YES * Step 1: 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 && 99 >= A && 99 >= D] (?,1) 2. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 99 >= A] (?,1) 3. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A] (?,1) 5. f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 99 >= A] (?,1) 6. f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0 && 98 >= D] (?,1) 8. f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 100] (?,1) 9. f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 99 >= A] (?,1) 10. f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0] 11. f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0 && 98 >= D] 12. f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 100] (?,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 2: FromIts 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 && 99 >= A && 99 >= D] (?,1) 2. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 99 >= A] (?,1) 3. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A] (?,1) 5. f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 99 >= A] (?,1) 6. f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0 && 98 >= D] (?,1) 8. f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 100] (?,1) 9. f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 99 >= A] (?,1) 10. f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0] 11. f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0 && 98 >= D] 12. f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 100] (?,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: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C) -> f8(0,B,C) True f8(A,B,C) -> f14(A,A,C) [A >= 0 && 99 >= A && 99 >= D] f8(A,B,C) -> f14(A,A,C) [A >= 0 && 99 >= A] f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A && 0 >= 1 + E] f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A] f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 99 >= A] f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0] f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0 && 98 >= D] f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 100] f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 99 >= A] f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0] f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0 && 98 >= D] f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 100] Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Rule 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: Decompose NoGreedy + 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: [1,2,10] | | | `- p:[9] c: [9] | `- p:[3,5,6,4,7] c: [7] | `- p:[3,5,6,4] c: [3,4,6] | `- p:[5] c: [5] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C) -> f8(0,B,C) True f8(A,B,C) -> f14(A,A,C) [A >= 0 && 99 >= A && 99 >= D] f8(A,B,C) -> f14(A,A,C) [A >= 0 && 99 >= A] f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A && 0 >= 1 + E] f23(A,B,C) -> f28(A,B,D) [A >= 0 && 99 >= A] f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 99 >= A] f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0] f28(A,B,C) -> f23(1 + A,B,C) [99 + -1*A >= 0 && A >= 0 && 98 >= D] f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 100] f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 99 >= A] f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0] f14(A,B,C) -> f8(1 + A,B,C) [99 + -1*B >= 0 && A + -1*B >= 0 && 198 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 99 + -1*A >= 0 && A >= 0 && 98 >= D] f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 100] Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Rule 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}] ,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: [1,2,10] | | | `- p:[9] c: [9] | `- p:[3,5,6,4,7] c: [7] | `- p:[3,5,6,4] c: [3,4,6] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES