YES Problem: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) Proof: DP Processor: DPs: a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) TDG Processor: DPs: a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) graph: c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(a(a(x1))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(a(a(x1))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) EDG Processor: DPs: a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) graph: a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> c#(a(a(x1))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(c(c(x1)))) -> c#(a(a(x1))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(c(c(x1)))) -> a#(x1) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(a(a(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(c(a(a(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(c(c(a(a(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> c#(c(c(c(a(a(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(b(b(x1))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(a(a(b(b(x1))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> c#(c(a(a(b(b(x1)))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) SCC Processor: #sccs: 1 #rules: 5 #arcs: 66/196 DPs: a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(b(b(x1)))) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) Arctic Interpretation Processor: dimension: 1 interpretation: [a#](x0) = x0, [c](x0) = x0, [b](x0) = x0, [a](x0) = 1x0 orientation: a#(a(c(c(x1)))) = 1x1 >= 1x1 = a#(a(x1)) a#(a(c(c(x1)))) = 1x1 >= x1 = a#(x1) a#(a(b(b(b(b(a(a(x1)))))))) = 3x1 >= 3x1 = a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) = 3x1 >= 2x1 = a#(c(c(a(a(b(b(x1))))))) a#(a(b(b(b(b(a(a(x1)))))))) = 3x1 >= 1x1 = a#(a(b(b(x1)))) a(a(b(b(b(b(a(a(x1)))))))) = 4x1 >= 4x1 = a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) = 2x1 >= 2x1 = c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) = x1 >= x1 = b(b(c(c(b(b(x1)))))) problem: DPs: a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) EDG Processor: DPs: a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) graph: a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(c(c(x1)))) -> a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) -> a#(a(b(b(b(b(a(a(x1)))))))) -> a#(a(c(c(a(a(b(b(x1)))))))) Matrix Interpretation Processor: dim=4 interpretation: [a#](x0) = [0 0 1 0]x0, [0 0 0 0] [0 0 1 0] [c](x0) = [0 1 0 0]x0 [0 0 0 0] , [0 0 0 0] [0 0 1 0] [b](x0) = [0 0 0 1]x0 [0 0 1 0] , [0 0 0 0] [0] [0 0 0 0] [0] [a](x0) = [0 1 0 0]x0 + [0] [0 0 0 0] [1] orientation: a#(a(c(c(x1)))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = a#(a(x1)) a#(a(b(b(b(b(a(a(x1)))))))) = [1] >= [0] = a#(a(c(c(a(a(b(b(x1)))))))) [0] [0] [0] [0] a(a(b(b(b(b(a(a(x1)))))))) = [0] >= [0] = a(a(c(c(a(a(b(b(x1)))))))) [1] [1] [0] [0] [0] [0] a(a(c(c(x1)))) = [0] >= [0] = c(c(c(c(a(a(x1)))))) [1] [0] [0 0 0 0] [0 0 0 0] [0 1 0 0] [0 0 0 0] c(c(c(c(c(c(x1)))))) = [0 0 1 0]x1 >= [0 0 1 0]x1 = b(b(c(c(b(b(x1)))))) [0 0 0 0] [0 0 0 0] problem: DPs: a#(a(c(c(x1)))) -> a#(a(x1)) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) EDG Processor: DPs: a#(a(c(c(x1)))) -> a#(a(x1)) TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) graph: a#(a(c(c(x1)))) -> a#(a(x1)) -> a#(a(c(c(x1)))) -> a#(a(x1)) Matrix Interpretation Processor: dim=3 interpretation: [a#](x0) = [0 0 1]x0, [0 0 0] [0] [c](x0) = [2 1 0]x0 + [1] [0 0 0] [0], [1 0 1] [b](x0) = [1 0 0]x0 [0 0 0] , [0 0 0] [0] [a](x0) = [1 0 1]x0 + [1] [1 2 0] [0] orientation: a#(a(c(c(x1)))) = [4 2 0]x1 + [4] >= [1 2 0]x1 = a#(a(x1)) [0 0 0] [0] [0 0 0] [0] a(a(b(b(b(b(a(a(x1)))))))) = [6 0 6]x1 + [7] >= [6 0 6]x1 + [7] = a(a(c(c(a(a(b(b(x1)))))))) [4 0 4] [6] [0 0 0] [2] [0 0 0] [0] [0 0 0] [0] a(a(c(c(x1)))) = [4 2 0]x1 + [5] >= [1 2 0]x1 + [5] = c(c(c(c(a(a(x1)))))) [0 0 0] [2] [0 0 0] [0] [0 0 0] [0] [0] c(c(c(c(c(c(x1)))))) = [2 1 0]x1 + [6] >= [0] = b(b(c(c(b(b(x1)))))) [0 0 0] [0] [0] problem: DPs: TRS: a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1)))))))) a(a(c(c(x1)))) -> c(c(c(c(a(a(x1)))))) c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1)))))) Qed