YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 2: FromIts YES + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 0] Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,7,5,6,4] c: [2,5,7] | `- p:[4,6] c: [4,6] * Step 4: CloseWith YES + Considered Problem: (Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 0] Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,7,5,6,4] c: [2,5,7] | `- p:[4,6] c: [4,6]) + Applied Processor: CloseWith True + Details: () YES