175.26/44.82 YES 175.56/44.83 175.56/44.83 Problem: 175.56/44.83 a(b(c(x1))) -> c(c(c(b(b(b(a(a(a(x1))))))))) 175.56/44.83 c(b(x1)) -> a(a(a(x1))) 175.56/44.83 a(x1) -> x1 175.56/44.83 b(x1) -> x1 175.56/44.83 c(x1) -> x1 175.56/44.83 175.56/44.83 Proof: 175.56/44.83 String Reversal Processor: 175.56/44.83 c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 b(c(x1)) -> a(a(a(x1))) 175.56/44.83 a(x1) -> x1 175.56/44.83 b(x1) -> x1 175.56/44.83 c(x1) -> x1 175.56/44.83 DP Processor: 175.56/44.83 DPs: 175.56/44.83 c#(b(a(x1))) -> c#(x1) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) 175.56/44.83 c#(b(a(x1))) -> b#(c(c(c(x1)))) 175.56/44.83 c#(b(a(x1))) -> b#(b(c(c(c(x1))))) 175.56/44.83 c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) 175.56/44.83 c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1))))))) 175.56/44.83 c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1)))))))) 175.56/44.83 c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 b#(c(x1)) -> a#(x1) 175.56/44.83 b#(c(x1)) -> a#(a(x1)) 175.56/44.83 b#(c(x1)) -> a#(a(a(x1))) 175.56/44.83 TRS: 175.56/44.83 c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 b(c(x1)) -> a(a(a(x1))) 175.56/44.83 a(x1) -> x1 175.56/44.83 b(x1) -> x1 175.56/44.83 c(x1) -> x1 175.56/44.83 TDG Processor: 175.56/44.83 DPs: 175.56/44.83 c#(b(a(x1))) -> c#(x1) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) 175.56/44.83 c#(b(a(x1))) -> b#(c(c(c(x1)))) 175.56/44.83 c#(b(a(x1))) -> b#(b(c(c(c(x1))))) 175.56/44.83 c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) 175.56/44.83 c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1))))))) 175.56/44.83 c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1)))))))) 175.56/44.83 c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 b#(c(x1)) -> a#(x1) 175.56/44.83 b#(c(x1)) -> a#(a(x1)) 175.56/44.83 b#(c(x1)) -> a#(a(a(x1))) 175.56/44.83 TRS: 175.56/44.83 c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 b(c(x1)) -> a(a(a(x1))) 175.56/44.83 a(x1) -> x1 175.56/44.83 b(x1) -> x1 175.56/44.83 c(x1) -> x1 175.56/44.83 graph: 175.56/44.83 c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) -> 175.56/44.83 b#(c(x1)) -> a#(a(a(x1))) 175.56/44.83 c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) -> 175.56/44.83 b#(c(x1)) -> a#(a(x1)) 175.56/44.83 c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) -> b#(c(x1)) -> a#(x1) 175.56/44.83 c#(b(a(x1))) -> b#(b(c(c(c(x1))))) -> 175.56/44.83 b#(c(x1)) -> a#(a(a(x1))) 175.56/44.83 c#(b(a(x1))) -> b#(b(c(c(c(x1))))) -> b#(c(x1)) -> a#(a(x1)) 175.56/44.83 c#(b(a(x1))) -> b#(b(c(c(c(x1))))) -> b#(c(x1)) -> a#(x1) 175.56/44.83 c#(b(a(x1))) -> b#(c(c(c(x1)))) -> b#(c(x1)) -> a#(a(a(x1))) 175.56/44.83 c#(b(a(x1))) -> b#(c(c(c(x1)))) -> b#(c(x1)) -> a#(a(x1)) 175.56/44.83 c#(b(a(x1))) -> b#(c(c(c(x1)))) -> b#(c(x1)) -> a#(x1) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> 175.56/44.83 c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> 175.56/44.83 c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1)))))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> 175.56/44.83 c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1))))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> 175.56/44.83 c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> b#(b(c(c(c(x1))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> b#(c(c(c(x1)))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> c#(c(c(x1))) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> c#(c(x1)) 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> c#(x1) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> 175.56/44.83 c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> 175.56/44.83 c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1)))))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1))))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(b(c(c(c(x1))))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(c(c(c(x1)))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(c(x1))) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) 175.56/44.83 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1)))))))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1))))))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(b(c(c(c(x1))))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(c(c(c(x1)))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(c(x1))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1)) 175.56/44.83 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1) 175.56/44.83 SCC Processor: 175.56/44.83 #sccs: 1 175.56/44.83 #rules: 3 175.56/44.83 #arcs: 36/144 175.56/44.83 DPs: 175.56/44.83 c#(b(a(x1))) -> c#(c(c(x1))) 175.56/44.83 c#(b(a(x1))) -> c#(x1) 175.56/44.84 c#(b(a(x1))) -> c#(c(x1)) 175.56/44.84 TRS: 175.56/44.84 c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.84 b(c(x1)) -> a(a(a(x1))) 175.56/44.84 a(x1) -> x1 175.56/44.84 b(x1) -> x1 175.56/44.84 c(x1) -> x1 175.56/44.84 Arctic Interpretation Processor: 175.56/44.84 dimension: 2 175.56/44.84 usable rules: 175.56/44.84 c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.84 b(c(x1)) -> a(a(a(x1))) 175.56/44.84 a(x1) -> x1 175.56/44.84 b(x1) -> x1 175.56/44.84 c(x1) -> x1 175.56/44.84 interpretation: 175.56/44.84 [c#](x0) = [-& 0 ]x0 + [1], 175.56/44.84 175.56/44.84 [0 2 ] [0 ] 175.56/44.84 [a](x0) = [-& 0 ]x0 + [-&], 175.56/44.84 175.56/44.84 [0 0] [1] 175.56/44.84 [b](x0) = [0 0]x0 + [3], 175.56/44.84 175.56/44.84 [0 2 ] [0] 175.56/44.84 [c](x0) = [-& 0 ]x0 + [0] 175.56/44.84 orientation: 175.56/44.84 c#(b(a(x1))) = [0 2]x1 + [3] >= [-& 0 ]x1 + [1] = c#(c(c(x1))) 175.56/44.84 175.56/44.84 c#(b(a(x1))) = [0 2]x1 + [3] >= [-& 0 ]x1 + [1] = c#(x1) 175.56/44.84 175.56/44.84 c#(b(a(x1))) = [0 2]x1 + [3] >= [-& 0 ]x1 + [1] = c#(c(x1)) 175.56/44.84 175.56/44.84 [2 4] [5] [2 4] [5] 175.56/44.84 c(b(a(x1))) = [0 2]x1 + [3] >= [0 2]x1 + [3] = a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.84 175.56/44.84 [0 2] [1] [0 2 ] [0 ] 175.56/44.84 b(c(x1)) = [0 2]x1 + [3] >= [-& 0 ]x1 + [-&] = a(a(a(x1))) 175.56/44.84 175.56/44.84 [0 2 ] [0 ] 175.56/44.84 a(x1) = [-& 0 ]x1 + [-&] >= x1 = x1 175.56/44.84 175.56/44.84 [0 0] [1] 175.56/44.84 b(x1) = [0 0]x1 + [3] >= x1 = x1 175.56/44.84 175.56/44.84 [0 2 ] [0] 175.56/44.84 c(x1) = [-& 0 ]x1 + [0] >= x1 = x1 175.56/44.84 problem: 175.56/44.84 DPs: 175.56/44.84 175.56/44.84 TRS: 175.56/44.84 c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1))))))))) 175.56/44.84 b(c(x1)) -> a(a(a(x1))) 175.56/44.84 a(x1) -> x1 175.56/44.84 b(x1) -> x1 175.56/44.84 c(x1) -> x1 175.56/44.84 Qed 175.56/44.84 EOF