YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (?,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (?,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (?,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,4)] * Step 2: FromIts YES + Considered Problem: Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (?,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (?,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (?,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Flow Graph: [0->{1},1->{2,3},2->{5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Rule Graph: [0->{1},1->{2,3},2->{5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,10,4,9,6,5,7,8] c: [2,4,5,6,7,8,9,10] * Step 4: CloseWith YES + Considered Problem: (Rules: evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Rule Graph: [0->{1},1->{2,3},2->{5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,10,4,9,6,5,7,8] c: [2,4,5,6,7,8,9,10]) + Applied Processor: CloseWith True + Details: () YES