MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f15(2,B,C) True (1,1) 1. f15(A,B,C) -> f18(A,A,C) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B,C) -> f18(A,-1 + B,F) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B,C) -> f15(1 + A,B,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (?,1) 4. f15(A,B,C) -> f28(A,B,C) [-2 + A >= 0 && A >= 11] (?,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1,4},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4)] * Step 2: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f15(2,B,C) True (1,1) 1. f15(A,B,C) -> f18(A,A,C) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B,C) -> f18(A,-1 + B,F) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B,C) -> f15(1 + A,B,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (?,1) 4. f15(A,B,C) -> f28(A,B,C) [-2 + A >= 0 && A >= 11] (?,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f15(2,B,C) True (1,1) 1. f15(A,B,C) -> f18(A,A,C) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B,C) -> f18(A,-1 + B,F) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B,C) -> f15(1 + A,B,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (?,1) 4. f15(A,B,C) -> f28(A,B,C) [-2 + A >= 0 && A >= 11] (1,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 9 p(f15) = 11 + -1*x1 p(f18) = 11 + -1*x1 p(f28) = 11 + -1*x1 Following rules are strictly oriented: [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] ==> f18(A,B,C) = 11 + -1*A > 10 + -1*A = f15(1 + A,B,C) Following rules are weakly oriented: True ==> f0(A,B,C) = 9 >= 9 = f15(2,B,C) [-2 + A >= 0 && 10 >= A] ==> f15(A,B,C) = 11 + -1*A >= 11 + -1*A = f18(A,A,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] ==> f18(A,B,C) = 11 + -1*A >= 11 + -1*A = f18(A,-1 + B,F) [-2 + A >= 0 && A >= 11] ==> f15(A,B,C) = 11 + -1*A >= 11 + -1*A = f28(A,B,C) * Step 4: KnowledgePropagation MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f15(2,B,C) True (1,1) 1. f15(A,B,C) -> f18(A,A,C) [-2 + A >= 0 && 10 >= A] (?,1) 2. f18(A,B,C) -> f18(A,-1 + B,F) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B,C) -> f15(1 + A,B,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (9,1) 4. f15(A,B,C) -> f28(A,B,C) [-2 + A >= 0 && A >= 11] (1,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 5: Failure MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f15(2,B,C) True (1,1) 1. f15(A,B,C) -> f18(A,A,C) [-2 + A >= 0 && 10 >= A] (10,1) 2. f18(A,B,C) -> f18(A,-1 + B,F) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0 && D >= 1 + E] (?,1) 3. f18(A,B,C) -> f15(1 + A,B,C) [10 + -1*B >= 0 && A + -1*B >= 0 && 20 + -1*A + -1*B >= 0 && 10 + -1*A >= 0 && -2 + A >= 0] (9,1) 4. f15(A,B,C) -> f28(A,B,C) [-2 + A >= 0 && A >= 11] (1,1) Signature: {(f0,3);(f15,3);(f18,3);(f28,3)} Flow Graph: [0->{1},1->{2,3},2->{2,3},3->{1,4},4->{}] + Applied Processor: Failing "Open problems left." + Details: Open problems left. MAYBE