172.33/43.96 YES 172.33/43.98 172.33/43.98 Problem: 172.33/43.98 a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 172.33/43.98 Proof: 172.33/43.98 DP Processor: 172.33/43.98 DPs: 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1)))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 TRS: 172.33/43.98 a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 EDG Processor: 172.33/43.98 DPs: 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1)))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 TRS: 172.33/43.98 a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 graph: 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1)))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1)))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(b(a(b(a(b(x1))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(b(a(b(a(b(x1)))))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) -> 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 SCC Processor: 172.33/43.98 #sccs: 1 172.33/43.98 #rules: 3 172.33/43.98 #arcs: 18/36 172.33/43.98 DPs: 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(a(b(x1)))))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) -> a#(b(x1)) 172.33/43.98 TRS: 172.33/43.98 a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 Matrix Interpretation Processor: dim=3 172.33/43.98 172.33/43.98 interpretation: 172.33/43.98 [a#](x0) = [1 0 0]x0, 172.33/43.98 172.33/43.98 [1 0 0] [1] 172.33/43.98 [b](x0) = [0 1 0]x0 + [0] 172.33/43.98 [1 0 0] [0], 172.33/43.98 172.33/43.98 [0 0 1] [0] 172.33/43.98 [a](x0) = [1 0 0]x0 + [1] 172.33/43.98 [0 1 0] [0] 172.33/43.98 orientation: 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) = [1 0 0]x1 + [2] >= [1 0 0]x1 + [1] = a#(b(a(b(a(b(x1)))))) 172.33/43.98 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) = [1 0 0]x1 + [2] >= [1 0 0]x1 + [1] = a#(b(a(b(x1)))) 172.33/43.98 172.33/43.98 a#(b(a(b(a(a(a(x1))))))) = [1 0 0]x1 + [2] >= [1 0 0]x1 + [1] = a#(b(x1)) 172.33/43.98 172.33/43.98 [1 0 0] [1] [1 0 0] [1] 172.33/43.98 a(b(a(b(a(a(a(x1))))))) = [1 0 0]x1 + [3] >= [1 0 0]x1 + [3] = a(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 [1 0 0] [3] [1 0 0] [3] 172.33/43.98 problem: 172.33/43.98 DPs: 172.33/43.98 172.33/43.98 TRS: 172.33/43.98 a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1))))))))) 172.33/43.98 Qed 172.33/43.98 EOF