172.59/44.01 YES 172.59/44.01 172.59/44.01 Problem: 172.59/44.01 a(x1) -> x1 172.59/44.01 a(b(x1)) -> b(c(a(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> a(c(x1)) 172.59/44.01 172.59/44.01 Proof: 172.59/44.01 String Reversal Processor: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 DP Processor: 172.59/44.01 DPs: 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 b#(a(x1)) -> c#(b(x1)) 172.59/44.01 b#(a(x1)) -> a#(c(b(x1))) 172.59/44.01 c#(x1) -> b#(x1) 172.59/44.01 c#(c(x1)) -> a#(x1) 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 TDG Processor: 172.59/44.01 DPs: 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 b#(a(x1)) -> c#(b(x1)) 172.59/44.01 b#(a(x1)) -> a#(c(b(x1))) 172.59/44.01 c#(x1) -> b#(x1) 172.59/44.01 c#(c(x1)) -> a#(x1) 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 graph: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) 172.59/44.01 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1) 172.59/44.01 c#(c(x1)) -> c#(a(x1)) -> c#(x1) -> b#(x1) 172.59/44.01 c#(x1) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 172.59/44.01 c#(x1) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 172.59/44.01 c#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1) 172.59/44.01 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(a(x1)) 172.59/44.01 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1) 172.59/44.01 b#(a(x1)) -> c#(b(x1)) -> c#(x1) -> b#(x1) 172.59/44.01 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 172.59/44.01 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 172.59/44.01 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 172.59/44.01 SCC Processor: 172.59/44.01 #sccs: 1 172.59/44.01 #rules: 4 172.59/44.01 #arcs: 12/36 172.59/44.01 DPs: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 c#(x1) -> b#(x1) 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 b#(a(x1)) -> c#(b(x1)) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 Arctic Interpretation Processor: 172.59/44.01 dimension: 2 172.59/44.01 usable rules: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 interpretation: 172.59/44.01 [c#](x0) = [0 0]x0 + [2], 172.59/44.01 172.59/44.01 [b#](x0) = [0 0]x0 + [2], 172.59/44.01 172.59/44.01 [1 1] [3] 172.59/44.01 [c](x0) = [0 0]x0 + [0], 172.59/44.01 172.59/44.01 [-& 0 ] [0] 172.59/44.01 [b](x0) = [-& 0 ]x0 + [0], 172.59/44.01 172.59/44.01 [0 0 ] [0] 172.59/44.01 [a](x0) = [-& 1 ]x0 + [3] 172.59/44.01 orientation: 172.59/44.01 c#(c(x1)) = [1 1]x1 + [3] >= [0 1]x1 + [3] = c#(a(x1)) 172.59/44.01 172.59/44.01 c#(x1) = [0 0]x1 + [2] >= [0 0]x1 + [2] = b#(x1) 172.59/44.01 172.59/44.01 b#(a(x1)) = [0 1]x1 + [3] >= [0 0]x1 + [2] = b#(x1) 172.59/44.01 172.59/44.01 b#(a(x1)) = [0 1]x1 + [3] >= [-& 0 ]x1 + [2] = c#(b(x1)) 172.59/44.01 172.59/44.01 [0 0 ] [0] 172.59/44.01 a(x1) = [-& 1 ]x1 + [3] >= x1 = x1 172.59/44.01 172.59/44.01 [-& 1 ] [3] [-& 1 ] [3] 172.59/44.01 b(a(x1)) = [-& 1 ]x1 + [3] >= [-& 1 ]x1 + [3] = a(c(b(x1))) 172.59/44.01 172.59/44.01 [1 1] [3] [-& 0 ] [0] 172.59/44.01 c(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = b(x1) 172.59/44.01 172.59/44.01 [2 2] [4] [1 2] [4] 172.59/44.01 c(c(x1)) = [1 1]x1 + [3] >= [0 1]x1 + [3] = c(a(x1)) 172.59/44.01 problem: 172.59/44.01 DPs: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 c#(x1) -> b#(x1) 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 Restore Modifier: 172.59/44.01 DPs: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 c#(x1) -> b#(x1) 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 EDG Processor: 172.59/44.01 DPs: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 c#(x1) -> b#(x1) 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 graph: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) -> c#(x1) -> b#(x1) 172.59/44.01 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) 172.59/44.01 c#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1) 172.59/44.01 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 172.59/44.01 SCC Processor: 172.59/44.01 #sccs: 2 172.59/44.01 #rules: 2 172.59/44.01 #arcs: 4/9 172.59/44.01 DPs: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 Usable Rule Processor: 172.59/44.01 DPs: 172.59/44.01 c#(c(x1)) -> c#(a(x1)) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 Arctic Interpretation Processor: 172.59/44.01 dimension: 4 172.59/44.01 usable rules: 172.59/44.01 a(x1) -> x1 172.59/44.01 interpretation: 172.59/44.01 [c#](x0) = [-& 0 -& 0 ]x0 + [0], 172.59/44.01 172.59/44.01 [0 0 0 0] [0 ] 172.59/44.01 [0 1 0 0] [-&] 172.59/44.01 [c](x0) = [0 1 0 0]x0 + [0 ] 172.59/44.01 [1 1 1 1] [1 ], 172.59/44.01 172.59/44.01 [0 0 0 1 ] [0] 172.59/44.01 [0 0 -& 0 ] [0] 172.59/44.01 [a](x0) = [0 0 0 0 ]x0 + [0] 172.59/44.01 [0 -& 0 0 ] [0] 172.59/44.01 orientation: 172.59/44.01 c#(c(x1)) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = c#(a(x1)) 172.59/44.01 172.59/44.01 [0 0 0 1 ] [0] 172.59/44.01 [0 0 -& 0 ] [0] 172.59/44.01 a(x1) = [0 0 0 0 ]x1 + [0] >= x1 = x1 172.59/44.01 [0 -& 0 0 ] [0] 172.59/44.01 problem: 172.59/44.01 DPs: 172.59/44.01 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 Qed 172.59/44.01 172.59/44.01 DPs: 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 TRS: 172.59/44.01 a(x1) -> x1 172.59/44.01 b(a(x1)) -> a(c(b(x1))) 172.59/44.01 c(x1) -> b(x1) 172.59/44.01 c(c(x1)) -> c(a(x1)) 172.59/44.01 Usable Rule Processor: 172.59/44.01 DPs: 172.59/44.01 b#(a(x1)) -> b#(x1) 172.59/44.01 TRS: 172.59/44.01 172.59/44.01 Arctic Interpretation Processor: 172.59/44.01 dimension: 4 172.59/44.01 usable rules: 172.59/44.01 172.59/44.01 interpretation: 172.59/44.01 [b#](x0) = [0 -& -& -&]x0, 172.59/44.01 172.59/44.01 [1 0 0 0] [0] 172.59/44.01 [0 0 0 0] [0] 172.59/44.01 [a](x0) = [1 0 0 0]x0 + [0] 172.59/44.01 [0 0 0 0] [0] 172.59/44.01 orientation: 172.59/44.01 b#(a(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = b#(x1) 172.59/44.01 problem: 172.59/44.01 DPs: 172.59/44.01 172.59/44.01 TRS: 172.59/44.01 172.59/44.01 Qed 172.59/44.02 EOF