180.64/46.28 YES 180.86/46.29 180.86/46.29 Problem: 180.86/46.29 a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 180.86/46.29 Proof: 180.86/46.29 DP Processor: 180.86/46.29 DPs: 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(b(c(a(b(c(a(b(c(x1)))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(b(c(a(b(c(a(b(c(x1))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 TRS: 180.86/46.29 a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 EDG Processor: 180.86/46.29 DPs: 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(b(c(a(b(c(a(b(c(x1)))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(b(c(a(b(c(a(b(c(x1))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 TRS: 180.86/46.29 a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 graph: 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(b(c(a(b(c(a(b(c(x1)))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(b(c(a(b(c(a(b(c(x1))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(b(c(a(b(c(a(b(c(x1)))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(b(c(a(b(c(a(b(c(x1))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(b(c(a(b(c(a(b(c(x1)))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(b(c(a(b(c(a(b(c(x1))))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) -> 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 SCC Processor: 180.86/46.29 #sccs: 1 180.86/46.29 #rules: 3 180.86/46.29 #arcs: 18/36 180.86/46.29 DPs: 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(a(b(c(x1)))))) 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) -> a#(b(c(x1))) 180.86/46.29 TRS: 180.86/46.29 a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 Matrix Interpretation Processor: dim=3 180.86/46.29 180.86/46.29 interpretation: 180.86/46.29 [a#](x0) = [1 0 0]x0, 180.86/46.29 180.86/46.29 [1 0 0] 180.86/46.29 [b](x0) = [1 0 1]x0 180.86/46.29 [1 0 0] , 180.86/46.29 180.86/46.29 [1 0 0] 180.86/46.29 [c](x0) = [0 0 0]x0 180.86/46.29 [0 1 0] , 180.86/46.29 180.86/46.29 [0 0 1] [0] 180.86/46.29 [a](x0) = [1 0 0]x0 + [1] 180.86/46.29 [0 1 0] [0] 180.86/46.29 orientation: 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) = [1 0 0]x1 + [1] >= [1 0 0]x1 = a#(b(c(a(b(c(a(b(c(x1))))))))) 180.86/46.29 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) = [1 0 0]x1 + [1] >= [1 0 0]x1 = a#(b(c(a(b(c(x1)))))) 180.86/46.29 180.86/46.29 a#(b(c(a(b(c(a(a(a(x1))))))))) = [1 0 0]x1 + [1] >= [1 0 0]x1 = a#(b(c(x1))) 180.86/46.29 180.86/46.29 [1 0 0] [1] [1 0 0] [1] 180.86/46.29 a(b(c(a(b(c(a(a(a(x1))))))))) = [1 0 0]x1 + [2] >= [1 0 0]x1 + [2] = a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 [2 0 0] [3] [2 0 0] [2] 180.86/46.29 problem: 180.86/46.29 DPs: 180.86/46.29 180.86/46.29 TRS: 180.86/46.29 a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) 180.86/46.29 Qed 180.86/46.30 EOF