/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: strict: a(a(c(x1))) -> a(c(c(x1))) b(b(c(x1))) -> a(b(b(x1))) weak: c(c(b(x1))) -> a(c(a(x1))) b(a(c(x1))) -> c(a(c(x1))) c(b(c(x1))) -> b(b(b(x1))) b(b(a(x1))) -> b(a(c(x1))) Proof: Root-Labeling Processor: strict: a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(b)(b(b)(b(a)(x1)))) c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(b)(b(b)(b(c)(x1)))) c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(b)(b(b)(b(b)(x1)))) b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(b)(b(b)(b(a)(x1)))) b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(b)(b(b)(b(c)(x1)))) b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(b)(b(b)(b(b)(x1)))) weak: a(c)(c(c)(c(b)(b(a)(x1)))) -> a(a)(a(c)(c(a)(a(a)(x1)))) a(c)(c(c)(c(b)(b(c)(x1)))) -> a(a)(a(c)(c(a)(a(c)(x1)))) a(c)(c(c)(c(b)(b(b)(x1)))) -> a(a)(a(c)(c(a)(a(b)(x1)))) c(c)(c(c)(c(b)(b(a)(x1)))) -> c(a)(a(c)(c(a)(a(a)(x1)))) c(c)(c(c)(c(b)(b(c)(x1)))) -> c(a)(a(c)(c(a)(a(c)(x1)))) c(c)(c(c)(c(b)(b(b)(x1)))) -> c(a)(a(c)(c(a)(a(b)(x1)))) b(c)(c(c)(c(b)(b(a)(x1)))) -> b(a)(a(c)(c(a)(a(a)(x1)))) b(c)(c(c)(c(b)(b(c)(x1)))) -> b(a)(a(c)(c(a)(a(c)(x1)))) b(c)(c(c)(c(b)(b(b)(x1)))) -> b(a)(a(c)(c(a)(a(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) b(b)(b(a)(a(a)(x1))) -> b(a)(a(c)(c(a)(x1))) b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) LPO Processor: precedence: b(c) ~ b(b) ~ a(b) ~ c(b) ~ c(c) ~ a(c) ~ a(a) > b(a) ~ c(a) problem: strict: a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) weak: a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) RT Transformation Processor: a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [a(c)](x0) = [0 0 1]x0 [1 0 0] , [1 0 0] [a(b)](x0) = [0 0 0]x0 [0 1 0] , [1 1 0] [a(a)](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [c(a)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [b(c)](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [0] [c(b)](x0) = [0 0 0]x0 + [0] [0 1 0] [1], [1 0 0] [b(a)](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [b(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [c(c)](x0) = [0 0 1]x0 [0 0 1] orientation: [1 0 0] [1 0 0] a(a)(a(c)(c(a)(x1))) = [0 0 0]x1 >= [0 0 0]x1 = a(c)(c(c)(c(a)(x1))) [1 0 0] [1 0 0] [1 0 1] [1 0 0] a(a)(a(c)(c(c)(x1))) = [0 0 1]x1 >= [0 0 1]x1 = a(c)(c(c)(c(c)(x1))) [1 0 0] [1 0 0] [1 1 1] [1] [1 0 1] [0] a(a)(a(c)(c(b)(x1))) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = a(c)(c(c)(c(b)(x1))) [1 0 1] [0] [1 0 1] [0] [1 0 0] [1 0 0] a(b)(b(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(a)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a(b)(b(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(c)(x1)))) [0 0 0] [0 0 0] [1 0 1] [1 0 0] a(b)(b(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(b)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(c)(c(a)(a(c)(c(a)(x1)))) [1 0 0] [1 0 0] [1 0 0] [1 0 0] a(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(c)(c(a)(a(c)(c(c)(x1)))) [1 0 0] [1 0 0] [1 0 1] [1 0 1] a(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(c)(c(a)(a(c)(c(b)(x1)))) [1 0 1] [1 0 1] [1 0 0] [0] [1 0 0] c(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c)(c(a)(a(c)(c(a)(x1)))) [1 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] c(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c)(c(a)(a(c)(c(c)(x1)))) [1 0 0] [1] [0 0 0] [1 0 1] [0] [1 0 1] c(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c)(c(a)(a(c)(c(b)(x1)))) [1 0 1] [1] [0 0 0] [1 0 0] [1 0 0] b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(a)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] b(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(c)(x1)))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] b(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(b)(x1)))) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] a(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(a)(x1)))) [1 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] a(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 1]x1 + [1] >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(c)(x1)))) [1 0 0] [0] [0 0 0] [1 0 1] [0] [1 0 0] a(c)(c(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(b)(x1)))) [1 0 1] [0] [0 0 0] [1 0 0] [0] [1 0 0] [0] c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = c(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] c(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 1]x1 + [1] >= [0 0 0]x1 + [0] = c(b)(b(b)(b(b)(b(c)(x1)))) [0 0 1] [1] [0 0 0] [1] [1 0 1] [0] [1 0 0] [0] c(c)(c(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = c(b)(b(b)(b(b)(b(b)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] b(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] b(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(b(b)(b(b)(b(c)(x1)))) [0 0 0] [0 0 0] [1 0 1] [1 0 0] b(c)(c(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(b(b)(b(b)(b(b)(x1)))) [0 0 0] [0 0 0] problem: a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [a(c)](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [a(b)](x0) = [0 0 0]x0 [1 0 1] , [1 0 0] [a(a)](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [c(a)](x0) = [0 0 0]x0 [0 1 0] , [1 0 0] [b(c)](x0) = [0 1 1]x0 [0 0 0] , [1 1 1] [c(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [b(a)](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 1 0] [b(b)](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [c(c)](x0) = [0 0 0]x0 [0 0 1] orientation: [1 0 0] [1 0 0] a(a)(a(c)(c(a)(x1))) = [0 0 0]x1 >= [0 0 0]x1 = a(c)(c(c)(c(a)(x1))) [1 0 0] [1 0 0] [1 1 0] [1 1 0] a(a)(a(c)(c(c)(x1))) = [0 0 0]x1 >= [0 0 0]x1 = a(c)(c(c)(c(c)(x1))) [1 1 0] [1 1 0] [1 1 0] [1 1 0] a(b)(b(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(a)(x1)))) [1 1 0] [1 1 0] [1 1 1] [1 1 1] a(b)(b(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(c)(x1)))) [1 1 1] [1 1 1] [1 1 1] [1 1 0] a(b)(b(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(b)(x1)))) [1 1 1] [1 1 0] [1 0 0] [0] [1 0 0] a(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(c)(c(a)(a(c)(c(a)(x1)))) [1 0 0] [1] [1 0 0] [1 1 0] [0] [1 1 0] a(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(c)(c(a)(a(c)(c(c)(x1)))) [1 1 0] [1] [1 1 0] [1 1 1] [0] [1 1 1] a(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(c)(c(a)(a(c)(c(b)(x1)))) [1 1 1] [1] [1 1 1] [1 0 0] [1] [1 0 0] c(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c)(c(a)(a(c)(c(a)(x1)))) [0 0 0] [0] [0 0 0] [1 1 0] [1] [1 1 0] c(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c)(c(a)(a(c)(c(c)(x1)))) [0 0 0] [0] [0 0 0] [1 1 1] [1] [1 1 1] c(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c)(c(a)(a(c)(c(b)(x1)))) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(a)(x1)))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] b(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(c)(x1)))) [0 0 0] [0 0 0] [1 1 1] [1 1 1] b(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(b)(x1)))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] a(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(a)(x1)))) [1 1 0] [1 1 0] [1 1 1] [1 1 1] a(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(c)(x1)))) [1 1 1] [1 1 1] [1 1 1] [1 1 0] a(c)(c(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(b)(x1)))) [1 1 1] [1 1 0] [1 1 0] [1 1 0] c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [0 0 0] [1 1 1] [1 1 1] c(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(c)(x1)))) [0 0 0] [0 0 0] [1 1 1] [1 1 0] c(c)(c(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(b)(x1)))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] b(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [0 0 0] [1 1 1] [1 1 1] b(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(b(b)(b(b)(b(c)(x1)))) [0 0 0] [0 0 0] [1 1 1] [1 1 0] b(c)(c(b)(b(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(b)(b(b)(b(b)(b(b)(x1)))) [0 0 0] [0 0 0] problem: a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) Matrix Interpretation Processor: dim=1 interpretation: [a(c)](x0) = x0 + 2, [a(b)](x0) = x0, [a(a)](x0) = x0, [c(a)](x0) = x0, [b(c)](x0) = 4x0, [c(b)](x0) = x0 + 1, [b(a)](x0) = 4x0, [b(b)](x0) = x0, [c(c)](x0) = x0 orientation: a(a)(a(c)(c(a)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(c)(c(c)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 >= 4x1 = a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) = 4x1 >= 4x1 = a(a)(a(b)(b(b)(b(c)(x1)))) a(b)(b(b)(b(c)(c(b)(x1)))) = 4x1 + 4 >= x1 = a(a)(a(b)(b(b)(b(b)(x1)))) a(b)(b(a)(a(c)(c(a)(x1)))) = 4x1 + 8 >= x1 + 4 = a(c)(c(a)(a(c)(c(a)(x1)))) a(b)(b(a)(a(c)(c(c)(x1)))) = 4x1 + 8 >= x1 + 4 = a(c)(c(a)(a(c)(c(c)(x1)))) a(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 12 >= x1 + 5 = a(c)(c(a)(a(c)(c(b)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) = 4x1 + 8 >= 4x1 + 8 = b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) = 4x1 + 8 >= 4x1 + 8 = b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 12 >= 4x1 + 12 = b(c)(c(a)(a(c)(c(b)(x1)))) a(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 3 >= 4x1 = a(b)(b(b)(b(b)(b(a)(x1)))) a(c)(c(b)(b(c)(c(c)(x1)))) = 4x1 + 3 >= 4x1 = a(b)(b(b)(b(b)(b(c)(x1)))) a(c)(c(b)(b(c)(c(b)(x1)))) = 4x1 + 7 >= x1 = a(b)(b(b)(b(b)(b(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 1 >= 4x1 + 1 = c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) = 4x1 + 1 >= 4x1 + 1 = c(b)(b(b)(b(b)(b(c)(x1)))) c(c)(c(b)(b(c)(c(b)(x1)))) = 4x1 + 5 >= x1 + 1 = c(b)(b(b)(b(b)(b(b)(x1)))) b(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 4 >= 4x1 = b(b)(b(b)(b(b)(b(a)(x1)))) b(c)(c(b)(b(c)(c(c)(x1)))) = 16x1 + 4 >= 4x1 = b(b)(b(b)(b(b)(b(c)(x1)))) b(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 20 >= x1 = b(b)(b(b)(b(b)(b(b)(x1)))) problem: a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [a(c)](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [a(b)](x0) = [1 1 0]x0 [0 0 0] , [1 0 1] [a(a)](x0) = [1 0 0]x0 [0 0 1] , [1 0 0] [c(a)](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [1] [b(c)](x0) = [0 0 0]x0 + [0] [0 1 0] [0], [1 0 0] [c(b)](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [1] [b(a)](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [b(b)](x0) = x0 , [1 0 1] [0] [c(c)](x0) = [1 0 0]x0 + [0] [0 0 0] [1] orientation: [1 0 0] [1] [1 0 0] [0] a(a)(a(c)(c(a)(x1))) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = a(c)(c(c)(c(a)(x1))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] a(a)(a(c)(c(c)(x1))) = [1 0 1]x1 + [0] >= [1 0 1]x1 + [0] = a(c)(c(c)(c(c)(x1))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] a(b)(b(b)(b(c)(c(a)(x1)))) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = a(a)(a(b)(b(b)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] a(b)(b(b)(b(c)(c(c)(x1)))) = [1 0 1]x1 + [1] >= [1 0 0]x1 + [1] = a(a)(a(b)(b(b)(b(c)(x1)))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 1]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] b(b)(b(a)(a(c)(c(c)(x1)))) = [1 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(c)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] b(b)(b(a)(a(c)(c(b)(x1)))) = [1 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(b)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] c(c)(c(b)(b(c)(c(a)(x1)))) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = c(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] c(c)(c(b)(b(c)(c(c)(x1)))) = [1 0 1]x1 + [1] >= [1 0 0]x1 + [1] = c(b)(b(b)(b(b)(b(c)(x1)))) [0 0 0] [1] [0 0 0] [0] problem: a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [a(c)](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [a(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [a(a)](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [0] [c(a)](x0) = [0 0 1]x0 + [0] [0 0 0] [1], [1 0 1] [b(c)](x0) = [0 0 0]x0 [0 1 0] , [1 0 1] [0] [c(b)](x0) = [0 0 0]x0 + [1] [0 1 0] [0], [1 0 1] [b(a)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [b(b)](x0) = [0 0 1]x0 + [0] [0 0 0] [1], [1 0 0] [0] [c(c)](x0) = [0 0 1]x0 + [1] [0 1 0] [0] orientation: [1 0 0] [1] [1 0 0] [0] a(a)(a(c)(c(c)(x1))) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = a(c)(c(c)(c(c)(x1))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] a(b)(b(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(a)(x1)))) [0 0 0] [0] [0 0 0] [1 1 1] [1] [1 1 1] a(b)(b(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(c)(x1)))) [0 0 0] [0] [0 0 0] [1 0 0] [1] [1 0 0] [1] b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] b(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(c)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] b(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(b)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 0 1] [1] c(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(b)(b(b)(b(b)(b(c)(x1)))) [0 0 0] [1] [0 0 0] [1] problem: b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [a(c)](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [c(a)](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [0] [b(c)](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [c(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [b(a)](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [0] [b(b)](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [0] [c(c)](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 1 0] [1] [1 1 0] [1] b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(a)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 1 0] [1] b(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(c)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] b(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(c(b)(x1)))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(a)(x1)))) [0 0 0] [1] [0 0 0] [1 1 1] [1] [1 0 1] c(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(c)(x1)))) [0 0 0] [1] [0 0 0] problem: b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [a(c)](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [1 0 0] [c(a)](x0) = [0 0 1]x0 [0 1 0] , [0] [b(c)](x0) = x0 + [1] [0], [1 0 0] [c(b)](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [1] [b(a)](x0) = [0 1 1]x0 + [0] [0 1 0] [0], [b(b)](x0) = x0 , [1 0 1] [c(c)](x0) = [0 1 0]x0 [0 1 1] orientation: [1 0 0] [1] [1 0 0] [0] b(b)(b(a)(a(c)(c(a)(x1)))) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(a)(a(c)(c(a)(x1)))) [0 1 0] [1] [0 1 0] [1] [1 0 1] [1] [1 0 1] [0] b(b)(b(a)(a(c)(c(c)(x1)))) = [0 1 1]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(a)(a(c)(c(c)(x1)))) [0 1 1] [1] [0 1 1] [1] [1 0 0] [1] [1 0 0] [0] b(b)(b(a)(a(c)(c(b)(x1)))) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(a)(a(c)(c(b)(x1)))) [0 1 0] [1] [0 1 0] [1] [1 0 1] [1] [1 0 0] [1] c(c)(c(b)(b(c)(c(a)(x1)))) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = c(b)(b(b)(b(b)(b(a)(x1)))) [0 1 1] [1] [0 1 1] [0] problem: c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [c(a)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [b(c)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [c(b)](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [b(a)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [b(b)](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [c(c)](x0) = [0 0 0]x0 + [0] [1 0 0] [0] orientation: [1 0 0] [1] [1 0 0] c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(a)(x1)))) [1 0 0] [0] [1 0 0] problem: Qed