/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO Problem: incr(nil()) -> nil() incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(nil()) -> nil() adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) nats() -> adx(zeros()) zeros() -> cons(0(),n__zeros()) head(cons(X,L)) -> X tail(cons(X,L)) -> activate(L) incr(X) -> n__incr(X) adx(X) -> n__adx(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Proof: Matrix Interpretation Processor: dim=1 interpretation: [tail](x0) = 4x0, [head](x0) = 4x0 + 1, [n__zeros] = 0, [0] = 0, [zeros] = 0, [nats] = 0, [n__adx](x0) = 2x0, [adx](x0) = 2x0, [n__incr](x0) = x0, [activate](x0) = x0, [s](x0) = x0, [cons](x0, x1) = 2x0 + 4x1, [incr](x0) = x0, [nil] = 0 orientation: incr(nil()) = 0 >= 0 = nil() incr(cons(X,L)) = 4L + 2X >= 4L + 2X = cons(s(X),n__incr(activate(L))) adx(nil()) = 0 >= 0 = nil() adx(cons(X,L)) = 8L + 4X >= 8L + 2X = incr(cons(X,n__adx(activate(L)))) nats() = 0 >= 0 = adx(zeros()) zeros() = 0 >= 0 = cons(0(),n__zeros()) head(cons(X,L)) = 16L + 8X + 1 >= X = X tail(cons(X,L)) = 16L + 8X >= L = activate(L) incr(X) = X >= X = n__incr(X) adx(X) = 2X >= 2X = n__adx(X) zeros() = 0 >= 0 = n__zeros() activate(n__incr(X)) = X >= X = incr(X) activate(n__adx(X)) = 2X >= 2X = adx(X) activate(n__zeros()) = 0 >= 0 = zeros() activate(X) = X >= X = X problem: incr(nil()) -> nil() incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(nil()) -> nil() adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) nats() -> adx(zeros()) zeros() -> cons(0(),n__zeros()) tail(cons(X,L)) -> activate(L) incr(X) -> n__incr(X) adx(X) -> n__adx(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [tail](x0) = x0 + 5, [n__zeros] = 1, [0] = 0, [zeros] = 1, [nats] = 4, [n__adx](x0) = 4x0, [adx](x0) = 4x0, [n__incr](x0) = x0, [activate](x0) = x0, [s](x0) = x0, [cons](x0, x1) = 4x0 + x1, [incr](x0) = x0, [nil] = 0 orientation: incr(nil()) = 0 >= 0 = nil() incr(cons(X,L)) = L + 4X >= L + 4X = cons(s(X),n__incr(activate(L))) adx(nil()) = 0 >= 0 = nil() adx(cons(X,L)) = 4L + 16X >= 4L + 4X = incr(cons(X,n__adx(activate(L)))) nats() = 4 >= 4 = adx(zeros()) zeros() = 1 >= 1 = cons(0(),n__zeros()) tail(cons(X,L)) = L + 4X + 5 >= L = activate(L) incr(X) = X >= X = n__incr(X) adx(X) = 4X >= 4X = n__adx(X) zeros() = 1 >= 1 = n__zeros() activate(n__incr(X)) = X >= X = incr(X) activate(n__adx(X)) = 4X >= 4X = adx(X) activate(n__zeros()) = 1 >= 1 = zeros() activate(X) = X >= X = X problem: incr(nil()) -> nil() incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(nil()) -> nil() adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) nats() -> adx(zeros()) zeros() -> cons(0(),n__zeros()) incr(X) -> n__incr(X) adx(X) -> n__adx(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__zeros] = [0] [0], [0] [0] = [0] [0], [0] [zeros] = [0] [0], [1] [nats] = [0] [0], [1 0 1] [1] [n__adx](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [1 0 1] [1] [adx](x0) = [1 0 0]x0 + [0] [1 0 0] [0], [1 0 0] [n__incr](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [activate](x0) = [0 1 1]x0 [0 1 1] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 0 0] [incr](x0) = [0 0 1]x0 [0 0 1] , [0] [nil] = [0] [0] orientation: [0] [0] incr(nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] incr(cons(X,L)) = [0 1 1]L + [0 0 0]X >= [0 0 0]L + [0 0 0]X = cons(s(X),n__incr(activate(L))) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [1] [0] adx(nil()) = [0] >= [0] = nil() [0] [0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [1] adx(cons(X,L)) = [1 0 0]L + [1 0 0]X + [0] >= [1 0 0]L + [0 0 0]X + [0] = incr(cons(X,n__adx(activate(L)))) [1 0 0] [1 0 0] [0] [1 0 0] [0 0 0] [0] [1] [1] nats() = [0] >= [0] = adx(zeros()) [0] [0] [0] [0] zeros() = [0] >= [0] = cons(0(),n__zeros()) [0] [0] [1 0 0] [1 0 0] incr(X) = [0 0 1]X >= [0 0 0]X = n__incr(X) [0 0 1] [0 0 1] [1 0 1] [1] [1 0 1] [1] adx(X) = [1 0 0]X + [0] >= [1 0 0]X + [0] = n__adx(X) [1 0 0] [0] [0 0 0] [0] [0] [0] zeros() = [0] >= [0] = n__zeros() [0] [0] [1 0 0] [1 0 0] activate(n__incr(X)) = [0 0 1]X >= [0 0 1]X = incr(X) [0 0 1] [0 0 1] [1 0 1] [1] [1 0 1] [1] activate(n__adx(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = adx(X) [1 0 0] [0] [1 0 0] [0] [0] [0] activate(n__zeros()) = [0] >= [0] = zeros() [0] [0] [1 0 0] activate(X) = [0 1 1]X >= X = X [0 1 1] problem: incr(nil()) -> nil() incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) nats() -> adx(zeros()) zeros() -> cons(0(),n__zeros()) incr(X) -> n__incr(X) adx(X) -> n__adx(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__zeros] = [0] [0], [0] [0] = [0] [0], [0] [zeros] = [0] [0], [1] [nats] = [0] [1], [1 0 0] [0] [n__adx](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [adx](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [n__incr](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [activate](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 1] , [1 1 1] [1 0 1] [cons](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [1 1 0] [incr](x0) = [0 0 0]x0 [0 0 0] , [0] [nil] = [0] [0] orientation: [0] [0] incr(nil()) = [0] >= [0] = nil() [0] [0] [1 1 1] [1 1 1] [1 1 1] [1 0 1] incr(cons(X,L)) = [0 0 0]L + [0 0 0]X >= [0 0 0]L + [0 0 0]X = cons(s(X),n__incr(activate(L))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 1 1] [1] [1 0 1] [1 1 1] [1] adx(cons(X,L)) = [0 0 0]L + [0 0 0]X + [0] >= [0 0 0]L + [0 0 0]X + [0] = incr(cons(X,n__adx(activate(L)))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1] [1] nats() = [0] >= [0] = adx(zeros()) [1] [1] [0] [0] zeros() = [0] >= [0] = cons(0(),n__zeros()) [0] [0] [1 1 0] [1 1 0] incr(X) = [0 0 0]X >= [0 0 0]X = n__incr(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [0] adx(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__adx(X) [0 0 0] [1] [0 0 0] [1] [0] [0] zeros() = [0] >= [0] = n__zeros() [0] [0] [1 1 0] [1 1 0] activate(n__incr(X)) = [0 0 0]X >= [0 0 0]X = incr(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] activate(n__adx(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = adx(X) [0 0 0] [1] [0 0 0] [1] [0] [0] activate(n__zeros()) = [0] >= [0] = zeros() [0] [0] [1 0 1] activate(X) = [0 1 0]X >= X = X [0 0 1] problem: incr(nil()) -> nil() incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) nats() -> adx(zeros()) zeros() -> cons(0(),n__zeros()) incr(X) -> n__incr(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__zeros] = [0] [0], [0] [0] = [0] [0], [0] [zeros] = [0] [0], [1] [nats] = [1] [1], [1 0 0] [1] [n__adx](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [adx](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 1 1] [n__incr](x0) = [0 1 0]x0 [0 0 1] , [activate](x0) = x0 , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 1] [incr](x0) = [0 1 0]x0 [0 0 1] , [0] [nil] = [1] [0] orientation: [1] [0] incr(nil()) = [1] >= [1] = nil() [0] [0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] incr(cons(X,L)) = [0 0 0]L + [0 0 0]X >= [0 0 0]L + [0 0 0]X = cons(s(X),n__incr(activate(L))) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] adx(cons(X,L)) = [0 0 0]L + [0 0 0]X + [0] >= [0 0 0]L + [0 0 0]X + [0] = incr(cons(X,n__adx(activate(L)))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1] [1] nats() = [1] >= [0] = adx(zeros()) [1] [0] [0] [0] zeros() = [0] >= [0] = cons(0(),n__zeros()) [0] [0] [1 1 1] [1 1 1] incr(X) = [0 1 0]X >= [0 1 0]X = n__incr(X) [0 0 1] [0 0 1] [0] [0] zeros() = [0] >= [0] = n__zeros() [0] [0] [1 1 1] [1 1 1] activate(n__incr(X)) = [0 1 0]X >= [0 1 0]X = incr(X) [0 0 1] [0 0 1] [1 0 0] [1] [1 0 0] [1] activate(n__adx(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = adx(X) [0 0 0] [0] [0 0 0] [0] [0] [0] activate(n__zeros()) = [0] >= [0] = zeros() [0] [0] activate(X) = X >= X = X problem: incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) nats() -> adx(zeros()) zeros() -> cons(0(),n__zeros()) incr(X) -> n__incr(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [n__zeros] = 0, [0] = 0, [zeros] = 0, [nats] = 2, [n__adx](x0) = 4x0, [adx](x0) = 4x0, [n__incr](x0) = x0, [activate](x0) = x0, [s](x0) = x0, [cons](x0, x1) = 2x0 + x1, [incr](x0) = x0 orientation: incr(cons(X,L)) = L + 2X >= L + 2X = cons(s(X),n__incr(activate(L))) adx(cons(X,L)) = 4L + 8X >= 4L + 2X = incr(cons(X,n__adx(activate(L)))) nats() = 2 >= 0 = adx(zeros()) zeros() = 0 >= 0 = cons(0(),n__zeros()) incr(X) = X >= X = n__incr(X) zeros() = 0 >= 0 = n__zeros() activate(n__incr(X)) = X >= X = incr(X) activate(n__adx(X)) = 4X >= 4X = adx(X) activate(n__zeros()) = 0 >= 0 = zeros() activate(X) = X >= X = X problem: incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) zeros() -> cons(0(),n__zeros()) incr(X) -> n__incr(X) zeros() -> n__zeros() activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__zeros] = [1] [1], [0] [0] = [0] [0], [1] [zeros] = [1] [1], [1 1 0] [n__adx](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [adx](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [n__incr](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [activate](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [s](x0) = [0 1 1]x0 [0 0 0] , [1 1 1] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [0 1 0] , [1 1 0] [incr](x0) = [0 0 0]x0 [0 0 0] orientation: [1 1 1] [1 1 1] [1 1 1] [1 1 1] incr(cons(X,L)) = [0 0 0]L + [0 0 0]X >= [0 0 0]L + [0 0 0]X = cons(s(X),n__incr(activate(L))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1 1 1] [1 1 1] adx(cons(X,L)) = [0 0 0]L + [0 0 0]X >= [0 0 0]L + [0 0 0]X = incr(cons(X,n__adx(activate(L)))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] zeros() = [1] >= [1] = cons(0(),n__zeros()) [1] [1] [1 1 0] [1 1 0] incr(X) = [0 0 0]X >= [0 0 0]X = n__incr(X) [0 0 0] [0 0 0] [1] [0] zeros() = [1] >= [1] = n__zeros() [1] [1] [1 1 0] [1 1 0] activate(n__incr(X)) = [0 0 0]X >= [0 0 0]X = incr(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] activate(n__adx(X)) = [0 0 0]X >= [0 0 0]X = adx(X) [0 0 0] [0 0 0] [1] [1] activate(n__zeros()) = [1] >= [1] = zeros() [1] [1] [1 0 1] activate(X) = [0 1 0]X >= X = X [0 0 1] problem: incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) zeros() -> cons(0(),n__zeros()) incr(X) -> n__incr(X) activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros()) -> zeros() activate(X) -> X Unfolding Processor: loop length: 5 terms: incr(cons(X,n__adx(cons(x3031,n__zeros())))) cons(s(X),n__incr(activate(n__adx(cons(x3031,n__zeros()))))) cons(s(X),n__incr(adx(cons(x3031,n__zeros())))) cons(s(X),n__incr(incr(cons(x3031,n__adx(activate(n__zeros())))))) cons(s(X),n__incr(incr(cons(x3031,n__adx(zeros()))))) context: cons(s(X),n__incr([])) substitution: X -> x3031 x3031 -> 0() Qed