181.56/46.32 YES 181.56/46.32 181.56/46.32 Problem: 181.56/46.32 a(x1) -> x1 181.56/46.32 a(b(x1)) -> b(a(c(b(a(c(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 181.56/46.32 Proof: 181.56/46.32 String Reversal Processor: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 DP Processor: 181.56/46.32 DPs: 181.56/46.32 b#(a(x1)) -> b#(x1) 181.56/46.32 b#(a(x1)) -> a#(b(x1)) 181.56/46.32 b#(a(x1)) -> c#(a(b(x1))) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 b#(a(x1)) -> a#(b(c(a(b(x1))))) 181.56/46.32 b#(a(x1)) -> c#(a(b(c(a(b(x1)))))) 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 TDG Processor: 181.56/46.32 DPs: 181.56/46.32 b#(a(x1)) -> b#(x1) 181.56/46.32 b#(a(x1)) -> a#(b(x1)) 181.56/46.32 b#(a(x1)) -> c#(a(b(x1))) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 b#(a(x1)) -> a#(b(c(a(b(x1))))) 181.56/46.32 b#(a(x1)) -> c#(a(b(c(a(b(x1)))))) 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 graph: 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> c#(a(b(c(a(b(x1)))))) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> a#(b(c(a(b(x1))))) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> c#(a(b(x1))) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> a#(b(x1)) 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(x1) 181.56/46.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(c(a(b(x1)))))) 181.56/46.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(c(a(b(x1))))) 181.56/46.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 181.56/46.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 181.56/46.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 181.56/46.32 SCC Processor: 181.56/46.32 #sccs: 1 181.56/46.32 #rules: 2 181.56/46.32 #arcs: 12/36 181.56/46.32 DPs: 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 b#(a(x1)) -> b#(x1) 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 Arctic Interpretation Processor: 181.56/46.32 dimension: 2 181.56/46.32 usable rules: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 interpretation: 181.56/46.32 [b#](x0) = [1 1]x0, 181.56/46.32 181.56/46.32 [0 0 ] 181.56/46.32 [c](x0) = [0 -&]x0, 181.56/46.32 181.56/46.32 [0 1 ] 181.56/46.32 [b](x0) = [-& 0 ]x0, 181.56/46.32 181.56/46.32 [0 1] 181.56/46.32 [a](x0) = [1 2]x0 181.56/46.32 orientation: 181.56/46.32 b#(a(x1)) = [2 3]x1 >= [2 3]x1 = b#(c(a(b(x1)))) 181.56/46.32 181.56/46.32 b#(a(x1)) = [2 3]x1 >= [1 1]x1 = b#(x1) 181.56/46.32 181.56/46.32 [0 1] 181.56/46.32 a(x1) = [1 2]x1 >= x1 = x1 181.56/46.32 181.56/46.32 [2 3] [2 3] 181.56/46.32 b(a(x1)) = [1 2]x1 >= [1 2]x1 = c(a(b(c(a(b(x1)))))) 181.56/46.32 181.56/46.32 [0 1 ] 181.56/46.32 b(x1) = [-& 0 ]x1 >= x1 = x1 181.56/46.32 181.56/46.32 [0 0] 181.56/46.32 c(c(x1)) = [0 0]x1 >= x1 = x1 181.56/46.32 problem: 181.56/46.32 DPs: 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 Restore Modifier: 181.56/46.32 DPs: 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 EDG Processor: 181.56/46.32 DPs: 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 graph: 181.56/46.32 b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(c(a(b(x1)))) 181.56/46.32 Arctic Interpretation Processor: 181.56/46.32 dimension: 2 181.56/46.32 usable rules: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 interpretation: 181.56/46.32 [b#](x0) = [1 0]x0 + [0], 181.56/46.32 181.56/46.32 [-& 0 ] [0] 181.56/46.32 [c](x0) = [0 0 ]x0 + [1], 181.56/46.32 181.56/46.32 [0 -&] [-&] 181.56/46.32 [b](x0) = [1 0 ]x0 + [0 ], 181.56/46.32 181.56/46.32 [2 1 ] [1] 181.56/46.32 [a](x0) = [-& 0 ]x0 + [0] 181.56/46.32 orientation: 181.56/46.32 b#(a(x1)) = [3 2]x1 + [2] >= [2 1]x1 + [1] = b#(c(a(b(x1)))) 181.56/46.32 181.56/46.32 [2 1 ] [1] 181.56/46.32 a(x1) = [-& 0 ]x1 + [0] >= x1 = x1 181.56/46.32 181.56/46.32 [2 1] [1] [2 1] [1] 181.56/46.32 b(a(x1)) = [3 2]x1 + [2] >= [3 2]x1 + [2] = c(a(b(c(a(b(x1)))))) 181.56/46.32 181.56/46.32 [0 -&] [-&] 181.56/46.32 b(x1) = [1 0 ]x1 + [0 ] >= x1 = x1 181.56/46.32 181.56/46.32 [0 0] [1] 181.56/46.32 c(c(x1)) = [0 0]x1 + [1] >= x1 = x1 181.56/46.32 problem: 181.56/46.32 DPs: 181.56/46.32 181.56/46.32 TRS: 181.56/46.32 a(x1) -> x1 181.56/46.32 b(a(x1)) -> c(a(b(c(a(b(x1)))))) 181.56/46.32 b(x1) -> x1 181.56/46.32 c(c(x1)) -> x1 181.56/46.32 Qed 181.56/46.33 EOF