174.27/44.50 YES 174.27/44.51 174.27/44.51 Problem: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> b(c(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 174.27/44.51 Proof: 174.27/44.51 String Reversal Processor: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 DP Processor: 174.27/44.51 DPs: 174.27/44.51 a#(x1) -> b#(x1) 174.27/44.51 a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 c#(c(c(x1))) -> b#(x1) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 TDG Processor: 174.27/44.51 DPs: 174.27/44.51 a#(x1) -> b#(x1) 174.27/44.51 a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 c#(c(c(x1))) -> b#(x1) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 graph: 174.27/44.51 c#(c(c(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1)) 174.27/44.51 c#(c(c(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) -> a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) -> a#(x1) -> b#(x1) 174.27/44.51 b#(b(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1) 174.27/44.51 a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(x1) 174.27/44.51 a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(a(x1)) 174.27/44.51 a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(x1) 174.27/44.51 Arctic Interpretation Processor: 174.27/44.51 dimension: 2 174.27/44.51 usable rules: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 interpretation: 174.27/44.51 [c#](x0) = [-& 0 ]x0 + [0], 174.27/44.51 174.27/44.51 [b#](x0) = [0 0]x0 + [0], 174.27/44.51 174.27/44.51 [a#](x0) = [0 0]x0 + [1], 174.27/44.51 174.27/44.51 [1 0 ] [1] 174.27/44.51 [b](x0) = [0 -&]x0 + [0], 174.27/44.51 174.27/44.51 [-& 0 ] [0] 174.27/44.51 [c](x0) = [0 1 ]x0 + [0], 174.27/44.51 174.27/44.51 [0 -&] [0] 174.27/44.51 [a](x0) = [1 0 ]x0 + [1] 174.27/44.51 orientation: 174.27/44.51 a#(x1) = [0 0]x1 + [1] >= [0 0]x1 + [0] = b#(x1) 174.27/44.51 174.27/44.51 a#(x1) = [0 0]x1 + [1] >= [0 -&]x1 + [0] = c#(b(x1)) 174.27/44.51 174.27/44.51 b#(b(x1)) = [1 0]x1 + [1] >= [0 0]x1 + [1] = a#(x1) 174.27/44.51 174.27/44.51 b#(b(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a#(a(x1)) 174.27/44.51 174.27/44.51 c#(c(c(x1))) = [1 2]x1 + [1] >= [0 0]x1 + [0] = b#(x1) 174.27/44.51 174.27/44.51 [0 -&] [0] 174.27/44.51 a(x1) = [1 0 ]x1 + [1] >= x1 = x1 174.27/44.51 174.27/44.51 [0 -&] [0] [0 -&] [0] 174.27/44.51 a(x1) = [1 0 ]x1 + [1] >= [1 0 ]x1 + [1] = c(b(x1)) 174.27/44.51 174.27/44.51 [2 1] [2] [0 -&] [0] 174.27/44.51 b(b(x1)) = [1 0]x1 + [1] >= [1 0 ]x1 + [1] = a(a(x1)) 174.27/44.51 174.27/44.51 [1 2] [1] [1 0 ] [1] 174.27/44.51 c(c(c(x1))) = [2 3]x1 + [2] >= [0 -&]x1 + [0] = b(x1) 174.27/44.51 problem: 174.27/44.51 DPs: 174.27/44.51 a#(x1) -> b#(x1) 174.27/44.51 a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 Restore Modifier: 174.27/44.51 DPs: 174.27/44.51 a#(x1) -> b#(x1) 174.27/44.51 a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 EDG Processor: 174.27/44.51 DPs: 174.27/44.51 a#(x1) -> b#(x1) 174.27/44.51 a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 graph: 174.27/44.51 b#(b(x1)) -> a#(a(x1)) -> a#(x1) -> b#(x1) 174.27/44.51 b#(b(x1)) -> a#(a(x1)) -> a#(x1) -> c#(b(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1) 174.27/44.51 b#(b(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1)) 174.27/44.51 a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(x1) 174.27/44.51 a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(a(x1)) 174.27/44.51 SCC Processor: 174.27/44.51 #sccs: 1 174.27/44.51 #rules: 3 174.27/44.51 #arcs: 6/16 174.27/44.51 DPs: 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 a#(x1) -> b#(x1) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 Arctic Interpretation Processor: 174.27/44.51 dimension: 2 174.27/44.51 usable rules: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 interpretation: 174.27/44.51 [b#](x0) = [0 -&]x0 + [0], 174.27/44.51 174.27/44.51 [a#](x0) = [1 -&]x0 + [1], 174.27/44.51 174.27/44.51 [1 0 ] [1] 174.27/44.51 [b](x0) = [0 -&]x0 + [0], 174.27/44.51 174.27/44.51 [-& 0 ] [0] 174.27/44.51 [c](x0) = [0 1 ]x0 + [0], 174.27/44.51 174.27/44.51 [0 -&] [0] 174.27/44.51 [a](x0) = [1 0 ]x0 + [1] 174.27/44.51 orientation: 174.27/44.51 b#(b(x1)) = [1 0]x1 + [1] >= [1 -&]x1 + [1] = a#(a(x1)) 174.27/44.51 174.27/44.51 a#(x1) = [1 -&]x1 + [1] >= [0 -&]x1 + [0] = b#(x1) 174.27/44.51 174.27/44.51 b#(b(x1)) = [1 0]x1 + [1] >= [1 -&]x1 + [1] = a#(x1) 174.27/44.51 174.27/44.51 [0 -&] [0] 174.27/44.51 a(x1) = [1 0 ]x1 + [1] >= x1 = x1 174.27/44.51 174.27/44.51 [0 -&] [0] [0 -&] [0] 174.27/44.51 a(x1) = [1 0 ]x1 + [1] >= [1 0 ]x1 + [1] = c(b(x1)) 174.27/44.51 174.27/44.51 [2 1] [2] [0 -&] [0] 174.27/44.51 b(b(x1)) = [1 0]x1 + [1] >= [1 0 ]x1 + [1] = a(a(x1)) 174.27/44.51 174.27/44.51 [1 2] [1] [1 0 ] [1] 174.27/44.51 c(c(c(x1))) = [2 3]x1 + [2] >= [0 -&]x1 + [0] = b(x1) 174.27/44.51 problem: 174.27/44.51 DPs: 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 Restore Modifier: 174.27/44.51 DPs: 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 EDG Processor: 174.27/44.51 DPs: 174.27/44.51 b#(b(x1)) -> a#(a(x1)) 174.27/44.51 b#(b(x1)) -> a#(x1) 174.27/44.51 TRS: 174.27/44.51 a(x1) -> x1 174.27/44.51 a(x1) -> c(b(x1)) 174.27/44.51 b(b(x1)) -> a(a(x1)) 174.27/44.51 c(c(c(x1))) -> b(x1) 174.27/44.51 graph: 174.27/44.51 174.27/44.51 SCC Processor: 174.27/44.51 #sccs: 0 174.27/44.51 #rules: 0 174.27/44.51 #arcs: 0/4 174.27/44.51 174.27/44.51 EOF