/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z Proof: DP Processor: DPs: c#(z,x,a()) -> f#(z) c#(z,x,a()) -> b#(f(z),z) c#(z,x,a()) -> b#(b(f(z),z),x) c#(z,x,a()) -> f#(b(b(f(z),z),x)) b#(y,b(z,a())) -> f#(a()) b#(y,b(z,a())) -> c#(f(a()),y,z) b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z)) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z TDG Processor: DPs: c#(z,x,a()) -> f#(z) c#(z,x,a()) -> b#(f(z),z) c#(z,x,a()) -> b#(b(f(z),z),x) c#(z,x,a()) -> f#(b(b(f(z),z),x)) b#(y,b(z,a())) -> f#(a()) b#(y,b(z,a())) -> c#(f(a()),y,z) b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z)) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z graph: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) -> b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z)) b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) -> b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) -> b#(y,b(z,a())) -> c#(f(a()),y,z) b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) -> b#(y,b(z,a())) -> f#(a()) b#(y,b(z,a())) -> c#(f(a()),y,z) -> c#(z,x,a()) -> f#(b(b(f(z),z),x)) b#(y,b(z,a())) -> c#(f(a()),y,z) -> c#(z,x,a()) -> b#(b(f(z),z),x) b#(y,b(z,a())) -> c#(f(a()),y,z) -> c#(z,x,a()) -> b#(f(z),z) b#(y,b(z,a())) -> c#(f(a()),y,z) -> c#(z,x,a()) -> f#(z) c#(z,x,a()) -> b#(b(f(z),z),x) -> b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z)) c#(z,x,a()) -> b#(b(f(z),z),x) -> b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) c#(z,x,a()) -> b#(b(f(z),z),x) -> b#(y,b(z,a())) -> c#(f(a()),y,z) c#(z,x,a()) -> b#(b(f(z),z),x) -> b#(y,b(z,a())) -> f#(a()) c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z)) c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> c#(f(a()),y,z) c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> f#(a()) SCC Processor: #sccs: 1 #rules: 4 #arcs: 16/64 DPs: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> c#(f(a()),y,z) c#(z,x,a()) -> b#(f(z),z) c#(z,x,a()) -> b#(b(f(z),z),x) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z Arctic Interpretation Processor: dimension: 1 usable rules: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z interpretation: [b#](x0, x1) = x0 + x1 + 0, [c#](x0, x1, x2) = 1x0 + x1 + 7, [b](x0, x1) = x0 + x1 + 7, [f](x0) = x0 + 4, [c](x0, x1, x2) = x0 + x1 + 7, [a] = 1 orientation: b#(y,b(z,a())) = y + z + 7 >= y + z + 7 = b#(c(f(a()),y,z),z) b#(y,b(z,a())) = y + z + 7 >= y + 7 = c#(f(a()),y,z) c#(z,x,a()) = x + 1z + 7 >= z + 4 = b#(f(z),z) c#(z,x,a()) = x + 1z + 7 >= x + z + 7 = b#(b(f(z),z),x) c(z,x,a()) = x + z + 7 >= x + z + 7 = f(b(b(f(z),z),x)) b(y,b(z,a())) = y + z + 7 >= y + z + 7 = f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) = x + z + 7 >= z = z problem: DPs: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> c#(f(a()),y,z) c#(z,x,a()) -> b#(b(f(z),z),x) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z Restore Modifier: DPs: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> c#(f(a()),y,z) c#(z,x,a()) -> b#(b(f(z),z),x) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z Arctic Interpretation Processor: dimension: 1 usable rules: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z interpretation: [b#](x0, x1) = 2x0 + 1x1 + 4, [c#](x0, x1, x2) = 5x0 + 2x1 + 1x2 + 6, [b](x0, x1) = x0 + 2x1 + -16, [f](x0) = -5x0 + 0, [c](x0, x1, x2) = 3x0 + -3x1 + 0, [a] = 3 orientation: b#(y,b(z,a())) = 2y + 1z + 6 >= -1y + 1z + 5 = b#(c(f(a()),y,z),z) b#(y,b(z,a())) = 2y + 1z + 6 >= 2y + 1z + 6 = c#(f(a()),y,z) c#(z,x,a()) = 2x + 5z + 6 >= 1x + 4z + 4 = b#(b(f(z),z),x) c(z,x,a()) = -3x + 3z + 0 >= -3x + -3z + 0 = f(b(b(f(z),z),x)) b(y,b(z,a())) = y + 2z + 7 >= -8y + -3z + 0 = f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) = -8x + 1z + 0 >= z = z problem: DPs: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> c#(f(a()),y,z) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z Restore Modifier: DPs: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) b#(y,b(z,a())) -> c#(f(a()),y,z) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z SCC Processor: #sccs: 1 #rules: 1 #arcs: 8/4 DPs: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z Size-Change Termination Processor: DPs: TRS: c(z,x,a()) -> f(b(b(f(z),z),x)) b(y,b(z,a())) -> f(b(c(f(a()),y,z),z)) f(c(c(z,a(),a()),x,a())) -> z The DP: b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) has the edges: 1 > 1 Qed