/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) Proof: DP Processor: DPs: h#(c(x,y),c(s(z),z),t(w)) -> t#(c(x,c(y,t(w)))) h#(c(x,y),c(s(z),z),t(w)) -> t#(t(c(x,c(y,t(w))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(x,c(y,z),t(w)) -> t#(c(t(w),w)) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(c(x,s(x))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(t(c(x,s(x)))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t#(t(x)) -> t#(c(t(x),x)) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) TDG Processor: DPs: h#(c(x,y),c(s(z),z),t(w)) -> t#(c(x,c(y,t(w)))) h#(c(x,y),c(s(z),z),t(w)) -> t#(t(c(x,c(y,t(w))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(x,c(y,z),t(w)) -> t#(c(t(w),w)) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(c(x,s(x))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(t(c(x,s(x)))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t#(t(x)) -> t#(c(t(x),x)) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) graph: t#(t(x)) -> t#(c(t(x),x)) -> t#(t(x)) -> t#(c(t(x),x)) h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(t(c(x,s(x)))) -> t#(t(x)) -> t#(c(t(x),x)) h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(c(x,s(x))) -> t#(t(x)) -> t#(c(t(x),x)) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(t(c(x,s(x)))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(c(x,s(x))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(x,c(y,z),t(w)) -> t#(c(t(w),w)) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(x,y),c(s(z),z),t(w)) -> t#(t(c(x,c(y,t(w))))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(x,y),c(s(z),z),t(w)) -> t#(c(x,c(y,t(w)))) h#(c(x,y),c(s(z),z),t(w)) -> t#(t(c(x,c(y,t(w))))) -> t#(t(x)) -> t#(c(t(x),x)) h#(c(x,y),c(s(z),z),t(w)) -> t#(c(x,c(y,t(w)))) -> t#(t(x)) -> t#(c(t(x),x)) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(t(c(x,s(x)))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(c(x,s(x))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(x,c(y,z),t(w)) -> t#(c(t(w),w)) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(x,y),c(s(z),z),t(w)) -> t#(t(c(x,c(y,t(w))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(x,y),c(s(z),z),t(w)) -> t#(c(x,c(y,t(w)))) h#(x,c(y,z),t(w)) -> t#(c(t(w),w)) -> t#(t(x)) -> t#(c(t(x),x)) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(t(c(x,s(x)))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> t#(c(x,s(x))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(x,c(y,z),t(w)) -> t#(c(t(w),w)) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(x,y),c(s(z),z),t(w)) -> t#(t(c(x,c(y,t(w))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(x,y),c(s(z),z),t(w)) -> t#(c(x,c(y,t(w)))) SCC Processor: #sccs: 2 #rules: 4 #arcs: 30/81 DPs: h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) EDG Processor: DPs: h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) graph: h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(x,y),c(s(z),z),t(w)) -> h#(z,c(y,x),t(t(c(x,c(y,t(w)))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) -> h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) Subterm Criterion Processor: simple projection: pi(c) = [0,1] pi(s) = 0 pi(h#) = [0,0,1,1] problem: DPs: h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) Usable Rule Processor: DPs: h#(c(s(x),c(s(0()),y)),z,t(x)) -> h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) TRS: t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) t(t(x)) -> t(c(t(x),x)) Matrix Interpretation Processor: dim=2 usable rules: interpretation: [h#](x0, x1, x2) = [0 1]x0 + [2 0]x1, [1] [0] = [0], [0] [t](x0) = [1], [0 2] [s](x0) = [1 0]x0, [1 0] [c](x0, x1) = [0 2]x0 + x1 orientation: h#(c(s(x),c(s(0()),y)),z,t(x)) = [2 0]x + [0 1]y + [2 0]z + [2] >= [2 0]x + [0 1]y + [2 0]z = h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) h#(x,c(y,z),t(w)) = [0 1]x + [2 0]y + [2 0]z >= [0 1]x + [2 0]y + [2 0]z = h#(c(s(y),x),z,t(c(t(w),w))) [0] t(x) = [1] >= x = x [0] [5] t(x) = [1] >= x + [0] = c(0(),c(0(),c(0(),c(0(),c(0(),x))))) [0] [0] t(t(x)) = [1] >= [1] = t(c(t(x),x)) problem: DPs: h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) TRS: t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) t(t(x)) -> t(c(t(x),x)) Restore Modifier: DPs: h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) Size-Change Termination Processor: DPs: TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) The DP: h#(x,c(y,z),t(w)) -> h#(c(s(y),x),z,t(c(t(w),w))) has the edges: 1 > 1 Qed DPs: t#(t(x)) -> t#(c(t(x),x)) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) EDG Processor: DPs: t#(t(x)) -> t#(c(t(x),x)) TRS: h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(t(x)) -> t(c(t(x),x)) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1