},5->{6,7,8,9},6->{5},7->{10,11},8->{10,11},9->{10,11},10->{12} ,11->{12},12->{5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,4),(6,5),(7,10)] * Step 2: FromIts YES + Considered Problem: Rules: 0. eval0(A,B,C,D) -> eval1(B,B,1,D) True (1,1) 1. eval1(A,B,C,D) -> end(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 101] (?,1) 2. eval1(A,B,C,D) -> eval3(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 100 >= A] (?,1) 3. eval3(A,B,C,D) -> eval3(11 + A,B,1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && 100 >= A] (?,1) 4. eval3(A,B,C,D) -> eval5(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && A >= 101] (?,1) 5. eval5(A,B,C,D) -> eval7(-10 + A,B,-1 + C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -102 + A + C >= 0 && 100 + -1*B >= 0 && -1 + A + -1*B >= 0 && -101 + A >= 0 && C >= 2] 6. eval7(A,B,C,D) -> eval5(A,B,C,-10 + A) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101 && C = 1] 7. eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] 8. eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 2 >= C] 9. eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && C >= 0] 10. eval9(A,B,C,D) -> eval11(-10 + A,B,-1 + C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101] 11. eval9(A,B,C,D) -> eval11(A,B,C,D) [-1 + C >= 0 (?,1) && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] 12. eval11(A,B,C,D) -> eval5(11 + A,B,1 + C,D) [C >= 0 && 100 + -1*B + C >= 0 && -91 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0] (?,1) Signature: {(end,4);(eval0,4);(eval1,4);(eval11,4);(eval3,4);(eval5,4);(eval7,4);(eval9,4)} Flow Graph: [0->{1,2},1->{},2->{3},3->{3,4},4->{5},5->{6,7,8,9},6->{},7->{11},8->{10,11},9->{10,11},10->{12},11->{12} ,12->{5}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: eval0(A,B,C,D) -> eval1(B,B,1,D) True eval1(A,B,C,D) -> end(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 101] eval1(A,B,C,D) -> eval3(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 100 >= A] eval3(A,B,C,D) -> eval3(11 + A,B,1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && 100 >= A] eval3(A,B,C,D) -> eval5(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && A >= 101] eval5(A,B,C,D) -> eval7(-10 + A,B,-1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -102 + A + C >= 0 && 100 + -1*B >= 0 && -1 + A + -1*B >= 0 && -101 + A >= 0 && C >= 2] eval7(A,B,C,D) -> eval5(A,B,C,-10 + A) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101 && C = 1] eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 2 >= C] eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && C >= 0] eval9(A,B,C,D) -> eval11(-10 + A,B,-1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101] eval9(A,B,C,D) -> eval11(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] eval11(A,B,C,D) -> eval5(11 + A,B,1 + C,D) [C >= 0 && 100 + -1*B + C >= 0 && -91 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0] Signature: {(end,4);(eval0,4);(eval1,4);(eval11,4);(eval3,4);(eval5,4);(eval7,4);(eval9,4)} Rule Graph: [0->{1,2},1->{},2->{3},3->{3,4},4->{5},5->{6,7,8,9},6->{},7->{11},8->{10,11},9->{10,11},10->{12},11->{12} ,12->{5}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | +- p:[3] c: [3] | `- p:[5,12,10,8,9,11,7] c: [10] | `- p:[5,12,11,7,8,9] c: [7] | `- p:[5,12,11,8,9] c: [5,8,9,11,12] * Step 4: CloseWith YES + Considered Problem: (Rules: eval0(A,B,C,D) -> eval1(B,B,1,D) True eval1(A,B,C,D) -> end(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 101] eval1(A,B,C,D) -> eval3(A,B,C,D) [1 + -1*C >= 0 && -1 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 100 >= A] eval3(A,B,C,D) -> eval3(11 + A,B,1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && 100 >= A] eval3(A,B,C,D) -> eval5(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && 100 + -1*B >= 0 && A + -1*B >= 0 && A >= 101] eval5(A,B,C,D) -> eval7(-10 + A,B,-1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -102 + A + C >= 0 && 100 + -1*B >= 0 && -1 + A + -1*B >= 0 && -101 + A >= 0 && C >= 2] eval7(A,B,C,D) -> eval5(A,B,C,-10 + A) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101 && C = 1] eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 2 >= C] eval7(A,B,C,D) -> eval9(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && C >= 0] eval9(A,B,C,D) -> eval11(-10 + A,B,-1 + C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && A >= 101] eval9(A,B,C,D) -> eval11(A,B,C,D) [-1 + C >= 0 && 99 + -1*B + C >= 0 && -92 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0 && 100 >= A] eval11(A,B,C,D) -> eval5(11 + A,B,1 + C,D) [C >= 0 && 100 + -1*B + C >= 0 && -91 + A + C >= 0 && 100 + -1*B >= 0 && 9 + A + -1*B >= 0 && -91 + A >= 0] Signature: {(end,4);(eval0,4);(eval1,4);(eval11,4);(eval3,4);(eval5,4);(eval7,4);(eval9,4)} Rule Graph: [0->{1,2},1->{},2->{3},3->{3,4},4->{5},5->{6,7,8,9},6->{},7->{11},8->{10,11},9->{10,11},10->{12},11->{12} ,12->{5}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | +- p:[3] c: [3] | `- p:[5,12,10,8,9,11,7] c: [10] | `- p:[5,12,11,7,8,9] c: [7] | `- p:[5,12,11,8,9] c: [5,8,9,11,12]) + Applied Processor: CloseWith True + Details: () YES