YES Problem: 0(0(*(*(x1)))) -> *(*(1(1(x1)))) 1(1(*(*(x1)))) -> 0(0(#(#(x1)))) #(#(0(0(x1)))) -> 0(0(#(#(x1)))) #(#(1(1(x1)))) -> 1(1(#(#(x1)))) #(#($($(x1)))) -> *(*($($(x1)))) #(#(#(#(x1)))) -> #(#(x1)) #(#(*(*(x1)))) -> *(*(x1)) Proof: DP Processor: DPs: 0#(0(*(*(x1)))) -> 1#(x1) 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) TRS: 0(0(*(*(x1)))) -> *(*(1(1(x1)))) 1(1(*(*(x1)))) -> 0(0(#(#(x1)))) #(#(0(0(x1)))) -> 0(0(#(#(x1)))) #(#(1(1(x1)))) -> 1(1(#(#(x1)))) #(#($($(x1)))) -> *(*($($(x1)))) #(#(#(#(x1)))) -> #(#(x1)) #(#(*(*(x1)))) -> *(*(x1)) TDG Processor: DPs: 0#(0(*(*(x1)))) -> 1#(x1) 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) TRS: 0(0(*(*(x1)))) -> *(*(1(1(x1)))) 1(1(*(*(x1)))) -> 0(0(#(#(x1)))) #(#(0(0(x1)))) -> 0(0(#(#(x1)))) #(#(1(1(x1)))) -> 1(1(#(#(x1)))) #(#($($(x1)))) -> *(*($($(x1)))) #(#(#(#(x1)))) -> #(#(x1)) #(#(*(*(x1)))) -> *(*(x1)) graph: ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> 1#(#(#(x1))) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> 1#(#(#(x1))) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> 1#(#(#(x1))) -> 1#(1(*(*(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(#(#(x1))) -> 1#(1(*(*(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> 0#(#(#(x1))) -> 0#(0(*(*(x1)))) -> 1#(1(x1)) ##(#(0(0(x1)))) -> 0#(#(#(x1))) -> 0#(0(*(*(x1)))) -> 1#(x1) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(1(x1)) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> 0#(#(#(x1))) -> 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> 0#(#(#(x1))) -> 0#(0(*(*(x1)))) -> 1#(x1) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(x1) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> ##(#(x1)) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> ##(x1) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> ##(#(x1)) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> ##(x1) CDG Processor: DPs: 0#(0(*(*(x1)))) -> 1#(x1) 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) TRS: 0(0(*(*(x1)))) -> *(*(1(1(x1)))) 1(1(*(*(x1)))) -> 0(0(#(#(x1)))) #(#(0(0(x1)))) -> 0(0(#(#(x1)))) #(#(1(1(x1)))) -> 1(1(#(#(x1)))) #(#($($(x1)))) -> *(*($($(x1)))) #(#(#(#(x1)))) -> #(#(x1)) #(#(*(*(x1)))) -> *(*(x1)) graph: ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(1(1(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> ##(x1) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(0(0(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) ##(#(0(0(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(x1) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(#(x1)) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(x1) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> ##(#(x1)) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(#(#(x1))) 1#(1(*(*(x1)))) -> ##(x1) -> ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(x1) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) -> 0#(0(*(*(x1)))) -> 1#(1(x1)) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> ##(x1) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> ##(#(x1)) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 0#(0(*(*(x1)))) -> 1#(1(x1)) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> ##(x1) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> ##(#(x1)) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> 0#(#(#(x1))) 0#(0(*(*(x1)))) -> 1#(x1) -> 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) SCC Processor: #sccs: 1 #rules: 11 #arcs: 64/196 DPs: ##(#(1(1(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> 1#(1(#(#(x1)))) 1#(1(*(*(x1)))) -> 0#(0(#(#(x1)))) 0#(0(*(*(x1)))) -> 1#(1(x1)) 1#(1(*(*(x1)))) -> ##(#(x1)) ##(#(1(1(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> 0#(0(#(#(x1)))) 0#(0(*(*(x1)))) -> 1#(x1) 1#(1(*(*(x1)))) -> ##(x1) ##(#(0(0(x1)))) -> ##(#(x1)) ##(#(0(0(x1)))) -> ##(x1) TRS: 0(0(*(*(x1)))) -> *(*(1(1(x1)))) 1(1(*(*(x1)))) -> 0(0(#(#(x1)))) #(#(0(0(x1)))) -> 0(0(#(#(x1)))) #(#(1(1(x1)))) -> 1(1(#(#(x1)))) #(#($($(x1)))) -> *(*($($(x1)))) #(#(#(#(x1)))) -> #(#(x1)) #(#(*(*(x1)))) -> *(*(x1)) KBO Processor: weight function: w0 = 1 w(##) = w(1#) = w($) = w(#) = w(1) = w(0) = w(*) = 1 w(0#) = 0 precedence: 0# > # > ## ~ 1 > 0 > 1# ~ $ ~ * problem: DPs: TRS: Qed