MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] (1,1) 1. f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] 2. f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] 3. f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] 4. f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 (?,1) && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f0(A,B,C,D,E) -> f11(8,F,0,D,8) [F >= 1] f11(A,B,C,D,E) -> f11(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11(A,B,C,D,E) -> f11(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] f21(A,B,C,D,E) -> f21(A,B,C,D,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0,5);(f11,5);(f21,5)} Rule Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f0.0(A,B,C,D,E) -> f11.1(8,F,0,D,8) [F >= 1] f0.0(A,B,C,D,E) -> f11.2(8,F,0,D,8) [F >= 1] f11.1(A,B,C,D,E) -> f11.1(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11.1(A,B,C,D,E) -> f11.2(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11.1(A,B,C,D,E) -> f11.3(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11.2(A,B,C,D,E) -> f11.1(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11.2(A,B,C,D,E) -> f11.2(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11.2(A,B,C,D,E) -> f11.3(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11.3(A,B,C,D,E) -> f21.4(A,B,C,D,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] f21.4(A,B,C,D,E) -> f21.4(A,B,C,D,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] Signature: {(f0.0,5);(f11.1,5);(f11.2,5);(f11.3,5);(f21.4,5)} Rule Graph: [0->{2,3,4},1->{5,6,7},2->{2,3,4},3->{5,6,7},4->{8},5->{2,3,4},6->{5,6,7},7->{8},8->{9},9->{9}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f0.0(A,B,C,D,E) -> f11.1(8,F,0,D,8) [F >= 1] f0.0(A,B,C,D,E) -> f11.2(8,F,0,D,8) [F >= 1] f11.1(A,B,C,D,E) -> f11.1(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11.1(A,B,C,D,E) -> f11.2(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11.1(A,B,C,D,E) -> f11.3(-1 + A,B,C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= F && A >= 1 && A >= 1 + B] f11.2(A,B,C,D,E) -> f11.1(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11.2(A,B,C,D,E) -> f11.2(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11.2(A,B,C,D,E) -> f11.3(-1 + A,-1 + B,1 + C,F,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && A >= 1 && F >= 1] f11.3(A,B,C,D,E) -> f21.4(A,B,C,D,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 16 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && 8 + -1*A + C >= 0 && 7 + -1*A + B >= 0 && 8 + -1*A >= 0 && 0 >= A] f21.4(A,B,C,D,E) -> f21.4(A,B,C,D,E) [8 + -1*E >= 0 && 8 + C + -1*E >= 0 && 8 + -1*A + -1*E >= 0 && -8 + E >= 0 && -8 + C + E >= 0 && -8 + -1*A + E >= 0 && 8 + -1*A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1*A + C >= 0 && 7 + -1*A + B >= 0 && -1*A >= 0] f21.4(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f21.4(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f21.4(A,B,C,D,E) -> exitus616(A,B,C,D,E) True f21.4(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(exitus616,5);(f0.0,5);(f11.1,5);(f11.2,5);(f11.3,5);(f21.4,5)} Rule Graph: [0->{2,3,4},1->{5,6,7},2->{2,3,4},3->{5,6,7},4->{8},5->{2,3,4},6->{5,6,7},7->{8},8->{9},9->{9,10,11,12 ,13}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[2,5,3,6] c: [2,3,5,6] | `- p:[9] c: [] MAYBE