/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [a__f](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [f](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [a__p](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [0] = [1] [0], [1 0 0] [0] [p](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1] [mark](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [s](x0) = [0 1 0]x0 [0 0 0] orientation: [1] [1] a__f(0()) = [0] >= [0] = cons(0(),f(s(0()))) [0] [0] [1] [1] a__f(s(0())) = [0] >= [0] = a__f(a__p(s(0()))) [0] [0] [0] [0] a__p(s(0())) = [1] >= [1] = 0() [0] [0] [1 1 0] [1] [1 1 0] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(p(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__p(mark(X)) [0 0 0] [1] [0 0 0] [0] [1] [0] mark(0()) = [1] >= [1] = 0() [1] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(s(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = s(mark(X)) [0 0 0] [1] [0 0 0] [0] [1 1 0] [1 1 0] a__f(X) = [0 0 0]X >= [0 0 0]X = f(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a__p(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = p(X) [0 0 0] [0] [0 0 0] [0] problem: a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [a__f](x0) = [0 1 0]x0 [0 1 0] , [1 0 0] [f](x0) = [0 1 0]x0 [0 1 0] , [a__p](x0) = x0 , [0] [0] = [1] [0], [p](x0) = x0 , [1 1 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [s](x0) = [0 1 0]x0 [0 0 0] orientation: [1] [0] a__f(0()) = [1] >= [1] = cons(0(),f(s(0()))) [1] [0] [1] [1] a__f(s(0())) = [1] >= [1] = a__f(a__p(s(0()))) [1] [1] [0] [0] a__p(s(0())) = [1] >= [1] = 0() [0] [0] [1 1 0] [1] [1 1 0] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X)) [0 1 0] [1] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(p(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__p(mark(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(mark(X)) [0 0 0] [1] [0 0 0] [0] [1 1 0] [1 0 0] a__f(X) = [0 1 0]X >= [0 1 0]X = f(X) [0 1 0] [0 1 0] a__p(X) = X >= X = p(X) problem: a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 0] [0 0 0] , [1 1 0] [a__f](x0) = [0 0 0]x0 [1 0 0] , [1 1 0] [f](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [a__p](x0) = [0 0 0]x0 [0 1 0] , [0] [0] = [0] [0], [1 0 0] [p](x0) = [0 0 0]x0 [0 1 0] , [1] [mark](x0) = x0 + [0] [1], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1] [0] a__f(s(0())) = [0] >= [0] = a__f(a__p(s(0()))) [0] [0] [0] [0] a__p(s(0())) = [0] >= [0] = 0() [1] [0] [1 1 0] [1] [1 1 0] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(p(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__p(mark(X)) [0 1 0] [1] [0 1 0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(mark(X1),X2) [0 1 0] [0 0 0] [1] [0 1 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = s(mark(X)) [0 0 0] [1] [0 0 0] [0] [1 1 0] [1 1 0] a__f(X) = [0 0 0]X >= [0 0 0]X = f(X) [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__p(X) = [0 0 0]X >= [0 0 0]X = p(X) [0 1 0] [0 1 0] problem: a__p(s(0())) -> 0() mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Matrix Interpretation Processor: dim=1 interpretation: [cons](x0, x1) = 4x0 + x1 + 4, [a__f](x0) = 2x0 + 1, [f](x0) = 2x0 + 1, [a__p](x0) = 2x0 + 2, [0] = 1, [p](x0) = 2x0 + 2, [mark](x0) = 4x0 + 2, [s](x0) = x0 orientation: a__p(s(0())) = 4 >= 1 = 0() mark(f(X)) = 8X + 6 >= 8X + 5 = a__f(mark(X)) mark(p(X)) = 8X + 10 >= 8X + 6 = a__p(mark(X)) mark(cons(X1,X2)) = 16X1 + 4X2 + 18 >= 16X1 + X2 + 12 = cons(mark(X1),X2) mark(s(X)) = 4X + 2 >= 4X + 2 = s(mark(X)) a__f(X) = 2X + 1 >= 2X + 1 = f(X) a__p(X) = 2X + 2 >= 2X + 2 = p(X) problem: mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [a__f](x0) = [0 0 0]x0 + [1] [1 0 1] [1], [1 0 0] [f](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1] [a__p](x0) = [1 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [p](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [mark](x0) = [0 0 1]x0 [0 1 0] , [1 1 0] [0] [s](x0) = [0 0 1]x0 + [1] [0 1 0] [1] orientation: [1 1 1] [1] [1 1 1] [0] mark(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(mark(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [0] [1 0 0] a__f(X) = [0 0 0]X + [1] >= [0 0 0]X = f(X) [1 0 1] [1] [0 0 0] [1 1 1] [1] [1 0 0] a__p(X) = [1 1 0]X + [1] >= [0 0 0]X = p(X) [0 0 0] [0] [0 0 0] problem: a__f(X) -> f(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [a__f](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [f](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1] [1 0 0] a__f(X) = [0 0 0]X + [0] >= [0 0 0]X = f(X) [0 0 1] [0] [0 0 0] problem: Qed