186.88/47.79 YES 186.88/47.80 186.88/47.80 Problem: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 186.88/47.80 Proof: 186.88/47.80 DP Processor: 186.88/47.80 DPs: 186.88/47.80 a#(b(b(x1))) -> a#(x1) 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 a#(b(b(x1))) -> c#(a(a(x1))) 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 TDG Processor: 186.88/47.80 DPs: 186.88/47.80 a#(b(b(x1))) -> a#(x1) 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 a#(b(b(x1))) -> c#(a(a(x1))) 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 graph: 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> c#(a(a(x1))) 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(x1) 186.88/47.80 a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(a(a(x1))) 186.88/47.80 a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1) 186.88/47.80 SCC Processor: 186.88/47.80 #sccs: 1 186.88/47.80 #rules: 2 186.88/47.80 #arcs: 6/9 186.88/47.80 DPs: 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 a#(b(b(x1))) -> a#(x1) 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 Arctic Interpretation Processor: 186.88/47.80 dimension: 2 186.88/47.80 usable rules: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 interpretation: 186.88/47.80 [a#](x0) = [0 0]x0, 186.88/47.80 186.88/47.80 [0 -&] 186.88/47.80 [c](x0) = [0 -&]x0, 186.88/47.80 186.88/47.80 [0 0] [0] 186.88/47.80 [b](x0) = [2 0]x0 + [2], 186.88/47.80 186.88/47.80 [0 -&] [-&] 186.88/47.80 [a](x0) = [2 0 ]x0 + [2 ] 186.88/47.80 orientation: 186.88/47.80 a#(b(b(x1))) = [2 2]x1 + [2] >= [2 0]x1 + [2] = a#(a(x1)) 186.88/47.80 186.88/47.80 a#(b(b(x1))) = [2 2]x1 + [2] >= [0 0]x1 = a#(x1) 186.88/47.80 186.88/47.80 [0 -&] [-&] 186.88/47.80 a(x1) = [2 0 ]x1 + [2 ] >= x1 = x1 186.88/47.80 186.88/47.80 [2 0] [2] [2 -&] [2] 186.88/47.80 a(b(b(x1))) = [4 2]x1 + [4] >= [4 -&]x1 + [4] = b(b(b(c(a(a(x1)))))) 186.88/47.80 186.88/47.80 [0 0] [0] 186.88/47.80 c(b(x1)) = [0 0]x1 + [0] >= x1 = x1 186.88/47.80 problem: 186.88/47.80 DPs: 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 Restore Modifier: 186.88/47.80 DPs: 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 EDG Processor: 186.88/47.80 DPs: 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 graph: 186.88/47.80 a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(a(x1)) 186.88/47.80 Arctic Interpretation Processor: 186.88/47.80 dimension: 2 186.88/47.80 usable rules: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 interpretation: 186.88/47.80 [a#](x0) = [1 0]x0, 186.88/47.80 186.88/47.80 [0 -&] 186.88/47.80 [c](x0) = [0 -&]x0, 186.88/47.80 186.88/47.80 [0 0] 186.88/47.80 [b](x0) = [1 0]x0, 186.88/47.80 186.88/47.80 [0 -&] 186.88/47.80 [a](x0) = [1 0 ]x0 186.88/47.80 orientation: 186.88/47.80 a#(b(b(x1))) = [2 1]x1 >= [1 0]x1 = a#(a(x1)) 186.88/47.80 186.88/47.80 [0 -&] 186.88/47.80 a(x1) = [1 0 ]x1 >= x1 = x1 186.88/47.80 186.88/47.80 [1 0] [1 -&] 186.88/47.80 a(b(b(x1))) = [2 1]x1 >= [2 -&]x1 = b(b(b(c(a(a(x1)))))) 186.88/47.80 186.88/47.80 [0 0] 186.88/47.80 c(b(x1)) = [0 0]x1 >= x1 = x1 186.88/47.80 problem: 186.88/47.80 DPs: 186.88/47.80 186.88/47.80 TRS: 186.88/47.80 a(x1) -> x1 186.88/47.80 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 186.88/47.80 c(b(x1)) -> x1 186.88/47.80 Qed 187.26/47.80 EOF