YES * Step 1: UnsatRules YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (?,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (?,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (?,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) 13. f5(A,B,C,D,E,F,G) -> f17(A,-2 + A,C,-2 + A,E,F,G) [0 >= 1 + A && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,12,13},1->{1,12,13},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7 ,8},7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{},13->{2,3,4,9,10,11}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [13] * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (?,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (?,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (?,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,12},1->{1,12},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7,8} ,7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12)] * Step 3: UnreachableRules YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (?,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (?,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (?,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1},1->{1,12},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7,8},7->{5 ,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [2,3,4,5,6,7,8,9,10,11] * Step 4: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1},1->{1,12},12->{}] + Applied Processor: FromIts + Details: () * Step 5: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Rule Graph: [0->{1},1->{1,12},12->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,12] | `- p:[1] c: [1] * Step 6: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Rule Graph: [0->{1},1->{1,12},12->{}] ,We construct a looptree: P: [0,1,12] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES