MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(C,B,A) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && 0 >= C] (?,1) 4. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && C >= B] (?,1) 5. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] (?,1) 6. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] (?,1) 7. evalfbb1in(A,B,C) -> evalfbb3in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,-1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] 9. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-2 + B >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{9},4->{9},5->{7},6->{8},7->{2,3,4},8->{2,3,4},9->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(1,4),(7,3),(8,4)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(C,B,A) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && 0 >= C] (?,1) 4. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && C >= B] (?,1) 5. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] (?,1) 6. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] (?,1) 7. evalfbb1in(A,B,C) -> evalfbb3in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,-1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] 9. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-2 + B >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2},2->{5,6},3->{9},4->{9},5->{7},6->{8},7->{2,4},8->{2,3},9->{}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb3in(C,B,A) [A >= 1 && B >= 1 + A] evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && 0 >= C] evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && C >= B] evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] evalfbb1in(A,B,C) -> evalfbb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] evalfbb2in(A,B,C) -> evalfbb3in(A,B,-1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-2 + B >= 0] Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Rule Graph: [0->{1},1->{2},2->{5,6},3->{9},4->{9},5->{7},6->{8},7->{2,4},8->{2,3},9->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb3in.2(C,B,A) [A >= 1 && B >= 1 + A] evalfbb3in.2(A,B,C) -> evalfbbin.5(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] evalfbb3in.2(A,B,C) -> evalfbbin.6(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] evalfbb3in.3(A,B,C) -> evalfreturnin.9(A,B,C) [-2 + B >= 0 && 0 >= C] evalfbb3in.4(A,B,C) -> evalfreturnin.9(A,B,C) [-2 + B >= 0 && C >= B] evalfbbin.5(A,B,C) -> evalfbb1in.7(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] evalfbbin.6(A,B,C) -> evalfbb2in.8(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] evalfbb1in.7(A,B,C) -> evalfbb3in.2(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] evalfbb1in.7(A,B,C) -> evalfbb3in.4(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] evalfbb2in.8(A,B,C) -> evalfbb3in.2(A,B,-1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] evalfbb2in.8(A,B,C) -> evalfbb3in.3(A,B,-1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] evalfreturnin.9(A,B,C) -> evalfstop.10(A,B,C) [-2 + B >= 0] Signature: {(evalfbb1in.7,3) ;(evalfbb2in.8,3) ;(evalfbb3in.2,3) ;(evalfbb3in.3,3) ;(evalfbb3in.4,3) ;(evalfbbin.5,3) ;(evalfbbin.6,3) ;(evalfentryin.1,3) ;(evalfreturnin.9,3) ;(evalfstart.0,3) ;(evalfstop.10,3)} Rule Graph: [0->{1},1->{2,3},2->{6},3->{7},4->{12},5->{12},6->{8,9},7->{10,11},8->{2,3},9->{5},10->{2,3},11->{4} ,12->{}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb3in.2(C,B,A) [A >= 1 && B >= 1 + A] evalfbb3in.2(A,B,C) -> evalfbbin.5(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] evalfbb3in.2(A,B,C) -> evalfbbin.6(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] evalfbb3in.3(A,B,C) -> evalfreturnin.9(A,B,C) [-2 + B >= 0 && 0 >= C] evalfbb3in.4(A,B,C) -> evalfreturnin.9(A,B,C) [-2 + B >= 0 && C >= B] evalfbbin.5(A,B,C) -> evalfbb1in.7(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] evalfbbin.6(A,B,C) -> evalfbb2in.8(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] evalfbb1in.7(A,B,C) -> evalfbb3in.2(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] evalfbb1in.7(A,B,C) -> evalfbb3in.4(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] evalfbb2in.8(A,B,C) -> evalfbb3in.2(A,B,-1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] evalfbb2in.8(A,B,C) -> evalfbb3in.3(A,B,-1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] evalfreturnin.9(A,B,C) -> evalfstop.10(A,B,C) [-2 + B >= 0] evalfstop.10(A,B,C) -> exitus616(A,B,C) True evalfstop.10(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in.7,3) ;(evalfbb2in.8,3) ;(evalfbb3in.2,3) ;(evalfbb3in.3,3) ;(evalfbb3in.4,3) ;(evalfbbin.5,3) ;(evalfbbin.6,3) ;(evalfentryin.1,3) ;(evalfreturnin.9,3) ;(evalfstart.0,3) ;(evalfstop.10,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{6},3->{7},4->{12},5->{12},6->{8,9},7->{10,11},8->{2,3},9->{5},10->{2,3},11->{4} ,12->{13,14}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[2,8,6,10,7,3] c: [] MAYBE