/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: strict: a(a(c(x1))) -> b(b(c(x1))) b(a(c(x1))) -> a(a(b(x1))) weak: a(c(a(x1))) -> a(b(b(x1))) b(b(b(x1))) -> c(c(b(x1))) b(a(c(x1))) -> a(a(c(x1))) c(a(a(x1))) -> a(a(a(x1))) Proof: Root-Labeling Processor: strict: a(a)(a(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) a(a)(a(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) a(a)(a(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) c(a)(a(a)(a(c)(c(a)(x1)))) -> c(b)(b(b)(b(c)(c(a)(x1)))) c(a)(a(a)(a(c)(c(c)(x1)))) -> c(b)(b(b)(b(c)(c(c)(x1)))) c(a)(a(a)(a(c)(c(b)(x1)))) -> c(b)(b(b)(b(c)(c(b)(x1)))) b(a)(a(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) b(a)(a(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) b(a)(a(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(a)(a(b)(b(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(a)(a(b)(b(a)(x1)))) c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(a)(a(b)(b(c)(x1)))) c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(a)(a(b)(b(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(a)(a(b)(b(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(a)(a(b)(b(b)(x1)))) weak: a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) a(c)(c(a)(a(c)(x1))) -> a(b)(b(b)(b(c)(x1))) a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) c(b)(b(b)(b(b)(b(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) c(b)(b(b)(b(b)(b(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) c(b)(b(b)(b(b)(b(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) b(b)(b(b)(b(b)(b(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) a(c)(c(a)(a(a)(a(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) a(c)(c(a)(a(a)(a(c)(x1)))) -> a(a)(a(a)(a(a)(a(c)(x1)))) a(c)(c(a)(a(a)(a(b)(x1)))) -> a(a)(a(a)(a(a)(a(b)(x1)))) c(c)(c(a)(a(a)(a(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) c(c)(c(a)(a(a)(a(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) c(c)(c(a)(a(a)(a(b)(x1)))) -> c(a)(a(a)(a(a)(a(b)(x1)))) b(c)(c(a)(a(a)(a(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) b(c)(c(a)(a(a)(a(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) b(c)(c(a)(a(a)(a(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) String Reversal Processor: strict: c(a)(a(c)(a(a)(a(a)(x1)))) -> c(a)(b(c)(b(b)(a(b)(x1)))) c(c)(a(c)(a(a)(a(a)(x1)))) -> c(c)(b(c)(b(b)(a(b)(x1)))) c(b)(a(c)(a(a)(a(a)(x1)))) -> c(b)(b(c)(b(b)(a(b)(x1)))) c(a)(a(c)(a(a)(c(a)(x1)))) -> c(a)(b(c)(b(b)(c(b)(x1)))) c(c)(a(c)(a(a)(c(a)(x1)))) -> c(c)(b(c)(b(b)(c(b)(x1)))) c(b)(a(c)(a(a)(c(a)(x1)))) -> c(b)(b(c)(b(b)(c(b)(x1)))) c(a)(a(c)(a(a)(b(a)(x1)))) -> c(a)(b(c)(b(b)(b(b)(x1)))) c(c)(a(c)(a(a)(b(a)(x1)))) -> c(c)(b(c)(b(b)(b(b)(x1)))) c(b)(a(c)(a(a)(b(a)(x1)))) -> c(b)(b(c)(b(b)(b(b)(x1)))) c(a)(a(c)(b(a)(a(b)(x1)))) -> b(a)(a(b)(a(a)(a(a)(x1)))) c(c)(a(c)(b(a)(a(b)(x1)))) -> b(c)(a(b)(a(a)(a(a)(x1)))) c(b)(a(c)(b(a)(a(b)(x1)))) -> b(b)(a(b)(a(a)(a(a)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> b(a)(a(b)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> b(c)(a(b)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> b(b)(a(b)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> b(a)(a(b)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> b(c)(a(b)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> b(b)(a(b)(a(a)(b(a)(x1)))) weak: a(a)(c(a)(a(c)(x1))) -> b(a)(b(b)(a(b)(x1))) a(c)(c(a)(a(c)(x1))) -> b(c)(b(b)(a(b)(x1))) a(b)(c(a)(a(c)(x1))) -> b(b)(b(b)(a(b)(x1))) b(a)(b(b)(b(b)(a(b)(x1)))) -> b(a)(c(b)(c(c)(a(c)(x1)))) b(c)(b(b)(b(b)(a(b)(x1)))) -> b(c)(c(b)(c(c)(a(c)(x1)))) b(b)(b(b)(b(b)(a(b)(x1)))) -> b(b)(c(b)(c(c)(a(c)(x1)))) b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(a(b)(x1)))) -> c(a)(a(c)(a(a)(a(a)(x1)))) c(c)(a(c)(b(a)(a(b)(x1)))) -> c(c)(a(c)(a(a)(a(a)(x1)))) c(b)(a(c)(b(a)(a(b)(x1)))) -> c(b)(a(c)(a(a)(a(a)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(a(c)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) a(c)(a(a)(c(a)(a(c)(x1)))) -> a(c)(a(a)(a(a)(a(a)(x1)))) a(b)(a(a)(c(a)(a(c)(x1)))) -> a(b)(a(a)(a(a)(a(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) -> a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) -> a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) -> a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) -> a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) -> a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) -> a(b)(a(a)(a(a)(b(a)(x1)))) LPO Processor: precedence: a(b) ~ a(c) > b(a) ~ c(b) ~ c(c) ~ b(c) ~ b(b) ~ c(a) ~ a(a) problem: strict: c(a)(a(c)(b(a)(c(b)(x1)))) -> b(a)(a(b)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> b(c)(a(b)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> b(b)(a(b)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> b(a)(a(b)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> b(c)(a(b)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> b(b)(a(b)(a(a)(b(a)(x1)))) weak: a(a)(c(a)(a(c)(x1))) -> b(a)(b(b)(a(b)(x1))) b(a)(b(b)(b(b)(a(b)(x1)))) -> b(a)(c(b)(c(c)(a(c)(x1)))) b(c)(b(b)(b(b)(a(b)(x1)))) -> b(c)(c(b)(c(c)(a(c)(x1)))) b(b)(b(b)(b(b)(a(b)(x1)))) -> b(b)(c(b)(c(c)(a(c)(x1)))) b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) -> a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) -> a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) -> a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) -> a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) -> a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) -> a(b)(a(a)(a(a)(b(a)(x1)))) RT Transformation Processor: c(a)(a(c)(b(a)(c(b)(x1)))) -> b(a)(a(b)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> b(c)(a(b)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> b(b)(a(b)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> b(a)(a(b)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> b(c)(a(b)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> b(b)(a(b)(a(a)(b(a)(x1)))) a(a)(c(a)(a(c)(x1))) -> b(a)(b(b)(a(b)(x1))) b(a)(b(b)(b(b)(a(b)(x1)))) -> b(a)(c(b)(c(c)(a(c)(x1)))) b(c)(b(b)(b(b)(a(b)(x1)))) -> b(c)(c(b)(c(c)(a(c)(x1)))) b(b)(b(b)(b(b)(a(b)(x1)))) -> b(b)(c(b)(c(c)(a(c)(x1)))) b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) -> a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) -> a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) -> a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) -> a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) -> a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) -> a(b)(a(a)(a(a)(b(a)(x1)))) Matrix Interpretation Processor: dim=1 interpretation: [a(c)](x0) = 2x0 + 2, [b(c)](x0) = 2x0, [a(a)](x0) = x0, [c(a)](x0) = 2x0, [c(b)](x0) = x0, [b(b)](x0) = 2x0, [b(a)](x0) = 2x0, [c(c)](x0) = x0, [a(b)](x0) = x0 + 1 orientation: c(a)(a(c)(b(a)(c(b)(x1)))) = 8x1 + 4 >= 4x1 + 2 = b(a)(a(b)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) = 4x1 + 2 >= 4x1 + 2 = b(c)(a(b)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) = 4x1 + 2 >= 4x1 + 2 = b(b)(a(b)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) = 16x1 + 4 >= 4x1 + 2 = b(a)(a(b)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) = 8x1 + 2 >= 4x1 + 2 = b(c)(a(b)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) = 8x1 + 2 >= 4x1 + 2 = b(b)(a(b)(a(a)(b(a)(x1)))) a(a)(c(a)(a(c)(x1))) = 4x1 + 4 >= 4x1 + 4 = b(a)(b(b)(a(b)(x1))) b(a)(b(b)(b(b)(a(b)(x1)))) = 8x1 + 8 >= 4x1 + 4 = b(a)(c(b)(c(c)(a(c)(x1)))) b(c)(b(b)(b(b)(a(b)(x1)))) = 8x1 + 8 >= 4x1 + 4 = b(c)(c(b)(c(c)(a(c)(x1)))) b(b)(b(b)(b(b)(a(b)(x1)))) = 8x1 + 8 >= 4x1 + 4 = b(b)(c(b)(c(c)(a(c)(x1)))) b(a)(b(b)(b(b)(c(b)(x1)))) = 8x1 >= 2x1 = b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) = 8x1 >= 2x1 = b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) = 8x1 >= 2x1 = b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) = 16x1 >= 4x1 = b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) = 16x1 >= 4x1 = b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) = 16x1 >= 4x1 = b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) = 8x1 + 4 >= 8x1 + 4 = c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) = 4x1 + 2 >= 4x1 + 2 = c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) = 4x1 + 2 >= 4x1 + 2 = c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) = 16x1 + 4 >= 8x1 + 4 = c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) = 8x1 + 2 >= 4x1 + 2 = c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) = 8x1 + 2 >= 4x1 + 2 = c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) = 2x1 >= 2x1 = a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) = 4x1 + 2 >= 4x1 + 2 = a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) = 2x1 + 1 >= 2x1 + 1 = a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) = 4x1 >= 2x1 = a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) = 8x1 + 2 >= 4x1 + 2 = a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) = 4x1 + 1 >= 2x1 + 1 = a(b)(a(a)(a(a)(b(a)(x1)))) problem: c(c)(a(c)(b(a)(c(b)(x1)))) -> b(c)(a(b)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> b(b)(a(b)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> b(c)(a(b)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> b(b)(a(b)(a(a)(b(a)(x1)))) a(a)(c(a)(a(c)(x1))) -> b(a)(b(b)(a(b)(x1))) b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) -> a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) -> a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) -> a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) -> a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) -> a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) -> a(b)(a(a)(a(a)(b(a)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [0] [a(c)](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [b(c)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [a(a)](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [c(a)](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [c(b)](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [b(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [b(a)](x0) = [0 0 0]x0 + [1] [0 1 0] [0], [1 0 0] [c(c)](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [a(b)](x0) = [0 0 0]x0 [0 0 0] orientation: [1 1 0] [1] [1 0 0] c(c)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(c)(a(b)(a(a)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1 1 0] [1] [1 0 0] c(b)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b)(a(b)(a(a)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [1 0 0] [1] [1 0 0] c(c)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(c)(a(b)(a(a)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] c(b)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b)(a(b)(a(a)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [1 1 1] [0] [1 0 0] [0] a(a)(c(a)(a(c)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(b(b)(a(b)(x1))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] b(a)(b(b)(b(b)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] b(c)(b(b)(b(b)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] b(b)(b(b)(b(b)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] b(a)(b(b)(b(b)(b(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] b(c)(b(b)(b(b)(b(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] b(b)(b(b)(b(b)(b(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [0 0 0] [1 1 0] [1] [1 0 0] [1] c(a)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(a)(a(c)(a(a)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [1] c(c)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(a(c)(a(a)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [1] c(b)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b)(a(c)(a(a)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] c(a)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(a)(a(c)(a(a)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] c(c)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(a(c)(a(a)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] c(b)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b)(a(c)(a(a)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] a(a)(a(a)(c(a)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a)(a(a)(a(a)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] a(c)(a(a)(c(a)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(a(a)(a(a)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] a(b)(a(a)(c(a)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(a(a)(a(a)(c(a)(x1)))) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a(a)(a(a)(c(a)(b(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a)(a(a)(a(a)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] a(c)(a(a)(c(a)(b(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(a(a)(a(a)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] a(b)(a(a)(c(a)(b(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(a(a)(a(a)(b(a)(x1)))) [0 0 0] [0 0 0] problem: a(a)(c(a)(a(c)(x1))) -> b(a)(b(b)(a(b)(x1))) b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) -> a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) -> a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) -> a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) -> a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) -> a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) -> a(b)(a(a)(a(a)(b(a)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [a(c)](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [b(c)](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [0] [a(a)](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [c(a)](x0) = [1 0 0]x0 [1 0 0] , [1 0 0] [c(b)](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [b(b)](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [b(a)](x0) = [0 0 1]x0 [0 0 1] , [1 0 0] [c(c)](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [a(b)](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1] [1 0 0] a(a)(c(a)(a(c)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a)(b(b)(a(b)(x1))) [0 0 0] [1] [0 0 0] [1 1 1] [1 1 0] b(a)(b(b)(b(b)(c(b)(x1)))) = [0 1 1]x1 >= [0 1 0]x1 = b(a)(c(b)(c(c)(c(c)(x1)))) [0 1 1] [0 1 0] [1 0 0] [1 0 0] b(c)(b(b)(b(b)(c(b)(x1)))) = [0 1 1]x1 >= [0 1 0]x1 = b(c)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] b(b)(b(b)(b(b)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(c(b)(c(c)(c(c)(x1)))) [0 1 1] [0 1 0] [1 0 1] [1 0 1] b(a)(b(b)(b(b)(b(b)(x1)))) = [0 0 1]x1 >= [0 0 1]x1 = b(a)(c(b)(c(c)(b(c)(x1)))) [0 0 1] [0 0 1] [1 0 0] [1 0 0] b(c)(b(b)(b(b)(b(b)(x1)))) = [0 0 1]x1 >= [0 0 1]x1 = b(c)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] b(b)(b(b)(b(b)(b(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(c(b)(c(c)(b(c)(x1)))) [0 0 1] [0 0 1] [1 1 1] [1] [1 1 0] [1] c(a)(a(c)(b(a)(c(b)(x1)))) = [1 1 1]x1 + [1] >= [1 1 0]x1 + [1] = c(a)(a(c)(a(a)(c(a)(x1)))) [1 1 1] [1] [1 1 0] [1] [1 1 1] [1] [1 1 0] [1] c(c)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(a(c)(a(a)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 1 0] [1] c(b)(a(c)(b(a)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b)(a(c)(a(a)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] c(a)(a(c)(b(a)(b(b)(x1)))) = [1 0 1]x1 + [1] >= [1 0 1]x1 + [1] = c(a)(a(c)(a(a)(b(a)(x1)))) [1 0 1] [1] [1 0 1] [1] [1 0 1] [1] [1 0 1] [1] c(c)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(a(c)(a(a)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] c(b)(a(c)(b(a)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b)(a(c)(a(a)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] a(a)(a(a)(c(a)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(a)(a(a)(a(a)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 1 0] [1] a(c)(a(a)(c(a)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(a(a)(a(a)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] a(b)(a(a)(c(a)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(a(a)(a(a)(c(a)(x1)))) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] a(a)(a(a)(c(a)(b(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(a)(a(a)(a(a)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] a(c)(a(a)(c(a)(b(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(a(a)(a(a)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 1] a(b)(a(a)(c(a)(b(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(a(a)(a(a)(b(a)(x1)))) [0 0 0] [0 0 0] problem: b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) -> c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) -> c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) -> c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) -> c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) -> c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) -> c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) -> a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) -> a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) -> a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) -> a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) -> a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) -> a(b)(a(a)(a(a)(b(a)(x1)))) Matrix Interpretation Processor: dim=1 interpretation: [a(c)](x0) = 2x0, [b(c)](x0) = 2x0 + 2, [a(a)](x0) = 2x0 + 3, [c(a)](x0) = 2x0, [c(b)](x0) = 2x0 + 2, [b(b)](x0) = 2x0 + 2, [b(a)](x0) = 2x0, [c(c)](x0) = 2x0 + 2, [a(b)](x0) = x0 + 1 orientation: b(a)(b(b)(b(b)(c(b)(x1)))) = 16x1 + 28 >= 16x1 + 28 = b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) = 16x1 + 30 >= 16x1 + 30 = b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) = 16x1 + 30 >= 16x1 + 30 = b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 28 >= 16x1 + 28 = b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 30 >= 16x1 + 30 = b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 30 >= 16x1 + 30 = b(b)(c(b)(c(c)(b(c)(x1)))) c(a)(a(c)(b(a)(c(b)(x1)))) = 16x1 + 16 >= 16x1 + 12 = c(a)(a(c)(a(a)(c(a)(x1)))) c(c)(a(c)(b(a)(c(b)(x1)))) = 16x1 + 18 >= 16x1 + 14 = c(c)(a(c)(a(a)(c(a)(x1)))) c(b)(a(c)(b(a)(c(b)(x1)))) = 16x1 + 18 >= 16x1 + 14 = c(b)(a(c)(a(a)(c(a)(x1)))) c(a)(a(c)(b(a)(b(b)(x1)))) = 16x1 + 16 >= 16x1 + 12 = c(a)(a(c)(a(a)(b(a)(x1)))) c(c)(a(c)(b(a)(b(b)(x1)))) = 16x1 + 18 >= 16x1 + 14 = c(c)(a(c)(a(a)(b(a)(x1)))) c(b)(a(c)(b(a)(b(b)(x1)))) = 16x1 + 18 >= 16x1 + 14 = c(b)(a(c)(a(a)(b(a)(x1)))) a(a)(a(a)(c(a)(c(c)(x1)))) = 16x1 + 25 >= 16x1 + 21 = a(a)(a(a)(a(a)(c(a)(x1)))) a(c)(a(a)(c(a)(c(c)(x1)))) = 16x1 + 22 >= 16x1 + 18 = a(c)(a(a)(a(a)(c(a)(x1)))) a(b)(a(a)(c(a)(c(c)(x1)))) = 8x1 + 12 >= 8x1 + 10 = a(b)(a(a)(a(a)(c(a)(x1)))) a(a)(a(a)(c(a)(b(c)(x1)))) = 16x1 + 25 >= 16x1 + 21 = a(a)(a(a)(a(a)(b(a)(x1)))) a(c)(a(a)(c(a)(b(c)(x1)))) = 16x1 + 22 >= 16x1 + 18 = a(c)(a(a)(a(a)(b(a)(x1)))) a(b)(a(a)(c(a)(b(c)(x1)))) = 8x1 + 12 >= 8x1 + 10 = a(b)(a(a)(a(a)(b(a)(x1)))) problem: b(a)(b(b)(b(b)(c(b)(x1)))) -> b(a)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(a)(b(b)(b(b)(b(b)(x1)))) -> b(a)(c(b)(c(c)(b(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [b(c)](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [c(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [b(b)](x0) = [0 0 0]x0 + [1] [0 1 0] [0], [1 1 0] [b(a)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [c(c)](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1] [1 0 0] b(a)(b(b)(b(b)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] b(c)(b(b)(b(b)(c(b)(x1)))) = [1 0 0]x1 >= [1 0 0]x1 = b(c)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] b(b)(b(b)(b(b)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b)(c(b)(c(c)(c(c)(x1)))) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 0] b(a)(b(b)(b(b)(b(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] b(c)(b(b)(b(b)(b(b)(x1)))) = [1 0 0]x1 >= [1 0 0]x1 = b(c)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] b(b)(b(b)(b(b)(b(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b)(c(b)(c(c)(b(c)(x1)))) [0 0 0] [1] [0 0 0] [0] problem: b(c)(b(b)(b(b)(c(b)(x1)))) -> b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) -> b(b)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(b)(c(b)(c(c)(b(c)(x1)))) Matrix Interpretation Processor: dim=1 interpretation: [b(c)](x0) = 2x0 + 1, [c(b)](x0) = 2x0 + 2, [b(b)](x0) = 2x0 + 1, [c(c)](x0) = 2x0 orientation: b(c)(b(b)(b(b)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 5 = b(c)(c(b)(c(c)(c(c)(x1)))) b(b)(b(b)(b(b)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 5 = b(b)(c(b)(c(c)(c(c)(x1)))) b(c)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 15 >= 16x1 + 13 = b(c)(c(b)(c(c)(b(c)(x1)))) b(b)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 15 >= 16x1 + 13 = b(b)(c(b)(c(c)(b(c)(x1)))) problem: Qed