YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C) -> f3(-1*A,B,C) True (?,1) 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1) 6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C] (?,1) 7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2] (?,1) 8. f4(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f5(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 11. f5(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4,5,6,7},1->{},2->{},3->{2,8,9},4->{2,8,9},5->{2,8,9},6->{2,8,9},7->{2,8,9},8->{1,4,5,6,7},9->{1,4 ,5,6,7},10->{1,4,5,6,7},11->{1,4,5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,2) ,(3,8) ,(4,8) ,(5,8) ,(6,2) ,(6,9) ,(7,2) ,(7,9) ,(8,1) ,(8,4) ,(8,5) ,(8,7) ,(9,5) ,(9,6) ,(9,7) ,(10,1) ,(10,4) ,(10,5) ,(10,7) ,(11,5) ,(11,6) ,(11,7)] * Step 2: UnreachableRules YES + Considered Problem: Rules: 0. f0(A,B,C) -> f3(-1*A,B,C) True (?,1) 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1) 6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C] (?,1) 7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2] (?,1) 8. f4(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f5(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 11. f5(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4,5,6,7},1->{},2->{},3->{9},4->{2,9},5->{2,9},6->{8},7->{8},8->{6},9->{1,4},10->{6},11->{1,4}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [0,5,6,7,8,10,11] * Step 3: FromIts YES + Considered Problem: Rules: 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [1->{},2->{},3->{9},4->{2,9},9->{1,4}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: f3(A,B,C) -> f7(0,D,C) [A = 0] f4(A,B,C) -> f7(0,D,C) [A = 0] f6(A,B,C) -> f4(A,B,1) [A >= 1] f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Rule Graph: [1->{},2->{},3->{9},4->{2,9},9->{1,4}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [1,2,3,4,9] | `- p:[9,4] c: [4,9] * Step 5: CloseWith YES + Considered Problem: (Rules: f3(A,B,C) -> f7(0,D,C) [A = 0] f4(A,B,C) -> f7(0,D,C) [A = 0] f6(A,B,C) -> f4(A,B,1) [A >= 1] f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Rule Graph: [1->{},2->{},3->{9},4->{2,9},9->{1,4}] ,We construct a looptree: P: [1,2,3,4,9] | `- p:[9,4] c: [4,9]) + Applied Processor: CloseWith True + Details: () YES