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: Matrix Interpretation Processor: dim=4 interpretation: [1 0 1 0] [0] [0 0 1 0] [0] [a](x0) = [0 0 0 0]x0 + [0] [0 1 1 0] [1], [1 0 1 0] [0] [0 0 1 0] [0] [c](x0) = [0 1 0 0]x0 + [0] [0 0 1 0] [1], [1 0 0 0] [0] [0 0 0 1] [0] [b](x0) = [0 0 0 0]x0 + [0] [0 0 0 1] [1] orientation: [1 0 0 1] [0] [1 0 0 1] [0] [0 0 0 1] [0] [0 0 0 1] [0] c(c(b(x1))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(c(b(x1))) [0 0 0 1] [1] [0 0 0 1] [1] [1 1 2 0] [1] [1 1 1 0] [0] [0 1 1 0] [1] [0 1 0 0] [1] a(c(b(a(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(c(c(x1))) [0 1 1 0] [2] [0 1 0 0] [2] [1 1 1 0] [0] [1 0 1 0] [0] [0 1 1 0] [1] [0 0 0 0] [0] b(a(c(x1))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(b(c(a(x1)))) [0 1 1 0] [2] [0 0 0 0] [2] [1 0 1 0] [0] [1 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [0] b(c(a(x1))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = c(a(b(x1))) [0 0 0 0] [2] [0 0 0 0] [1] problem: c(c(b(x1))) -> a(c(b(x1))) b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) Arctic Interpretation Processor: dimension: 1 interpretation: [a](x0) = x0, [c](x0) = 2x0, [b](x0) = 2x0 orientation: c(c(b(x1))) = 6x1 >= 4x1 = a(c(b(x1))) b(a(c(x1))) = 4x1 >= 4x1 = a(b(c(a(x1)))) b(c(a(x1))) = 4x1 >= 4x1 = c(a(b(x1))) problem: b(a(c(x1))) -> a(b(c(a(x1)))) b(c(a(x1))) -> c(a(b(x1))) String Reversal Processor: c(a(b(x1))) -> a(c(b(a(x1)))) a(c(b(x1))) -> b(a(c(x1))) Bounds Processor: bound: 3 enrichment: match automaton: final states: {6,1} transitions: c3(48) -> 49* b1(26) -> 27* b1(11) -> 12* b1(23) -> 24* a1(25) -> 26* a1(10) -> 11* a1(22) -> 23* a1(28) -> 29* c1(27) -> 28* c1(9) -> 10* c1(21) -> 22* b2(37) -> 38* b2(44) -> 45* a2(46) -> 47* a2(36) -> 37* a2(43) -> 44* f30() -> 2* c2(45) -> 46* c2(35) -> 36* a0(5) -> 1* a0(7) -> 8* a0(2) -> 3* b3(50) -> 51* c0(2) -> 7* c0(4) -> 5* a3(49) -> 50* b0(8) -> 6* b0(3) -> 4* 1 -> 7,10 3 -> 9* 6 -> 3,9,8 8 -> 21* 11 -> 25* 12 -> 1* 23 -> 43* 24 -> 23,11 26 -> 35* 29 -> 22* 38 -> 29* 44 -> 48* 47 -> 49,36 51 -> 47,36 problem: Qed