YES Problem: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) Proof: DP Processor: DPs: c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> c#(x1) a#(c(b(a(x1)))) -> c#(c(x1)) a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> a#(x1) b#(a(c(x1))) -> c#(a(x1)) b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> c#(a(b(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) TDG Processor: DPs: c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> c#(x1) a#(c(b(a(x1)))) -> c#(c(x1)) a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> a#(x1) b#(a(c(x1))) -> c#(a(x1)) b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> c#(a(b(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) graph: b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> c#(a(b(x1))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> a#(b(x1)) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> b#(x1) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> c#(a(x1)) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> a#(x1) b#(a(c(x1))) -> a#(b(c(a(x1)))) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) -> a#(c(b(a(x1)))) -> c#(c(x1)) b#(a(c(x1))) -> a#(b(c(a(x1)))) -> a#(c(b(a(x1)))) -> c#(x1) b#(a(c(x1))) -> a#(x1) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> a#(x1) -> a#(c(b(a(x1)))) -> c#(c(x1)) b#(a(c(x1))) -> a#(x1) -> a#(c(b(a(x1)))) -> c#(x1) b#(a(c(x1))) -> c#(a(x1)) -> c#(c(b(x1))) -> a#(c(b(x1))) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> c#(a(b(x1))) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> c#(a(x1)) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> a#(x1) b#(c(a(x1))) -> a#(b(x1)) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(c(a(x1))) -> a#(b(x1)) -> a#(c(b(a(x1)))) -> c#(c(x1)) b#(c(a(x1))) -> a#(b(x1)) -> a#(c(b(a(x1)))) -> c#(x1) b#(c(a(x1))) -> c#(a(b(x1))) -> c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> c#(a(b(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> a#(b(x1)) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> b#(x1) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> c#(a(x1)) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> a#(x1) a#(c(b(a(x1)))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(b(x1))) c#(c(b(x1))) -> a#(c(b(x1))) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) c#(c(b(x1))) -> a#(c(b(x1))) -> a#(c(b(a(x1)))) -> c#(c(x1)) c#(c(b(x1))) -> a#(c(b(x1))) -> a#(c(b(a(x1)))) -> c#(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [b#](x0) = 2x0, [a#](x0) = 1x0, [c#](x0) = 1x0, [a](x0) = x0, [c](x0) = x0, [b](x0) = 1x0 orientation: c#(c(b(x1))) = 2x1 >= 2x1 = a#(c(b(x1))) a#(c(b(a(x1)))) = 2x1 >= 1x1 = c#(x1) a#(c(b(a(x1)))) = 2x1 >= 1x1 = c#(c(x1)) a#(c(b(a(x1)))) = 2x1 >= 2x1 = b#(c(c(x1))) b#(a(c(x1))) = 2x1 >= 1x1 = a#(x1) b#(a(c(x1))) = 2x1 >= 1x1 = c#(a(x1)) b#(a(c(x1))) = 2x1 >= 2x1 = b#(c(a(x1))) b#(a(c(x1))) = 2x1 >= 2x1 = a#(b(c(a(x1)))) b#(c(a(x1))) = 2x1 >= 2x1 = b#(x1) b#(c(a(x1))) = 2x1 >= 2x1 = a#(b(x1)) b#(c(a(x1))) = 2x1 >= 2x1 = c#(a(b(x1))) c(c(b(x1))) = 1x1 >= 1x1 = a(c(b(x1))) a(c(b(a(x1)))) = 1x1 >= 1x1 = b(c(c(x1))) b(a(c(x1))) = 1x1 >= 1x1 = a(b(c(a(x1)))) b(c(a(x1))) = 1x1 >= 1x1 = c(a(b(x1))) problem: DPs: c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> c#(a(b(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) EDG Processor: DPs: c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> c#(a(b(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) graph: b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> b#(x1) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> a#(b(x1)) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> c#(a(b(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> c#(a(b(x1))) b#(c(a(x1))) -> a#(b(x1)) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(c(a(x1))) -> c#(a(b(x1))) -> c#(c(b(x1))) -> a#(c(b(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> b#(x1) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> a#(b(x1)) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> c#(a(b(x1))) c#(c(b(x1))) -> a#(c(b(x1))) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [0], [a#](x0) = [0], [c#](x0) = [0 0 1 0]x0, [0 0 1 0] [0 0 0 0] [a](x0) = [0 0 0 0]x0 [0 0 0 0] , [1 0 0 0] [0 0 0 0] [c](x0) = [1 0 0 0]x0 [0 0 0 0] , [1] [0] [b](x0) = [0] [0] orientation: c#(c(b(x1))) = [1] >= [0] = a#(c(b(x1))) a#(c(b(a(x1)))) = [0] >= [0] = b#(c(c(x1))) b#(a(c(x1))) = [0] >= [0] = b#(c(a(x1))) b#(a(c(x1))) = [0] >= [0] = a#(b(c(a(x1)))) b#(c(a(x1))) = [0] >= [0] = b#(x1) b#(c(a(x1))) = [0] >= [0] = a#(b(x1)) b#(c(a(x1))) = [0] >= [0] = c#(a(b(x1))) [1] [1] [0] [0] c(c(b(x1))) = [1] >= [0] = a(c(b(x1))) [0] [0] [1] [1] [0] [0] a(c(b(a(x1)))) = [0] >= [0] = b(c(c(x1))) [0] [0] [1] [0] [0] [0] b(a(c(x1))) = [0] >= [0] = a(b(c(a(x1)))) [0] [0] [1] [0] [0] [0] b(c(a(x1))) = [0] >= [0] = c(a(b(x1))) [0] [0] problem: DPs: a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> c#(a(b(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) EDG Processor: DPs: a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> c#(a(b(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) graph: b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> c#(a(b(x1))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> a#(b(x1)) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> b#(x1) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> c#(a(b(x1))) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(c(a(x1))) -> a#(b(x1)) -> a#(c(b(a(x1)))) -> b#(c(c(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> c#(a(b(x1))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> a#(b(x1)) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(c(a(x1))) -> b#(x1) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) a#(c(b(a(x1)))) -> b#(c(c(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) SCC Processor: #sccs: 1 #rules: 5 #arcs: 17/36 DPs: b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) a#(c(b(a(x1)))) -> b#(c(c(x1))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [0], [a#](x0) = [1 0 0 0]x0, [0 0 0 0] [0] [0 0 0 0] [1] [a](x0) = [1 0 0 0]x0 + [0] [0 0 0 1] [0], [0 0 1 0] [0] [0 0 0 0] [1] [c](x0) = [0 0 1 0]x0 + [0] [0 0 0 1] [0], [0 0 0 0] [0] [0 1 0 0] [0] [b](x0) = [0 1 0 0]x0 + [0] [0 0 0 1] [1] orientation: b#(a(c(x1))) = [0] >= [0] = b#(c(a(x1))) b#(a(c(x1))) = [0] >= [0] = a#(b(c(a(x1)))) a#(c(b(a(x1)))) = [1] >= [0] = b#(c(c(x1))) b#(c(a(x1))) = [0] >= [0] = b#(x1) b#(c(a(x1))) = [0] >= [0] = a#(b(x1)) [0 1 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] c(c(b(x1))) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = a(c(b(x1))) [0 0 0 1] [1] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] a(c(b(a(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(c(c(x1))) [0 0 0 1] [1] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] b(a(c(x1))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = a(b(c(a(x1)))) [0 0 0 1] [1] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] b(c(a(x1))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = c(a(b(x1))) [0 0 0 1] [1] [0 0 0 1] [1] problem: DPs: b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) EDG Processor: DPs: b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> a#(b(x1)) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) graph: b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> b#(x1) b#(a(c(x1))) -> b#(c(a(x1))) -> b#(c(a(x1))) -> a#(b(x1)) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> b#(c(a(x1))) b#(c(a(x1))) -> b#(x1) -> b#(a(c(x1))) -> a#(b(c(a(x1)))) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1) b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> a#(b(x1)) SCC Processor: #sccs: 1 #rules: 2 #arcs: 8/16 DPs: b#(a(c(x1))) -> b#(c(a(x1))) b#(c(a(x1))) -> b#(x1) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) Matrix Interpretation Processor: dim=3 interpretation: [b#](x0) = [1 0 0]x0, [1 1 0] [a](x0) = [0 0 0]x0 [0 1 0] , [1 0 0] [1] [c](x0) = [0 1 1]x0 + [0] [0 1 0] [0], [1 0 0] [0] [b](x0) = [0 0 0]x0 + [0] [0 0 0] [1] orientation: b#(a(c(x1))) = [1 1 1]x1 + [1] >= [1 1 0]x1 + [1] = b#(c(a(x1))) b#(c(a(x1))) = [1 1 0]x1 + [1] >= [1 0 0]x1 = b#(x1) [1 0 0] [2] [1 0 0] [2] c(c(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(c(b(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [2] [1 0 0] [2] a(c(b(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c(c(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 0] [1] b(a(c(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(c(a(x1)))) [0 0 0] [1] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] b(c(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(a(b(x1))) [0 0 0] [1] [0 0 0] [0] problem: DPs: b#(a(c(x1))) -> b#(c(a(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) EDG Processor: DPs: b#(a(c(x1))) -> b#(c(a(x1))) TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) graph: b#(a(c(x1))) -> b#(c(a(x1))) -> b#(a(c(x1))) -> b#(c(a(x1))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [0 0 1 0]x0, [0 0 0 0] [0] [0 0 0 1] [0] [a](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [0 0 0 0] [0 1 0 0] [c](x0) = [0 0 0 1]x0 [0 1 0 0] , [0] [1] [b](x0) = [1] [0] orientation: b#(a(c(x1))) = [1] >= [0] = b#(c(a(x1))) [0] [0] [1] [1] c(c(b(x1))) = [1] >= [1] = a(c(b(x1))) [1] [0] [0] [0] [1] [1] a(c(b(a(x1)))) = [1] >= [1] = b(c(c(x1))) [0] [0] [0] [0] [1] [0] b(a(c(x1))) = [1] >= [1] = a(b(c(a(x1)))) [0] [0] [0] [0] [1] [0] b(c(a(x1))) = [1] >= [0] = c(a(b(x1))) [0] [0] problem: DPs: TRS: c(c(b(x1))) -> a(c(b(x1))) a(c(b(a(x1)))) -> b(c(c(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) Qed