40.52/10.64 YES 40.52/10.66 40.52/10.66 Problem: 40.52/10.66 a(b(x1)) -> b(c(a(x1))) 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 40.52/10.66 Proof: 40.52/10.66 DP Processor: 40.52/10.66 DPs: 40.52/10.66 a#(b(x1)) -> a#(x1) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) 40.52/10.66 b#(c(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(a(x1)) -> b#(x1) 40.52/10.66 b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 TRS: 40.52/10.66 a(b(x1)) -> b(c(a(x1))) 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 TDG Processor: 40.52/10.66 DPs: 40.52/10.66 a#(b(x1)) -> a#(x1) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) 40.52/10.66 b#(c(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(a(x1)) -> b#(x1) 40.52/10.66 b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 TRS: 40.52/10.66 a(b(x1)) -> b(c(a(x1))) 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 graph: 40.52/10.66 b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 b#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) 40.52/10.66 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 40.52/10.66 b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) 40.52/10.66 b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> b#(c(a(x1))) 40.52/10.66 b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> a#(x1) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(x1) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1)) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1) 40.52/10.66 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1))) 40.52/10.66 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) 40.52/10.66 Polynomial Interpretation Processor: 40.52/10.66 dimension: 1 40.52/10.66 interpretation: 40.52/10.66 [b#](x0) = x0, 40.52/10.66 40.52/10.66 [a#](x0) = x0 + 1, 40.52/10.66 40.52/10.66 [c](x0) = x0, 40.52/10.66 40.52/10.66 [a](x0) = x0 + 1, 40.52/10.66 40.52/10.66 [b](x0) = x0 40.52/10.66 orientation: 40.52/10.66 a#(b(x1)) = x1 + 1 >= x1 + 1 = a#(x1) 40.52/10.66 40.52/10.66 a#(b(x1)) = x1 + 1 >= x1 + 1 = b#(c(a(x1))) 40.52/10.66 40.52/10.66 b#(c(x1)) = x1 >= x1 = b#(x1) 40.52/10.66 40.52/10.66 b#(c(x1)) = x1 >= x1 = b#(b(x1)) 40.52/10.66 40.52/10.66 b#(a(x1)) = x1 + 1 >= x1 = b#(x1) 40.52/10.66 40.52/10.66 b#(a(x1)) = x1 + 1 >= x1 + 1 = a#(c(b(x1))) 40.52/10.66 40.52/10.66 a(b(x1)) = x1 + 1 >= x1 + 1 = b(c(a(x1))) 40.52/10.66 40.52/10.66 b(c(x1)) = x1 >= x1 = c(b(b(x1))) 40.52/10.66 40.52/10.66 b(a(x1)) = x1 + 1 >= x1 + 1 = a(c(b(x1))) 40.52/10.66 problem: 40.52/10.66 DPs: 40.52/10.66 a#(b(x1)) -> a#(x1) 40.52/10.66 a#(b(x1)) -> b#(c(a(x1))) 40.52/10.66 b#(c(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 TRS: 40.52/10.66 a(b(x1)) -> b(c(a(x1))) 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 Polynomial Interpretation Processor: 40.52/10.66 dimension: 1 40.52/10.66 usable rules: 40.52/10.66 40.52/10.66 interpretation: 40.52/10.66 [b#](x0) = 1, 40.52/10.66 40.52/10.66 [a#](x0) = x0 + 1, 40.52/10.66 40.52/10.66 [c](x0) = 0, 40.52/10.66 40.52/10.66 [a](x0) = 0, 40.52/10.66 40.52/10.66 [b](x0) = x0 + 1 40.52/10.66 orientation: 40.52/10.66 a#(b(x1)) = x1 + 2 >= x1 + 1 = a#(x1) 40.52/10.66 40.52/10.66 a#(b(x1)) = x1 + 2 >= 1 = b#(c(a(x1))) 40.52/10.66 40.52/10.66 b#(c(x1)) = 1 >= 1 = b#(x1) 40.52/10.66 40.52/10.66 b#(c(x1)) = 1 >= 1 = b#(b(x1)) 40.52/10.66 40.52/10.66 b#(a(x1)) = 1 >= 1 = a#(c(b(x1))) 40.52/10.66 40.52/10.66 a(b(x1)) = 0 >= 1 = b(c(a(x1))) 40.52/10.66 40.52/10.66 b(c(x1)) = 1 >= 0 = c(b(b(x1))) 40.52/10.66 40.52/10.66 b(a(x1)) = 1 >= 0 = a(c(b(x1))) 40.52/10.66 problem: 40.52/10.66 DPs: 40.52/10.66 b#(c(x1)) -> b#(x1) 40.52/10.66 b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(a(x1)) -> a#(c(b(x1))) 40.52/10.66 TRS: 40.52/10.66 a(b(x1)) -> b(c(a(x1))) 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 SCC Processor: 40.52/10.66 #sccs: 1 40.52/10.66 #rules: 2 40.52/10.66 #arcs: 20/9 40.52/10.66 DPs: 40.52/10.66 b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(c(x1)) -> b#(x1) 40.52/10.66 TRS: 40.52/10.66 a(b(x1)) -> b(c(a(x1))) 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 Usable Rule Processor: 40.52/10.66 DPs: 40.52/10.66 b#(c(x1)) -> b#(b(x1)) 40.52/10.66 b#(c(x1)) -> b#(x1) 40.52/10.66 TRS: 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 Polynomial Interpretation Processor: 40.52/10.66 dimension: 1 40.52/10.66 usable rules: 40.52/10.66 b(c(x1)) -> c(b(b(x1))) 40.52/10.66 b(a(x1)) -> a(c(b(x1))) 40.52/10.66 interpretation: 40.52/10.66 [b#](x0) = x0, 40.52/10.66 40.52/10.66 [c](x0) = x0 + 1, 40.76/10.66 40.76/10.66 [a](x0) = 1, 40.76/10.66 40.76/10.66 [b](x0) = x0 40.76/10.66 orientation: 40.76/10.66 b#(c(x1)) = x1 + 1 >= x1 = b#(b(x1)) 40.76/10.66 40.76/10.66 b#(c(x1)) = x1 + 1 >= x1 = b#(x1) 40.76/10.66 40.76/10.66 b(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1))) 40.76/10.66 40.76/10.66 b(a(x1)) = 1 >= 1 = a(c(b(x1))) 40.76/10.66 problem: 40.76/10.66 DPs: 40.76/10.66 40.76/10.66 TRS: 40.76/10.66 b(c(x1)) -> c(b(b(x1))) 40.76/10.66 b(a(x1)) -> a(c(b(x1))) 40.76/10.66 Qed 40.76/10.66 EOF